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Chapter 19 The theory of effective demand In essence the “Keynesian revolution” was a shift of emphasis from one type of short-run equilibrium to another type as providing the appropriate theory for actual unemployment situations. −Edmund Malinvaud (1977), p. 29. In this and the following chapters the focus is shifted from long-run macroeconomics to short-run macroeconomics. The long-run models concentrated on factors that are important for the economic evolution over a time horizon of at least 10-15 years. With such a horizon it is the development on the supply side (think of capital accumulation, population growth, and technological progress) that is the primary determinant of cumulative changes in output and consumption − the trend. The demand side and monetary factors are important for the fluctuations about the trend. In a long-run perspective these fluctuations are generally considered of only secondary quantitative importance. But within shorter horizons, they are the focal point and this brings the demand-side, monetary factors, market imperfections, nominal rigidities, and expectation errors to the fore. The present and subsequent chapters deal with the role of these short- and medium-run factors. This chapter introduces building blocks of Keynesian theory for the short run. The basic concept of effective demand is presented. We take up the Keynesian criticism of pre-Keynesian (Walrasian) macroeconomic theory for not distinguishing systematically between ex ante demand and supply on the one hand and actual transactions on the other. Attention to this distinction leads to a refutation of Say’s law. Next some microfoundation for the notion of nominal price stickiness is presented, in particular the menu cost theory. We also address the conception of “abundant capacity” as the “normal” state of affairs in an industrialized economy. 705 706 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND In the last sections of the chapter we revisit the conventional static ISLM model, well-known from elementary macroeconomics. Keynesian tenets known as spending multipliers, the balanced budget multiplier, the paradox of thrift, and the liquidity trap are surveyed. This will serve as an introduction to dynamic versions of the IS-LM model with endogenous forward-looking expectations, presented in subsequent chapters. Until further notice we shall use the term “Keynesian theory” in a broad sense as denoting a macroeconomic framework dealing with states of the economy where output and employment are in the main determined by aggregate demand and involuntary unemployment is present. Whether a particular building block in this framework comes from Keynes himself, post-war Keynesians, or New Keynesians of some sort is not our concern here. 19.1 Stylized facts about the short run The idea that prices of goods and services are sticky in the short run rests on the empirical observation that in the short run firms in the manufacturing and service industries typically let output do the adjustment to changes in demand while keeping prices unchanged. In industrialized societies firms are able to do that because under “normal circumstances” there is “abundant production capacity” available in the economy. Three of the most salient short-run features that arise from macroeconomic time series analysis of industrialized market economies are the following (cf. Blanchard and Fischer, 1989, Nishimura, 1992, Christiano et al., 1999): 1) Shifts in aggregate demand (induced by sudden changes in the state of confidence, exports, fiscal or monetary policy, or other events) are largely accommodated by changes in quantities rather than changes in nominal prices − nominal price insensitiveness. 2) Large movements in quantities are often associated with little or no movement in relative prices − real price insensitiveness. The real wage, for instance, exhibits such insensitiveness in the short run. 3) Nominal prices are sensitive to general changes in input costs. These stylized facts pertain to final goods and services. It is not the case that all nominal prices in the economy are in the short run insensitive vis-a-vis demand changes. One must distinguish between production of final goods and services on the one hand and production of primary foodstuff and raw materials on the other. This leads to the associated distinction between “cost-determined” and “demand- determined” prices. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 707 Final goods and services are typically differentiated goods (imperfect substitutes). Their production takes place under conditions of imperfect competition. As a result of existing reserves of production capacity, generally speaking, the production is elastic w.r.t. demand. An upward shift in demand tends to be met by a rise in production rather than price. The price changes which do occur are mostly a response to general changes in costs of production. Hence the name “cost-determined” prices. For primary foodstuff and many raw materials the situation is different. To increase the supply of most agricultural products requires considerable time. This is also true (though not to the same extent) with respect to mining of raw materials as well as extraction and transport of crude oil. When production is inelastic w.r.t. demand in the short run, an increase in demand results in a diminution of stocks and a rise in price. Hence the name “demand-determined prices”. The price rise may be enhanced by a speculative element: temporary hoarding in the expectation of further price increases. The price of oil and coffee − two of the most traded commodities in the world market − fluctuate a lot.1 Through the channel of costs the changes in these demand-determined prices spill over to the prices of final goods. As macroeconomics by and large deals with industrialized economies, where manufacturing and services are the main sectors, the general price level is typically regarded as cost-determined rather than demand determined. Two further aspects are important. First, many wages and prices are set in nominal terms by price setting agents, say, craft unions and firms operating in imperfectly competitive markets. Second, these wages and prices are in general deliberately kept unchanged for some time even if changes in the environment of the agent occurs; this aspect, interpreted as reflecting the presence of pecuniary as well as non-pecuniary costs associated with changing prices, is called nominal price stickiness. Both aspects have vast consequences for the functioning of the economy as a whole compared with a regime of perfect competition and flexible prices. 19.2 A simple short-run model The simple model presented below is close to what Paul Krugman named the World’s Smallest Macroeconomic Model.2 The model is useful in at least three ways: 1 2 See, e.g., Fig. 15.1 in Chapter 15. Krugman (1999). Krugman tells he learned the model back in 1975 from Robert Hall. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 708 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND • the model demonstrates the fundamental difference in the functioning of an economy with flexible prices and one with sticky prices; • the model is a suitable point of departure for a definition of the Keynesian concept of effective demand; • the model displays the logic behind the Keynesian refutation of Say’s law. 19.2.1 Elements of the model We consider a monetary closed economy which produces a consumption good. There are three sectors in the economy, a production sector, a household sector, and a public sector with a consolidated government/central bank. Time is discrete. There is a current period and “the future”, compressing the second period and onward. Labor is the only input in production. To simplify notation, the model presents its story as if there is just one representative household and one representative firm owned by the household, but the reader should imagine that there are numerous agents of each kind. The production function has CRS, = 0 (19.1) where is aggregate output of a consumption good which cannot be stored, is a technology parameter, and is aggregate employment, both in the current period. The price of the consumption good in terms of money, i.e., the nominal price, is the wage rate in terms of money, the nominal wage, is Suppose the representative firm takes these current prices as given. The nominal profit is Π = − (19.2) There is free exit from the production sector in the sense that the representative firm can decide to produce nothing. Hence, an equilibrium with positive production requires that profits are non-negative. The representative household supplies labor inelastically in the amount ̄ and receives the profit obtained by the firm, if any. The household demands the consumption good in the amount in the current period. Current income not consumed is saved for the future. We assume that the only non-human asset available is fiat money, which is thus the only asset on hand for saving. There is no private banking sector in the economy. So “money” means the monetary base (think of currency in circulation) and is on net an asset in the private sector as a whole. Until further notice the money supply is not changed. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 709 The preferences of the household are given by the intertemporal utility function, 0 0 1 (19.3) = ln + ln Here, is the utility discount factor (equal to (1 + )−1 if is the utility discount rate), 0 is the amount of money transferred to “the future”, and is the expected future price level. Consider the household’s choice problem. Facing and and expecting that the future price level will be the household chooses and 0 to maximize s.t. + 0 = + + Π ≡ (19.4) Here, 0 is the stock of money held at the beginning of the current period and is predetermined. The actual employment is denoted and equals the minimum of the amount of employment offered by the firm and the labor supply, ̄ (the voluntary trade principle). The sum of initial financial wealth, and nominal income, + Π constitutes the budget, 3 Nominal financial wealth at the beginning of the next period is 0 = + + Π − i.e., the sum of initial financial wealth and saving where the latter equals + Π − The benefit obtained by transferring 0 depends on the expected purchasing power of 0 hence it is 0 that enters the utility function. This minimalist way of taking the future into account is of course a shortcut. Substituting 0 = − into (19.3), we get the first-order condition 1 = + (− ) = 0 − which gives = 1 1+ (19.5) We see that the marginal (= average) propensity to consume is (1 + )−1 hence inversely related to the patience parameter The resulting stock of money held at the end of the period is 0 = (1 − 1 ) = 1+ 1+ 3 As time is discrete, expressions like + + Π are legitimate. Although it is meaningless to add a stock and a flow (since they have different denominations), the sum + + Π should be interpreted as + ( + Π)∆ where ∆ is the period length equal to one time unit. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 710 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND So the expected price level, in the future does not affect the demands, and 0 This is a special feature, due to the additive logarithmic specification of the utility function in (19.3). Inserting (19.4) and (19.2) into (19.5) gives + + + Π = = = (1 + ) (1 + ) 1+ (19.6) Suppose there is equilibrium in the output market in the sense that = Inserting this into (19.6), we can find expressed in terms of : = (19.7) This is so far no solution for since also is an endogenous variable. We have assumed that agents take prices as given when making their demand and supply decisions. But we have said nothing about whether nominal prices are flexible or rigid. 19.2.2 The case of fully flexible and What Keynes called “classical economics” has by later writers been called “Walrasian macroeconomics” or simply “pre-Keynesian macroeconomics”. In this theoretical tradition both wages and prices are assumed fully flexible and all markets perfectly competitive. Both and are thus thought to adjust immediately so as to clear the labor and output markets like in a centralized auction market. Clearing in the labor market requires = ̄ (19.8) that is, labor demand, equals the exogenous labor supply, ̄ In view of the constant returns to scale production function (19.1), this requires that firms have zero profit. In turn, by (19.1) and (19.2), zero profit requires that the real wage equals labor productivity: = (19.9) Given clearing in the labor market, output equals full-employment output, = ̄ ≡ where the superscript “ ” stands for “full employment”. Output and employment are here said to be supply-determined, i.e., determined by the supply of c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 711 production factors, here labor. The profit is Π = − ̄ = ( − ̄) = 0 in view of (19.9) and the definition of . The condition (19.7) can now be solved for the equilibrium price level = ≡ (19.10) where the superscript “” stands for “classical”. This, together with (19.9), gives the “classical” equilibrium wage = ≡ (19.11) General equilibrium also requires that the desired money holding at the end of the period equals the money supply. By Walras’ law this equality follows automatically from the household’s Walrasian budget constraint and equilibrium in the output and labor markets. Indeed, we define the household’s Walrasian budget constraint as given by (19.4) with the employment term, interpreted as labor supply, ̄ and the profit term, Π interpreted as the hypothetical profit calculated on the basis of firms’ desired supply evaluated at the announced price vector, ( 1). Then, for an arbitrary price vector ( 1) with 0 and 0 the values of excess demands add up to ( − ̄) + ( − ) + 0 − = −Π − ̄ + + 0 − = −Π − ̄ + + + ̄ + Π − − = 0 where the first equality comes from the definition of Π in (19.2) and the second from the Walrasian budget constraint. This result reflects that when households satisfy their Walrasian budget constraints, then the economy as a whole has to satisfy an aggregate budget constraint for the period in question. It follows that the equilibrium condition 0 = is ensured as soon as there is clearing in the output and labor markets. Consequently, with ( ) = ( ) there is general equilibrium in this flexwage-flexprice economy with perfect competition. Such an equilibrium is called a classical or Walrasian equilibrium. The intuitive mechanism behind it is the following adjustment process. Imagine that in an ultra-short subperiod − 6= 0 In case − 0 ( 0) there will be excess supply (demand) in the labor market. This drives down (up). Only when = and full employment obtains, can the system be at rest. Next imagine that − 6= 0 In case − 0 ( 0) there is excess supply (demand) in the output market. This drives down (up). Again, only when = c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 712 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND and = (whereby = ), so that the output market clears under full employment, will the system be at rest. This adjustment process is fictional, however, because outside equilibrium the Walrasian supplies and demands which supposedly drive the adjustment are artificial constructs. Being functions only of initial resources and price signals, the Walrasian supplies and demands are mutually inconsistent outside equilibrium and can therefore not tell what quantities will be traded during an adjustment process. The story needs a considerable refinement unless one is willing to let the mythical “Walrasian auctioneer” enter the scene and bring about adjustment toward the equilibrium prices without allowing trade until these prices are found. Anyway, by comparative statics based on (19.10) and (19.11) we see that in the classical regime, and are higher the higher is Output is at the unchanged full-employment level whatever the level of . This is the neutrality of money result of classical macroeconomics. The neutrality result also holds in a dynamic context where we consider an actual change in the money supply occurring in historical time. Since by assumption money is the only asset in the economy, such a change in the money supply can not be brought about through open market operations where the central bank buys or sells another financial asset. Instead we imagine that the government at the beginning of the period brings about lump-sum transfers to the households in the total amount ∆ 0 As there is no taxation, this implies a budget deficit which we thus assume fully financed by money issue. So (19.4) is replaced by + 0 = + ∆ + + Π ≡ (19.12) If we replace in the previous formulas by ̂ ≡ + ∆ we see that money neutrality still holds. Now there is nominal private saving of size = ∆ + + Π − = 0 − = ∆ On the other hand the government dissaves, in that its saving is = −∆ where ∆ is the government budget deficit. So national saving is and remains ≡ + = 0 (it must be nil as there are no durable produced goods). 19.2.3 The case of sticky and In standard Keynesian macroeconomics nominal wages are considered predetermined in the short run, fixed in advance by wage bargaining between workers (or workers’ unions) and employers (or employers’ unions). Nominal prices are also fixed in advance and set by price setting firms facing downward sloping demand curves. It is understood that there is a large spectrum c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 713 of differentiated products. This heterogeneity ought of course be visible in the model − and it will become so in Section 19.3. But at this point the model takes an easy way out and entirely ignores the involved aggregation issues. Let in the current period be given at the level ̄ Because firms have market power, the profit-maximizing price involves a mark-up on marginal cost, ̄ = ̄ (which is also the average cost). We assume that the price setting occurs under circumstances where the chosen mark-up becomes a constant 0, so that = (1 + ) ̄ ≡ ̄ (19.13) While ̄ is considered exogenous (not determined within the model), ̄ is endogenously determined by the given ̄ and Because of the fixed wage and price, the different markets may feature excess demand or excess supply (to be defined more precisely below). According to the principle that no agent can be forced to trade more than desired, the actual amount traded in a market must equal the minimum of demand and supply. So in the output market and the labor market the actual quantities traded are = min( ) and = min( ) (19.14) respectively, where the superscripts “” and “” denote demand and supply, respectively. This principle, that the short side of the market determines the traded quantity, is called the short-side rule. The other side of the market is said to be quantity rationed or just rationed if there is discrepancy between and . There are in the present framework two alternative cases − or “regimes” − to consider plus a border case. The Keynesian regime: ̄ (1 + ) In view of (19.13), in this regime we must have ̄ ≡ . From the condition (19.7), we find that the aggregate demand consistent with = is = ( ̄ ) Firms would loose by producing more than they are able to sell at their preset price, ̄ . This price is and remains the profit maximizing price since marginal costs are constant and there is nothing in the situation to defy the constant mark-up assumption. Actual output will therefore be = = ≡ = ≡ ̄ c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° (19.15) 714 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where the superscript “” stands for “Keynesian” and the inequality is implied by ̄ . From (19.1) and the short-side rule now follows that employment is = = = ̄ = ̄ (19.16) Profits are Π = ̄ − ̄ = (1 − ̄̄ )̄ = (1 − (1 + )−1 ) −1 0 where we have used, first, (19.1) and then (19.13) and (19.15). This solution for ( ) is known as a Keynesian equilibrium for the current period. It is named an equilibrium because the system is “at rest” in the following sense: (a) agents do the best they can given the constraints (which include the preset prices and the quantities offered by the other side of the market); and (b) the chosen actions are mutually compatible (purchases and sales match). The equilibrium is said to be Keynesian because there is unemployment and at the same time it is aggregate demand in the output market, not the real wage, which is the binding constraint on the employment level. A higher propensity to consume (lower discount factor ) results in higher aggregate demand, and thereby a higher equilibrium output, . In contrast, lowering the real wage through a higher mark-up, or a lower marginal (= average) labor productivity, does not result in a higher . On the contrary, becomes lower; in view of (19.13) and (19.15), the causal chain goes via a higher ̄ . Lowering the nominal wage, however, stimulates and thereby via the negative effect on ̄ 4 A compact characterization of the Keynesian regime is thus that it leads to an equilibrium where output as well as employment are demand-determined. In the language of the microeconomic theory of quantity rationing we may say that in the Keynesian equilibrium both the output market and the labor market are buyers’ markets (sale less than desired). We shall not, however, categorize the state in the output market as one of “excess supply”. The going price level as well as the output level are in the Keynesian regime entirely voluntary on the part of the price-setting firms. The “Keynesian cross” and effective demand The situation is illustrated by the “Keynesian cross” in the ( ) plane shown in Fig. 19.1, where = = (1 + )−1 ( + ̄ ) We see the vicious circle. Output is below the full-employment level because of low consumption demand; and 4 This latter result does not necessarily go through if the expected price in the future, plays a role for the current consumption decision (and at the same time depends on prices in the current period). Our specification of the utility function, however, rules this out. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 715 d Y M Y Yd P 1 M P 1 O 45 Yk Y Yf Figure 19.1: The Keynesian regime (̄ (1 + ) and given, ̄ fixed). consumption demand is low because of the low employment. The economy is in a unemployment trap. Even though at we have Π 0 and there are constant returns to scale, the individual firm has no incentive to increase production because the firm already produces as much as it rightly perceives it can sell at its preferred price. We also see that here money is not neutral. For a given = ̄ and thereby a given = ̄ a higher results in higher output and higher employment. Although the microeconomic background we have alluded to is a specific “market power story” (one with differentiated goods and downward sloping demand curves), the Keynesian cross in Fig. 19.1 is valid for any microeconomic story leading to a fixed ̄ and a fixed ̄ ̄ The fundamental difference between the Walrasian and the present framework is that the latter allows trade outside Walrasian equilibrium. In that situation the households’ consumption demand depends not on how much labor the households would prefer to sell at the going wage, but on how much they are able to sell, that is, on a quantity signal received from the labor market. Indeed, it is the actual employment, that enters the operative budget constraint, (19.4), not the desired employment as in classical or Walrasian theory. On this background Keynesian theory defines a household’s effective budget constraint as the budget constraint conditional on the perceived price signals and the perceived quantity signals from the markets. These quantity signals are in the present context the employment level offered and the c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 716 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND perceived profit to be paid out from the firms. A household’s effective consumption demand is the consumption demand conditional on the effective budget constraint; the formula (19.6) illustrates this concept. The level of aggregate effective demand is given by the Keynesian cross in Fig. 19.1 as . The repressed inflation regime: ̄ (1 + ) This regime represents the “opposite” case of the Keynesian regime. In view of (19.13), we must in this regime have ̄ ≡ . Hence ( ̄ ) ( ) = = ̄ In spite of the high demand, combined with a realwage level which does not deter profitable production, the shortage of labor hinders the firms to produce more than at the going price. With = output demand, which in this model is always the same as consumption demand, is, from (19.6), = = ̄ + = = = 1+ (19.17) where is the realized consumption. We have here defined to equal full-employment output, Thereby consistency with the short-side rule (19.14) is maintained. Presumably, the excess demand, − 0 generates pressure for a price increase, but the outcome (19.17) is based on the assumption that is sticky so that the price change does not materialize until possibly the next period. This explains the name repressed inflation. Fig. 19.2 illustrates. As the real-wage level does not deter profitable production, the firms’ would like to employ people up to the point where output demand is satisfied, i.e., = But in view of the short side rule, actual employment will be = = ̄ = So there is excess demand in the labor market which presumably will generate pressure for wage increases. By the assumed nominal wage stickiness, this does not materialize until possibly the next period. The equilibrium outcome in the repressed inflation regime is thus ( ) = ( ̄) Consumers are quantity rationed in the goods market, as Firms are quantity rationed in the labor market, as . This is the background for the parlance that in the repressed inflation regime, output and employment are not demand-determined but supply-determined. In the language of the microeconomic theory of quantity rationing we may say that in contrast to the Keynesian regime, the repressed inflation regime is c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 717 Yd M Y f P 1 Cf M Y Y P 1 d M P 1 O 45 Y f Y Figure 19.2: The repressed inflation regime (̄ (1 + ) and given, ̄ fixed). characterized by both the output market and the labor market being sellers’ markets (purchase less than desired). Presumably, the repressed inflation regime will not last long unless possibly in a war situation with wage and price controls. The border case between the two regimes: ̄ = (1 + ) In this case, by (19.13) follows that ̄ = . So no market has quantity rationing and we may speak of both the output market and the labor market as balanced markets. There are two differences compared with the classical equilibrium, however. The first is that due to market power, there is a wedge between the real wage and the marginal productivity of labor. In the present context, though, where labor supply is inelastic, this does not imply inefficiency but only a higher profit/wage-income ratio than under perfect competition (where the profit/wage-income ratio is zero). The second difference compared with the classical equilibrium is that due to price stickiness, the impact of shifts in exogenous variables will be different. For instance a lower will in the present framework with ̄ = (1 + ) result in unemployment, while in the classical model it will just raise and and not affect employment. With effective budget constraints Walras’ law does not hold As we saw above, with Walrasian budget constraints, the aggregate value of excess c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 718 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND demands in the given period is zero for any given price vector, ( 1) with 0 and 0 In contrast, with effective budget constraints the aggregate value of excess demands is for any given price vector, ( 1) with 0 and 0 ( − ̄) + ( − ) + 0 − = −Π − ̄ + + 0 − = −Π − ̄ + + + + Π − − (19.18) = ( − ̄) where the first equality comes from the definition of Π in (19.2) and the second from the effective budget constraint, (19.4). We get that Walras’ law does not hold in a setting where effective budget constraints are operative rather than Walrasian budget constraints. Consider a state of affairs where there is clearing in the output market ( = ) and at the same time actual money holding ends up equal to desired money holding at the end of the period ( = 0 ). The result (19.18) tells us that this is compatible with 6= ̄ Hence clearing in the labor market is not guaranteed. Consider for instance the Keynesian regime where and 0 For any such pair, ( ) we get ̄ as in Fig. 19.1. According to (19.18), thereby the aggregate value of excess demands equals ( − ̄) 0 Equivalently, the aggregate value of excess supplies is positive. So the positive excess supply in the labor market need not be accompanied by a presumably expansionary positive excess demand in the output market. We can only say: If and only if the labor market clears, then the aggregate value of excess demands equals zero (a “conditional Walras’ law”). This takes us to Keynes’ refutation of Say’s law. Say’s law and its refutation The classical principle “supply creates its own demand” (or “income is automatically spent on goods”) is named Say’s law after the French economist and business man Jean-Baptiste Say (17671832). In line with other classical economists like David Ricardo and John Stuart Mill, but in sharp contrast to the views of Thomas Malthus and Karl Marx, Say maintained that although mismatch between demand and production can occur, it can only occur in the form of excess supply in some industries at the same time as there is excess demand in other industries − general excess supply of goods is impossible. Or, by another classical catchphrase: Whatever the relative prices, every offer to sell a good implies a demand for some other good. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.2. A simple short-run model 719 By “good” is here meant a produced good rather than just any traded article, including for instance money. Otherwise Say’s law would be a platitude (a simple implication of the definition of trade). So, interpreting “good” to mean a produced good, let us evaluate Say’s law from the point of view of the result (19.18). By subtracting ( − ̄) on both sides of (19.18), we see that ( − ) + 0 − = 0 (19.19) for any 0 Consider the case and as in Fig. 19.1. First of all, the figure illustrates that aggregate demand is rising with aggregate production. And if aggregate production is in the interval 0 then = ; this amounts to general excess demand for goods and in effect, by (19.19), excess supply of money. So far Say’s law is not contradicted. But if instead aggregate production is in the interval then = ; now there is general excess supply of goods. Or, which is the same, a general shortfall of demand. In effect, by (19.19), there is excess demand for money. General excess supply of produced goods is thus possible and Say’s law thereby falsified.5 This is not to deny that a state of affairs with general excess supply may trigger quantity and/or price responses. Keynes emphasized that in a modern economy the resulting piles of unsold goods induces firms to cut production and employment rather than prices. Keynes’ contemporary, A. C. Pigou, maintained an opposite view namely that the general excess supply would result in a falling price level, thus leading to higher purchasing power of (the “real balance effect”). Anyway, whatever the price response of the system, it takes time and will thus not occur until the next short period. We shall therefore categorize it as belonging to dynamic analysis which is considered in later chapters. It should be noted that the refutation of Say’s law does not hinge on money being the asset available for transferring purchasing power from one period to the next. We may imagine an economy where represents land available in limited supply. As land is also a non-produced good, the above analysis goes through − with one exception, though. The exception is that ∆ in (19.12) can no more be interpreted as a policy choice. Instead, a positive ∆ could be due to discovery of new land. 5 Keynes’ reasoning (Keynes, 1936) is similar. It might be objected that this “aggregate” reply to Say’s law is not to the point since Say had a disaggregate structure with many industries in mind. But considering an explicit disaggregate production sector makes no essential difference as we shall see towards the end of this chapter. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 720 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND Digging deeper As it stands the above theoretical framework has many limitations. The remainder of this chapter outlines how the following problems have been dealt with in the literature: (a) The wage and price setting should be explicitly modelled and in this connection there should be an explanation of the wage and price stickiness. (b) It should be made clear how to come from the existence of many differentiated goods and markets with imperfect competition to aggregate output and income which in turn constitute the environment conditioning individual agents’ actions. (c) To incorporate better the role of asset markets, including the primary role of money as a medium of exchange rather than a store of value, at least one alternative asset should enter, an interest-bearing asset. In subsequent chapters we consider a fourth problem: (d) The model should be truly dynamic with forward-looking endogenous expectations and gradual wage and price changes depending on the market conditions, in particular the employment situation. Let us first consider point (a) and (b). 19.3 Price setting and menu costs The classical theory of perfectly flexible wages and prices and neutrality of money treats the wages and goods prices as if they were prices on assets traded in centralized auction markets. In reality the general price level is an aggregate of millions of individual prices set by price setters in different markets and localities. The dominant market form is not perfect competition. Wage and price setters have market power. And there may be costs associated with changing prices (and wages). 19.3.1 Imperfect competition with price setters To understand what determines prices and their sometimes slow response to changed circumstances, we need a theory with agents who set prices and decide when to change them and by how much. This brings agents with market power into the picture and tells us why imperfect competition is a key ingredient in macroeconomics.6 The challenge is to explain the behavior 6 Under perfect competition all firms are price takers. So who is left to change prices? This is a sign of a logical difficulty within standard competitive theory (as pointed out by c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 721 of price-setting suppliers on the basis of their objectives and constraints. Suppose the market structure is one with monopolistic competition: 1. There is a given large number, of firms and equally many (horizontally) differentiated products. 2. Each firm supplies its own differentiated product on which it has a monopoly and which is an imperfect substitute for the other products. 3. A price change by one firm has only a negligible effect on the demand faced by any other firm. Another way of stating property 3 is to say that firms are “small” so that each good constitutes only a small fraction of the sales in the overall market system. Each firm faces a perceived downward-sloping demand curve and chooses a price which maximizes the firm’s expected profit, thus implying a mark-up on marginal costs.7 There is no perceivable reaction from the firm’s (imperfect) competitors. So the monopolistic competition setup abstracts from strategic interaction between the firms and is in that respect different from oligopoly. With respect to assets, so far our framework corresponds to the World’s Smallest Macroeconomic Model of Section 19.2 in the sense that there are no bank-created money and no other non-human assets than base money. Price setting firms In the short run there is a given large number, of firms and equally many (horizontally) differentiated products. Firm has the production function = where is labor input (raw materials and physical capital ignored).8 For notational convenience we imagine measurement units are such that = 1 Thereby, 1 = 0 ≤ 1 = 1 2 (19.20) To extend the perspective compared with Section 19.2, the possibility of rising marginal costs ( 1) is now included. The demand constraint faced by the firm is perceived by the firm to be µ ¶− = ≡ ( ) 1 (19.21) Arrow, 1959). To assign the price setting role to abstract “market forces” or an abstract omnipotent “Walrasian auctioneer” is not a convincing solution. 7 For estimations of the markup in various U.S. industries, see Hall (1988). 8 The following can be seen as an application of the more general framework with pricesetting firms outlined at the end of Chapter 2. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 722 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where is the price set by the firm and fixed for some time, is the “general price level”, is the expectation of the overall level of demand in the economy (this expectation is shared by all firms), and is the (absolute) price elasticity of demand (assumed above one since otherwise there is no finite profit maximizing price).9 So the firm faces a downward sloping demand curve the position of which is given by the expected general level of demand. Let firm choose at the end of the previous period with a view to maximization of expected nominal profit in the current period: max Π = − s.t. (19.21). Here we may substitute the constraint (19.21) into the profit function and then solve the unconstrained maximization problem w.r.t. The more intuitive approach, however, is to apply the rule that the profit maximizing quantity of a monopolist (in the standard case with non-decreasing marginal cost) is the quantity at which marginal revenue equals marginal cost, = = 1 −1 (19.22) Total revenue is = = ( ) where, from (19.21), ( ) = µ ¶− 1 So 0 ( ) 1 0 ) = ( )(1 − ) = ( ) + ( ) = ( )(1 + = ( ) Inserting this into (19.22), we find the expected (or planned) individual output level, Thereby, the chosen price is ̄ = ( ) = 1 1 −1 ( ) ≡ (1 + ) ( ) −1 −1 (19.23) where is the mark-up equal to ( − 1)−1 − 1 = ( − 1)−1 . This outcome is illustrated in Fig. 19.3 for the case 1 (decreasing returns to scale). For fixed and the demand curve faced by firm is shown as the solid downward-sloping curve ( ) to which corresponds the marginal revenue curve, For fixed the marginal costs faced by the firm are shown as the upward-sloping marginal cost curve, It is c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs Pi 723 W , P, Y e , and Yd given W 1 1 yi 1 Pi Pi d ,Y P D Pi , Y e P D MC 0 MR yi e yi Figure 19.3: Firm ’s price choice under the expectation that the general demand level will be (the case 1). The demand curve for a higher level of general demand, , is also shown. assumed that firm somehow knows in advance. The chosen price ̄ is set optimally in accordance with the = rule. Because of the symmetry, all firms end up choosing the same price, which therefore becomes the general price level, i.e., = = 1 2. . . . So all firms’ expected output level equals the expected average real spending per consumption good, i.e., P 1 2. . . . Expectations are = =P consistent in the sense that ( ) = = · ( ) = If there are no expectation errors, firm ’s actual output, equals the expected output, As this holds for all we have in this case P X X ≡ = = = = (19.24) where is the actual level of overall demand in the period, that is, actual aggregate demand. In some New-Keynesian models the labor market is described in an analogue way with heterogeneous labor organized in craft unions and monop9 Chapter 22 gives an account of the class of consumer preferences that underlie the constancy of this price elasticity. That chapter also presents a precise definition of the “general price level“. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 724 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND olistic competition between these. To avoid complicating the exposition, however, we here treat labor as homogeneous. To put it differently, at this stage we prefer not to be specific about the modeling of the labor market. No matter what the details of the labor market are, we shall raise the question: If aggregate demand in the current period turns out different from expected, what will the firms do: change the price or output or both? To fix ideas we will concentrate on the case where the wage level, is unchanged. In that case the answer will be that “only output will be adjusted” if one of the following conditions is present: (a) The marginal cost curve is horizontal and the price elasticity of demand is constant. (b) The perceived cost of price adjustment exceeds the potential benefit. That point (a) is sufficient for the “only output” answer follows from (19.23) with = 1 With rising marginal costs ( 1) however, the presence of sufficient price adjustment costs becomes decisive. 19.3.2 Price adjustment costs The literature has modelled price adjustment costs in two different ways. Menu costs refer to the case where there are fixed costs of changing price. Another case considered in the literature is the case of strictly convex adjustment costs, where the marginal price adjustment cost is increasing in the size of the price change. As to menu costs, the most obvious examples are costs associated with 1. remarking commodities with new price labels, 2. reprinting price lists (“menu cards”) and catalogues. But “menu costs” should be interpreted in a broader sense, including pecuniary as well as non-pecuniary costs of: 3. information-gathering and recomputing optimal prices, 4. conveying rapidly the new directives to the sales force, 5. the risk of offending customers by frequent price changes (in particular when they are upward), 6. search for new customers willing to pay a higher price, c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 725 7. rapid renegotiation of contracts. Menu costs induce firms to change prices less often than if no such costs were present. And some of the points mentioned in the list above, in particular point 6 and 7, may be relevant also in the different labor markets. The menu cost theory provides the more popular explanation of nominal price stickiness. Another explanation rests on the presumption of strictly convex price adjustment costs. In this theory the cost for firm of changing price is assumed to be = ( − −1 )2 0 Under this assumption the firm is induced to avoid large price changes, which means that it tends to make frequent, but small price adjustments. This theory is related to the customer market theory. Customers search less frequently than they purchase. A large upward price change may be provocative to customers and lead them to do search in the market, thereby perhaps becoming aware of attractive offers from other stores. The implied “kinked demand curve” can explain that firms are reluctant to suddenly increase their price.10 Below we describe the role of the first kind of price adjustment costs, menu costs, in more detail. The menu cost theory The menu cost theory originated almost simultaneously in Akerlof and Yellen (1985) and Mankiw (1985). It makes up the predominant microfoundation for the presumption that nominal prices and wages are sticky in the short run. For simplicity, here we shall concentrate on prices and price-setting firms. The key theoretical insight of the menu cost theory is that even small menu costs can be enough to prevent firms from changing their price. This is because the opportunity cost of not changing price is only of second order, that is, “small”; this is a reflection of the envelope theorem described in Appendix A; hence the potential benefit of changing price can easily be smaller than the cost of changing price. Yet, owing to imperfect competition (price MC ), the effect on aggregate output, employment, and welfare of not changing prices is of first order, i.e., “large”. As in the World’s Smallest Macroeconomic Model, suppose the aggregate demand is proportional to the real money supply: = 10 For details in a macro context, see McDonald (1990). c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° (19.25) 726 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where ∈ (0 1) is a parameter reflecting consumers’ patience. Consider now firm = 1 2 contemplating its pricing policy. With actual aggregate demand given by (19.25), the nominal profit as a function of the chosen price, is Π = − 1 = µ ¶− − õ ¶− !1 ≡ Π( ) Suppose that initially, = ̄ where ̄ is the price that maximizes Π given and ; that is, ̄ is given by (19.23) with = ( ) Thus, maximum profit in firm is Π(̄ ) ≡ Π̄ as illustrated in Fig. 19.4. As noted at the end of Section 19.3.1, the interesting case in relation to menu costs is the case with rising marginal costs. So we here assume that 1 In this case a higher for unchanged and will imply higher ̄ (see Exercise 19.??). Given the price = ̄ set in advance there is an unexpected shift in money supply to the level 0 through an unanticipated lump-sum “helicopter drop” at the beginning of the period.11 Suppose no other agents respond by changing price, neither price setters nor wage setters. In Fig. 19.4, ̄0 indicates the new price level that would be profit maximizing in the case of rising marginal costs ( 1) and absence of menu costs. Will firm have an incentive to change its price to ̄0 ? Not necessarily. The menu cost may exceed the opportunity cost associated with not changing price. Indeed, the opportunity cost to firm of not changing price tends to be small since Π Π Π (̄ ) = + (̄ ) (̄ ) Π =0+ (̄ ) (19.26) The first term on the right-hand side of (22.34) vanishes at the profit maxiΠ mum because (̄ ) = 0 i.e., the profit curve is flat at the profit maximizing price ̄ Moreover, since our thought experiment is one where and remain unchanged, there is no indirect effect of the rise in via or . Thus, only the direct effect through the fourth argument of the c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 727 i ( Pi , P,W , M ') i ( Pi , P,W , M ) Pi Pi ' Pi Figure 19.4: The profit curve is flat at the top ( 1 and are fixed, shifts to 0 ) profit function is left. And this effect is the same whether or not the price is changed. The result reflects a general principle, called the envelope theorem: in an interior optimum, the total derivative of a maximized function w.r.t. a parameter equals the partial derivative w.r.t. that parameter.12 The relevant parameter here is the aggregate money supply, . Hence, the effect of a change in on the profit is approximately the same (to a first order) whether or not the firm adjusts its price. Indeed, owing to the envelope theorem, for an infinitesimal change in , the profit of firm is not affected by a marginal change the price in response to the change in For finite changes in this is so only approximately. Indeed, given a finite change, 0 − = ∆, the opportunity cost of not changing price can, by taking a second-order Taylor approximation, be shown to be of “second order”, i.e., proportional to (∆)2 .13 This is a very small number, when |∆| is small. Therefore, in view of the menu cost, say it may be advantageous not to change price. Indeed, the net gain (= − opportunity cost) by not changing price may be positive. Each individual firm is in the same situation as long as the other firms have not changed price. The outcome that no firm changes its price is thus an equilibrium. Since there is 11 As by assumption there are no other non-human assets than base money, changes in the money supply can not be brought about through open market operations. 12 See Appendix A. 13 See Appendix B. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 728 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND no change in the general price level in this equilibrium, a higher output level results. What about the labor market? The considerations above presuppose that workers or workers’ unions do not immediately increase their wage demands in response to the increased demand for labor. This assumption can be rationalized in two different ways. One way is to assume that also the labor market is characterized by monopolistic competition between craft unions, each of which supplies its specific type of labor. If there are menu costs associated with changing the wage claim and they are not too small, the same envelope theorem logic as above applies and so, theoretically, an increase in labor demand need not in the short run have any effect on the wage claims. There is an alternative way of rationalizing absence of an immediate upward wage pressure. This alternative way is more apt since we have treated labor as homogeneous, implying that there is no basis for existence of many different craft unions.14 Instead we will simply assume that there is involuntary unemployment in the labor market. This means that there are people around without a job although they are as qualified as the employed workers and are ready and willing to take a job at the going wage or even a somewhat lower wage. Such a situation is in fact what several labor market theories tell us we should expect often to be present. Both efficiency wage theory, insider-outsider theory, collective bargaining theory, and search theory imply that wages tend to be above the individual reservation wage (see Chapter 23). The resulting presence of involuntary unemployment implies that employment can change with negligible effect on the wage level in the short run. 19.3.3 Menu costs in action So even small menu costs can be enough to prevent firms from changing their price in response to a change in demand. This also implies that even small menu costs can have sizeable effects on aggregate output, employment, and social welfare. To understand this latter point, note that under monopolistic competition neither output, employment or social welfare are maximized in the initial equilibrium. Therefore the envelope theorem does not apply to these variables. 14 Even with heterogenous labor, the craft union explanation runs into an empirical problem in the form of a “too low” wage elasticity of labor supply according to the microeconometric evidence. We come back to this issue in Chapter 22 and 23. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 729 This line of reasoning is illustrated in Fig. 19.5. There are two differences compared with Fig. 19.3. First, the specification (19.24) of aggregate demand is now introduced. Second, along the vertical axis we have set off the relative price, so that marginal revenue, MR as well as marginal costs, MC are indicated in real terms, i.e., MR = and MC = For fixed the demand curve faced by firm is shown as the solid downward-sloping curve ( ( )) to which corresponds the real marginal revenue curve, MR For fixed the real marginal costs faced by the firm are shown as the upward-sloping real marginal cost curve, MC (recall that we consider the case 1) If firms have rational (model consistent) expectations and know and in advance, we have = ( ) The price chosen by firm in advance, given this expectation, is then the price ̄ shown in Fig. 19.3. As the chosen price will be the same for all firms, the relative price, equals 1 for all The equilibrium output level for every firm will then be ( ) as indicated in the figure. If the actual money supply turned out to be higher than expected, say 0 = 1 and there were no price and wage adjustment costs and if wages were also multiplied by the factor , prices would be multiplied by the same factor and real money supply, production, and employment be unchanged. With menu costs, however, it is possible that prices and wages do not change. The menu cost may make it advantageous for each single firm not to change price. Then, the higher nominal money supply translates into higher real money supply and the demand curve is shifted to the right, as indicated by the stippled demand curve in Fig. 19.5. As long as ̄ MC still holds, each firm is willing to deliver the extra output corresponding to the higher demand. The extra profit obtainable this way is marked as the hatched area in Fig. 19.5. Firms in the other production lines are in the same situation and also willing to raise output. As a result, aggregate employment is on the point of increasing. The only thing that could hold back a higher employment is a concomitant rise in in response to the higher demand for labor. But the presence of involuntary unemployment in the labor market hinders this. So the tendency to higher employment is realized and firm ’s production ends up at 0 in Fig. 19.5, while the price ̄ is maintained. The other firms act similarly and the final outcome is higher aggregate consumption and higher welfare. Thus, the effects on aggregate output, employment, and social welfare of not changing price can be substantial; they are of “first order”, namely proportional to |∆| In the real world, nominal aggregate demand (here proportional to money supply) fluctuates up and down around some expected level. Sometimes the c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 730 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND Pi W , M , M ', and P given P W 1 P 1 1 yi 1 Pi M ' , P P D Pi M , P P D MC MR 0 M m P yi ' yi Figure 19.5: The impact in general equilibrium of a shift to 0 when menu costs are binding (the case 1) welfare effects of menu costs will be positive, sometimes negative. Hence, on average the welfare effects would appear to cancel out to a first order. This does not affect the basic point of the menu cost theory, however, which is that changes in money supply can have first-order real effects (in the same direction) because the opportunity costs by not adjusting prices are only of second order. A reservation As presented here, the menu-cost story is not entirely convincing. The rather static nature of the whole setup is a drawback. A first weakness is that the setup does not give a clear answer to the question: To what extent is it a change from a given past price, ̄−1 to the preset price, ̄ for the current period that is costly and to what extent is it a change from the preset price, ̄ for the current period to another ex-post price for this period that is costly? Besides, considering a sequence of periods featuring some price stickiness, there would in any period be some prices that are not at their ex ante “ideal” level. The firms in question are then not at the flat part of their profit curve. The menu cost necessary to prevent price adjustment will then be higher for these firms, thus making it more demanding for menu costs to be decisive. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 731 Moreover, in an intertemporal perspective it is present values of the expected stream of future gains and costs that matter rather than instantaneous gains and costs. An aspect of a complete dynamic modeling is also that ongoing inflation would have to be taken into account. It is well-known that in modern times where money is paper money (or electronic money), there is usually an underlying upward trend in the general input price level. To maintain profitability, the individual producers will therefore surely have to adjust their prices from time to time. The decision about when and how much to change price will be made with a view to maximizing the present value of the expected future cash flow taking the expected menu costs into account. This is a different situation compared with the purely static profit maximization in the above analysis.15 The rule of the minimum For a given price, ̄ it is beneficial for the firm to satisfy demand as long as the corresponding output level is within the area where nominal marginal cost is below the price. Returning to Fig. 19.3, let the demand faced by firm be denoted , that is, = (̄ ) Compare this demand to , defined as the production level at which = ̄ (assuming 1) This is the production level known as the Walrasian or classical or competitive supply of firm (the superscript “” stands for “classical” or “competitive”). It is the output that would prevail under perfect competition, given and = ̄ As this output level is a function of only and ̄ we write = ( ̄ ) So, as long as we get = If demand exceeds however, the firm will stick to producing in that producing beyond this level would entail a loss (marginal cost above price). The general rule is therefore that given the predetermined price = ̄ , production becomes ∙ ¸ ̄ = min ( ) ( ̄ ) (19.27) saying that production is determined as the minimum of demand and the classical supply at the given price. This rule is known as the rule of the minimum. According to this rule, under “normal circumstances” the production will be determined by the demand since the demand will be the most narrow limit when actual aggregate demand is not greatly above the expected level. When the market for good is in the “normal” state where − ( ̄ ) 0 it is natural to say that this market is a “buyers’ market”. It is, however, 15 As to contributions within this dynamic perspective, see Literature notes. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 732 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND not natural to categorize the state as one of “excess supply”. The difference − ( ̄ ) is completely voluntary on the part of the price-setting firm The output level given by the rule of the minimum represents the effective output supply by firm . The corresponding effective labor demand by firm 1 is given as = from the production function. While postponing details about the labor market to Chapter 22 and 23, we have above presumed that involuntary unemployment is present. This means both that offered jobs can be filled and that unemployed people are still around. If at the same time in most of the goods markets, the binding constraint in (30.1) is the demand, then Keynesian unemployment is said to prevail. If instead in most of the goods markets, the binding constraint in (30.1) is the classical supply, then classical unemployment is said to prevail. This type of unemployment corresponds to the way non-Keynesian writers in the interwar period interpreted the existence of huge unemployment as a temporary phenomenon caused by a “too high real wage”. It is in this context that the quote by Edmond Malinvaud at the head of this chapter should be seen. In the World’s Smallest Macroeconomic Model of Section 19.2 classical unemployment can not occur because of constant marginal costs combined with a positive mark-up. Similarly, if = 1 in the present model we have = a constant. Then classical unemployment is impossible here as well. Indeed ̄ = (1 + ) Hence ( ̄ ) = ∞ and so (30.1) gives = (̄ ) ( ̄ ) automatically for all (since is assumed the same for all ). All the goods markets are demand-constrained and any unemployment is thereby Keynesian. Note also that because of constant combined with the constant mark-up, no menu costs are needed to maintain that only output not prices respond to changes in aggregate demand, 19.3.4 Abundant capacity One of the stylized facts listed in Section 19.1 was that under “normal circumstances” a majority of firms in an industrialized economy respond to shortrun shifts in aggregate demand by adjusting production rather than price. Key elements of an explanation of this phenomenon have been sketched: (a) the distinction between Walrasian demand and effective demand; (b) price setting agents in markets with imperfect competition; (c) the “secondorder argument” that the potential benefit of adjusting the price can easily be smaller than the cost of adjusting; and (d) because prices are generally above marginal costs, firms are disposed to rapid quantity adjustment when aggregate demand shocks occur. The next problem is whether rapid quantity adjustment is in the main realizable. Under the assumption that involuntary unemployment is present, c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 733 lack of workers will not be an impediment. But the production capacity of firms depends on their capital equipment. To throw light on this aspect we now let the production function have two inputs, capital and labor. Putty-clay technology Suppose firm has the production function = ( ) (19.28) where is the installed capital stock and the labor input, = 1 2 16 Because of strictly convex installation costs, is given in the short run. As raw materials and energy are ignored, in the short run it is only that can be varied. So in the short run the capital costs are fixed but labor costs variable. Realistic short-run analysis also makes a distinction between the “ex ante” and the “ex post” production function. By “ex ante” is meant the point in time where the decision about investment in plant and equipment is to be made. We may imagine that this decision is made on the basis of the ex ante production function, in (19.28). The decision will be made with a forwardlooking perspective. Construction and installation are time consuming and to some extent irreversible. By “ex post” is meant “when construction and installation are finished and the capital ready for use”. In this situation, the substitutability between capital and labor tends to be limited. Our long-run models in previous chapters implicitly ignored this aspect by assuming that substitutability between capital and labor is the same ex ante and ex post. In reality, however, when a machine has been designed and installed, its functioning will often require a more or less fixed number of machine operators. What can be varied is just the degree of utilization of the machine per time unit. In the terminology of Section 2.5, technologies tend in a short-run perspective to be “putty-clay” rather than “putty-putty”. An example: Suppose the production function, in (19.28), is a neoclassical production function. This could then be the ex ante production function. Ex post, however, this function no longer describes the choice opportunities for firm . These are instead given by a Leontief production function with CRS: = min( ̄ ) 0 0 16 (19.29) Note that, contrary to earlier chapters, is here not the capital-labor ratio, but simply the capital stock in firm c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 734 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where and are given technical coefficients, ̄ is the size of the installed capital (now a fixed factor), and is its utilization rate (0 ≤ ≤ 1) = 1 17 Presumably the firms would have acquired their capital equipment under different circumstances at different points in time in the past so that, generally, the equipment would be somewhat heterogeneous and and would be index numbers and differ across the firms. But to make aggregation simple, the analyst may be tempted in a first approach to ignore this and assume and are the same across the firms. Capacity utilization in a Keynesian equilibrium Under “full capacity utilization” we have = 1 (each machine operating “full time” seven days a week, allowing for surplus time for repairs and maintenance); “capacity” is given as ̄ per week. Producing efficiently at capacity requires = ̄ But if demand, is less than capacity, satisfying this demand efficiently requires = (̄ ) 1 and = As long as 1 there is unused capacity and marginal productivity of labor in firm is a constant, The (pure) profit of firm is Π = − C( ) where C( ) = + is the cost function with denoting the fixed costs deriving from the fixed production factor, ̄ . Average cost is = C( ) = + and marginal cost is a constant = for ̄ Fig. 19.6 depicts these cost curves together with a downward-sloping demand curve. A monopolistic-competition market structure as described in Section 19.3.1 is assumed but now only a subset of the firms produce differentiated consumption goods. The other firms produce differentiated capital goods, also under conditions of monopolistic competition and with the same price elasticity of demand. Firm presets the price of good at = ̄ in the expectation that the level of demand will be as indicated by the downward sloping D curve in Fig. 19.6. The point in the figure represents a standard shortrun equilibrium under monopolistic competition with output level such that = Assuming full symmetry across the different firms, the point would also reflect a Keynesian equilibrium if the actual demand level (position of the demand curve) had turned out to be as expected by the firms when fixing their price. But in the figure it is assumed that the demand level turned out lower. The produced quantity is reduced while the price remains unchanged (because of either menu costs or simply the constant marginal costs combined with constant price elasticity of demand). Firm ends up 17 The link between the ex ante production function and the technical coefficients and was described in Chapter 2. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 735 Pi AC MC Pi MC ESR D D' MR y´i Aki yi Figure 19.6: Firm in a Keynesian equilibrium (̄ is production capacity; MC curve first horizontal and then vertical at = ̄ ). with actual production equal to 0 in Fig. 19.6. The obtained profit is indicated by the hatched rectangle constructed by the help of the average cost curve . If instead the actual demand level had turned up higher than expected, firm would be induced to raise production. There is scope for this because price is above marginal costs the whole way up to full capacity utilization. Profits will in this manner become substantially higher than expected because the AC curve is downward-sloping up to ̄ . Such a situation where the quantity produced is less than the quantity at which average costs are at the minimum, here at ̄ , is in the theory of industrial organization said to reflect “excess capacity”. As “excess” sounds as if the situation reveals a kind of inefficiency, which in fact need not be the case, we prefer the term “abundant capacity”. A monopolistic-competition long-run equilibrium The picture is essentially the same in a “free-entry-and-exit equilibrium” where all pure profit is eliminated; in the theory of industrial organization this is traditionally called a “long-run equilibrium”. Suppose that initially some of the firms obtain positive pure profits as illustrated in Fig. 19.6. This state of affairs invites entry of new firms. Over time these set up new plants and begin to supply new differentiated goods from a large set of as yet unutilized possible imperfect substitutes for the existing goods. The c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 736 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND entry process continues until equilibrium with zero pure profits obtains in all product lines. When this state is reached, prices equal both short-run and long-run average costs, and each firm operates where the downward-sloping demand curve is tangent to both AC curves. We here use the terms “shortrun” and “long-run” as they are used in the theory of industrial organization. That is, “short run” refers to a time horizon where only a subset of the production factors are variable, while “long run” refers to a long-enough time horizon for all production factors to be variable. From a macroeconomic perspective the important conclusion is that the “transition” from short-run equilibrium to long-run equilibrium in no way tends to lessen the presence of abundant capacity in the firms. To portray a long-run equilibrium, we only need to let the AC curve for firm ’s chosen plant and equipment be tangent to the demand curve at the point . This is what we have done in Fig. 19.7 where also the long-run marginal and average cost curves are visible, denoted LMC and LAC, respectively. The LMC curve is assumed U-shaped. This implies a U-shaped LAC curve. The downward-sloping part of the LMC curve may be due to indivisibilities of plant and equipment and the upward-sloping part as reflecting coordination problems or an implicit production factor which is tacitly held fixed (a special managerial expertise, say). In Fig. 19.7 we have moreover assumed that the short-run marginal cost curve, is horizontal only up to certain output level. It then rises gradually to end up as vertical at full capacity utilization. This may reflect that less efficient standby equipment is being brought to use, and the wear and tear on the machinery is gradually increased. This amounts to a plausible rounding off of the probably too “sharp” Leontief production (19.29). In relation to the production function in Section 19.3.1, this roughly corresponds to assuming that for production up to a certain level, in (19.20) equals 1 whereas beyond this level is less than 1. An additional reason for the MC curve to be upward-sloping at high capacity utilization is wage bonuses for working on the night shift or in the weekend. Also in this more realistic setup is abundant capacity revealed as a sustainable equilibrium phenomenon. In long-run equilibrium each firm produces at a point where: • price is above marginal costs so as to exactly cover fixed costs; • the quantity produced is less than the quantity at which average costs are at the minimum (i.e., where the MC curve crosses the AC curve in Fig. 19.7), given the firm’s preferred plant and equipment. The conclusion is that as long as the AC curve does not shift (this would c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.3. Price setting and menu costs 737 Pi AC MC LMC ESR Pi MC D MR yi * LAC A*k i* yi Figure 19.7: Firm in a monopolistic-competition long-run equilibrium (∗ is longrun equilibrium output and ∗ ∗ is long-run production capacity). happen if the wage level changed), firms are more than willing to accommodate an increased demand (outward shift of the demand curve) at an unchanged price or even at a lower price by an increase in production. Similarly, an inward shift of the demand curve will not induce a temptation to reduce the price, rather the opposite if the menu cost is immaterial. These observations fit well with the empirical evidence that measured total factor productivity and profits rise in an economic upturn and fall in a downturn, an issue to which we return in Part VII of this book. In the real world some markets are better characterized by strategic interaction between a few big firms than by monopolistic competition. But also such firms may have an incentive to maintain abundant capacity. This will make credible a threat to cut price in response to unwelcome entry by a competitor. The role of indivisibilities The downward-sloping part of the LAC curve, reflecting indivisibilities in plant and equipment, is important also from another perspective. Without indivisibilities it may be difficult to see why involuntarily unemployed workers could not just employ and support themselves in the backyard, financing the needed tiny bits of capital by tiny bank loans. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 738 19.4 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND The IS-LM model After these reflections about the context of short-run analysis, we are ready to present the IS-LM model. The key new element compared with the World’s Smallest Macroeconomic Model is that an interest-bearing asset is added. The version of the IS-LM model presented here is in many respects similar to the familiar one known from introductory and intermediate textbooks. It is essentially static and deals with mechanisms that are likely to be operative within a single period of length a quarter of a year, say, or at least not more than one year. The focus is on the interaction between the output market and the asset markets. The model conveys the central message of Keynes’ theory: the equilibrating role in the output and money markets is taken by output and nominal interest rate changes. 19.4.1 The building blocks We consider a closed economy with a private sector, a government, and a central bank. The produce of the economy consists mainly of manufacturing goods and services, supplied under conditions of imperfect competition and price stickiness of some sort. “Money supply” means money in the broad sense and thus includes bank created money in addition to currency in circulation. The model starts out directly from presumed aggregate behavioral relationships that are supposed to roughly characterize aggregate behavioral responses to changes in exogenous variables, at least under “normal circumstances”. The aim is to deliver qualitatively valid rather than quantitatively precise answers to questions about the functioning of the economy in the short run. The output market Demand Aggregate output demand is given as = ( +1 ) + (+1 ) + + (19.30) 0 0 + + 1 () 0 ≤ 0 0 +1 +1 +1 +1 0 0 where the function (·) represents private consumption, the function (·) represents private fixed capital investment, is public spending on goods and services, and is a shift parameter (possibly stochastic) summarizing the role of unspecified exogenous variables that may matter for aggregate output c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.4. The IS-LM model 739 demand. One of these variables could be the general “state of confidence” and another the preference for the present relative to the future. Arguments appearing in the consumption and investment functions include which is current private disposable income, +1 which is expected output the next period (or periods), and which are commented on below, and finally which is the expected short-term real interest rate. In this first version of the model we assume there is only one short-term real interest rate in the economy. The signs of the partial derivatives of the consumption and investment functions in (19.30) are explained as follows. A general tenet from earlier chapters is that consumption depends positively on household wealth. One component of household wealth is financial wealth, here represented by the market value, · of the capital stock (including the housing stock). Another component is perceived human wealth (the present value of the expected labor earnings stream), which tends to be positively related to both and +1 . The separate role of disposable income, reflects the hypothesis that a substantial fraction of households are credit constrained. The role of the interest rate, reflects the hypothesis that the negative substitution and wealth effects on current consumption of a rise in the real interest rate dominate the positive income effect. Firms’ investment depends positively on +1 . This is because the productive capacity needed next period depends on the expected level of demand next period. In addition, investment in new technologies is more paying when expected sales are high. On the other hand, the more capital firms already have, the less they need to invest, hence 0. Finally, the cost of investing is higher the higher is the real interest rate. These features are consistent with the -theory of investment when considering an economy where firms’ production is demand constrained. Disposable income is given by ≡ − T (19.31) where is aggregate factor income (= GDP) and T is real net tax revenue (equal to gross tax revenue minus transfers). We assume a quasi-linear net tax revenue function T = + ( ) 0 ≤ 0 1 (19.32) where is a constant parameter reflecting “tightness” of discretionary fiscal policy. Fiscal policy is thus described by two variables, representing government spending on goods and services and representing the discretionary element in taxation. A balanced primary budget is the special case + ( ) c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 740 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND = The endogenous part, ( ) of the tax revenue is determined by the given taxation rules; when 0 0 these rules act as “automatic stabilizers” by softening the effects on disposable income, and thereby on consumption, of changes in output and employment. With regard to expected output next period, +1 the model takes a shortcut and assumes +1 is simply an increasing function of current output and nothing else: +1 = ( ) 0 0 ≤ 1 (19.33) We may write aggregate private output demand in a more compact way. First, since we only consider a single period, we can treat the amount of installed capital as a given constant, ̄ Hence, for convenience we suppress the explicit reference to ̄ and ̄ in the consumption and investment func˜ tions, respectively, and write these functions as ̃(·) and (·) respectively. Second, inserting (19.31) and 19.33) into (19.30), we can then express aggregate private demand as a function ( ) ≡ ̃( − − ( ) ( ) ) ˜ +(( ) ) So total output demand is = ( ) + + where 0 0 + ) ( ) 1 0 = (1 − ) + (+1 +1 = + 0 and = · (−1) ∈ (−1 0) (19.34) (19.35) Production and employment Prices on goods and services have been set in advance by firms operating in markets with monopolistic competition. In response to shifts in demand, owing to either constant marginal costs or the presence of menu costs, firms change production rather than price. There is scope for maintaining profitability this way because prices are normally above marginal costs. Behind the scene there is an aggregate production function, = (̄ ) where is the level of employment. The conception is that under “normal circumstances” there is abundant capacity. That is, ̄ is large enough so that for some ̄, where ̄ is the labor force, output demand can be satisfied, i.e., (̄ ) = (19.36) without violating the rule of the minimum as defined in Section 19.3. Assuming 0 we can solve the equation (19.36) for the desired employment, and write = N ( ) where N 0 and N 0 under the assumption that 0. The desired employment can and will be realized provided it is smaller than ̄ − ̃ where ̃ is the sum of frictional unemployment (which is inevitable when workers change jobs and location in a vibrant economy) and c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.4. The IS-LM model 741 voluntary unemployment (unemployed people with reservation wage above the going wage). The remainder of the labor force is ready for work here and now at the going wage. The IS-LM model assumes this group is normally large enough to allow realization of = N ( ). The remaining part of the labor force is called ̂ and consists of those who are involuntarily unemployed (i.e., those who are ready and willing to work at the going wage or even a somewhat lower wage). With denoting total unemployment, the labor force is hereby decomposed this way: ̄ ≡ + ≡ + ̃ + ̂ In an alternative decomposition of unemployment one writes = + where is the natural unemployment level and the remainder unemployment, often called the cyclical unemployment level (a positive number in a recession, a negative number in a boom). So is defined as the level of unemployment that prevails when the unemployment rate, ̄ equals the natural (or structural) rate of unemployment. This is defined as that rate of unemployment which generates neither upward nor downward pressure on the inflation rate. An alternative name for this is the NAIRU.18 The term “natural” has become standard although it is a misnomer since there is nothing natural about that unemployment rate. Besides, identifying absence of pressure on the inflation rate with a particular rate of unemployment may be problematic. There are empirics as well as theories around saying that there tends to be a range of unemployment rates within which no pressure on the inflation rate is generated, neither upward nor downward.19 Many textbooks ignore this rate-versus-range issue and speak of the natural level of output as a unique level of output, realized when the unemployment is at the supposed unique natural rate: = (̄ ) where ≡ ̄ − is denoted the natural level of employment. Until further notice, we stick to this convenient terminology − with the proviso mentioned. Some authors use the term full-employment output as synonymous with others are reluctant to do that. In any case, and are affected by legal institutions and economic policy 18 Non-Accelerating-Inflation-Rate-of-Unemployment. At least at low levels of inflation this should be so, cf. Akerlof et al. (2000) and Hendry and ? (2013). In Chapter 23 we go into detail with the labor market. 19 c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 742 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND While the size and composition of unemployment matter for wage and price inflation, the IS-LM model considers such effects as not materializing until at the earliest the next period. Being concerned about only a single short period, the model is therefore usually tacit about production and employment aspects and leave them “behind the scene”. Asset markets In this first version of the IS-LM model we assume that only two financial assets exist, money and an interest-bearing short-term bond. The latter may be issued by private agents and the government. Although not directly visible in the model, there are commercial banks that accept deposits and provide bank loans to households and firms. Bank deposits are assumed to earn no interest at all but they are attractive because they in general provide a fairly secure store of liquidity due to government-guaranteed deposit insurance.20 The bank lending rate allows the banks a revenue to cover the costs associated with banking. Let denote the money supply in a broad sense. That is, in addition to currency in circulation, the bank-created money in the form of liquid deposits in the banks is included in We may thereby think of as close to what is in the statistics denoted 1 or 2 , cf. Chapter 16. The bank lending rate equals the short-term nominal interest rate, on government bonds. All interest-bearing assets are considered perfect substitutes from the point of view of the investor and will from now just be called “bonds”. The demand for money is assumed given by = · (( ) + ) 0 0 (19.37) where is the output price level (the GDP deflator) and is a shift parameter (possibly stochastic) summarizing the role of unspecified exogenous variables that may matter for real money demand. Apart from the shift term, real money demand is given by the function ( ) which is called the liquidity preference function. The first partial derivative of this function is positive reflecting the transaction motive for holding money. The output level is an approximate statistic (a “proxy”) for the flow of transactions for which money is needed. The negative sign of the second partial derivative reflects that the interest rate, is the opportunity cost of holding money instead of interest-bearing assets. The part of non-human wealth not held in the form of money is held in the form of an interest-bearing one-period bond. This bond yields a payoff 20 In practice even checkable deposits in banks usually earn a small nominal interest, but this is ignored by the model. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.4. The IS-LM model 743 equal to 1 unit of account at the end of the period. Let the market price of the bond at the beginning of the period be units of money. The implicit nominal interest rate, is then determined by the equation (1 + ) = 121 i.e., = (1 − ) (19.38) There is a definitional link between the nominal interest rate and the expected short-term real interest rate, . In continuous time we would have = − with as the instantaneous nominal interest rate (with continuous compounding) and (≡ ̇ ) as the (forward-looking) instantaneous inflation rate, the superscript indicating expected value. In discrete time the appropriate way of defining is more involved. The holding of money is motivated by the need, or at least convenience, of ready liquidity to carry out expected as well as unexpected spending in the near future. To perform this role, money must be held in advance, that is, at the beginning of the (short) period in which the purchases are to be made (“cash in advance”). If the price of a good is euro to be paid at the end of the period and you have to hold this money already from the beginning of the period, you effectively pay + for the good, namely the purchase price, plus the opportunity cost, Postponing the purchase one period thus gives a saving equal to + . The price of the good next period is +1 which, with cash in advance, must be held already from the beginning of that period. So the real gross rate of return obtained by postponing the purchase one period is 1+ 1 = 1 + = (1 + ) +1 1 + +1 where +1 ≡ (+1 − ) is the inflation rate from the current to the next period. As seen from the current period, +1 and +1 are generally not known. So decisions are based on the expected real interest rate, 1+ − 1 ≈ − +1 (19.39) = 1 + +1 where the approximation is valid for “small” and +1 19.4.2 Keynesian equilibrium The model assumes clearing in both the output and the money market: 21 = ( − +1 ) + + = ( ) + In continuous time with compound interest, = 1 so that = − ln c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° (IS) (LM) 744 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where, for simplicity, we have used the approximation in (19.39), and where is the available money stock at the beginning of the period. In reality the central bank has direct control only over the monetary base. Yet the traditional understanding of the model is that through this, the central bank has under “normal circumstances” control also over With given by monetary policy, the interpretation of the equations (IS) and (LM) is therefore that output and the nominal interest rate quickly adjust so as to clear the output and money markets. The equation (IS), often named the IS equation, asserts clearing in a flow market: so much output per time unit matches the demand per time unit for this output. The name comes from an alternative way of writing it, namely as = (investment = saving, where saving = − − − ) In contrast, the equation (LM), often called the LM equation, asserts clearing in a stock market: so much liquidity demand matches the available money stock, at a given point in time, here the start of the period. At the theoretical level the period length is thus understood to be very short. At the empirical level we have data for and on a daily basis, whereas the period length of data for aggregate output, consumption, and investment, is usually a year or at best a quarter of a year. So in econometric analyses, instead of letting the model’s and refer to a point in time, the average money stock and interest rate over a year or a quarter of a year may be used. Having specified the LM equation, should we not also specify a condition for clearing in the market for bonds? The answer is that we do not have to. The balance sheet constraint guarantees that clearing in the money market implies clearing in the bond market − and vice versa. To see this, let denote the nominal financial wealth of the non-bank public and let denote the number of one-period bonds held net by the non-bank public. Then + ≡ With denoting the demanded quantity of bonds, we have + = This is called the balance sheet constraint and implies a kind of “Walras’ law for stocks”. Subtracting the first from the second of these two equations yields (19.40) − + ( − ) = 0 Given 0 it follows that if and only if = then = That is, clearing in one of the asset markets implies clearing in the other. Hence it suffices to consider just one of these two markets explicitly. Usually the money market is considered. The IS and LM equations constitute the traditional IS-LM model. The exogenous variables are +1 and, in the traditional interpretation, . Given the values of these variables, a solution, ( ) to the equation system consisting of (IS) and (LM) is an example of a Keynesian c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 745 equilibrium. The current price level, is seen as predetermined and maintained through the period, but the price level +1 set for the next period will presumably not be independent of current events. So expected inflation, +1 ought to be endogenous. It is therefore a deficiency of the model that +1 is treated as exogenous. Yet this may give an acceptable approximation as long as the sensitivity of expected inflation to current events is small. 19.5 Alternative monetary policy regimes We shall analyze the functioning of the described economy in three alternative monetary policy regimes. We first consider the traditional case where the central bank is assumed to maintain the money supply at a given target level. Next we consider the case where the central bank, trough open market operations, maintains at a certain target level. The third monetary policy regime to be considered is a counter-cyclical interest rate rule where both and are endogenous. 19.5.1 Money stock as target Here the central bank maintains the money supply at a certain target level, In addition to the output level, the interest rate is endogenous. The determination of the endogenous variables, and is conveniently illustrated by an IS-LM diagram. Until further notice it is assumed that circumstances are such that the solutions for and are strictly positive. Consider the IS-LM diagram in Fig. 19.8. The IS curve is the locus of combinations of and that are consistent with clearing in the output market, i.e., consistent with the IS equation. Since 0 (·) is a monotonic function of Consequently, (IS) gives as an implicit function of +1 and : = ( +1 ) The partial derivatives of this function can be found by taking the differential on both sides of (IS): = + ( − +1 ) + + + (19.41) We find | by setting +1 = = = = 0 and reordering: = | 1 − 0 c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° (19.42) 746 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where the sign comes from (19.35). That is, higher aggregate demand in equilibrium requires that the interest rate is lower. Similarly, the LM curve is the locus of combinations of and that are consistent with clearing in the money market, i.e., consistent with the equation (LM). The liquidity preference function, (·) is a monotonic function of since 0. Therefore, (LM) gives as an implicit function of and : = ( ) The partial derivatives can be found by taking the differential on both sides of (LM): ( ) = + + (19.43) We find | by setting ( ) = = 0 and reordering: = | − 0 (19.44) That is, for real money demand to equal real money supply, a higher volume of transactions must go hand in hand with a higher interest rate. Fig. 19.8 shows the downward sloping IS curve and the upward sloping LM curve. A solution ( ) to the model is unique and we can write and as implicit functions of all the exogenous variables: ) +1 = ( +1 ) = ( (19.45) (19.46) Comparative statics How do and depend on the exogenous variables? A qualitative answer can easily be derived by taking into account in what direction the IS curve or the LM curve in Fig. 19.8 shifts in response to a change in an exogenous variable. A quantitative answer is obtained by finding the partial derivatives of the implicit functions (·) and (·) evaluated in the equilibrium point. A convenient method is based on Cramer’s rule as follows. The two equations, (19.41) and (19.43), constitute a new equation system with two new endogenous variables, the changes and The changes, +1 ( ) and in the exogenous variables are our new exogenous variables. The coefficients to the endogenous and exogenous variables are c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 747 i IS LM G 0 M 0 Yn Y Figure 19.8: The IS-LM cross when is exogenous; a case with equilibrium output below the natural level, ( +1 and given). derivatives evaluated at the equilibrium point. Like the old system the new system is simultaneous (not recursive). The key point is that the new system is linear. We first reorder (19.41) and (19.43) so that and appear on the left-hand side and the differentials of the exogenous variables on the right-hand side of each equation: (1 − ) − = − +1 + + + + = − From this linear system we find and by Cramer’s rule: ¯ ¯ ¯ − +1 + + + − ¯ ¯ ¯ ¯ − ¯ = ∆ (− +1 + + + ) + ( − ) (19.47) = ∆ and ¯ ¯ ¯ 1 − − +1 + + + ¯ ¯ ¯ ¯ ¯ − = ∆ (1 − )( − ) − (− +1 + + + ) = ∆ c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 748 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND where the determinant ∆ is defined by ¯ ¯ ¯ 1 − − ¯ ¯ ¯ = (1 − ) + 0 ∆=¯ ¯ (19.48) Finally, we get the partial derivatives of (·) and (·) respectively, w.r.t. the real money supply, by setting +1 = = = = = 0 and reordering. Thereby 0 = = (1 − ) + ( ) 1 − 0 = = (1 − ) + ( ) in view of (19.35) and (19.48). Such partial derivatives of the endogenous variables w.r.t. an exogenous variable, evaluated at the equilibrium point, are called multipliers. The short-run effect on of a small increase in can be calculated as ∆ ≈ ( ( ))∆ Thus, the partial derivative w.r.t. acts as a multiplier on the increase, ∆ , in the exogenous variable, .22 The intuitive interpretation of the signs of these multipliers is the following. The central bank increases the money supply through an open market purchase of bonds held by the private sector. Immediately after this, the supply of money is higher than before and the supply of bonds available to the public is lower. At the initial interest rate there is now excess supply of money and excess demand for bonds. But the attempt of agents to get rid of their excess cash in exchange for more bonds can not succeed in the aggregate because the supplies of bonds and money are given. Instead, what happens is that the price of bonds goes up, that is, the interest rate goes down, cf. (19.38), until the available supplies of money and bonds are willingly held by the agents. Money is therefore not neutral. The output multiplier w.r.t. government spending on goods and services, often just called the spending multiplier, is 1 = = = (1 − ) + 1 − + 22 (19.49) Instead of using Cramer’s rule, in the present case we could just substitute , as determined from (19.43), into (19.41) and then find from this equation. In the next step, the found solution for can be inserted into (19.43), which then gives the solution for However, if were a function that could become nil, this procedure might invite a temptation to rule this out by assumption. That would imply an unnecessary reduction of the domain of (·) and (·) The only truly necessary assumption is that ∆ 6= 0 and that is automatically satisfied in the present problem. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 749 evaluated at the current equilibrium, ( ) Under the assumed monetary policy we thus have 0 1(1 − ) The difference, 1(1 − ) − is due to the financial crowding-out effect, represented by the term 0 in (19.49). Owing to the fixed money supply, the expansionary effect of a rise in is partly offset by a rise in the interest rate induced by the increased money demand resulting from the “initial rise” in economic activity. Without the financial crowding-out effect, the spending multiplier would be above one. Another “moderator” comes from the marginal net tax rate, 0 ( ) which by reducing the private sector’s marginal propensity to spend, cf. (19.35), acts as an “automatic stabilizer”. When income (economic activity) rises, disposable income rises less, partly because of higher taxation, partly because of lower aggregate transfers, for example unemployment compensation. Shifts in the values of the exogenous variables, and should be interpreted as shocks (disturbances) coming from unspecified sources outside the system. A positive demand shock, 0 may be due to an upward shift in households’ and firms’ general level of “confidence”. A positive liquidity preference shock may reflect a downward shift in “confidence”, that is, higher perceived risk associated with bond holdings. On the other hand, improvements in the payment technology (widespread transition to electronic home banking, say) may shift both the money multiplier and money velocity, ( ) upward which in the model would be represented by 0 To see how demand shocks and liquidity preference shocks, respectively, affect output under the given monetary policy, we first set +1 = = = = 0 in the equation (19.47). Then, setting = 0 (or = 0), we find the partial derivative of w.r.t. (or ) : 1 = = = (1 − ) + 1 − + − = = 0 (1 − ) + As expected, a positive demand shock is expansionary, while a positive liquidity preference shock is contractionary because it raises the interest rate. Note that = (from (19.49)) in view of the way enters the IS equation. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 750 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND How does higher expected inflation affect and ? We find − = = 0 +1 +1 (1 − ) + = +1 = ∈ (0 1) (19.50) +1 (1 − ) + ( − +1 ) −(1 − ) = = +1 − 1 = ∈ (−1 0) +1 +1 (1 − ) + A higher expected inflation rate thus leads to a less than one-to-one increase in the nominal interest rate and thereby a smaller expected real interest rate. Only if money demand were independent of the nominal interest rate ( = 0) as the quantity theory of money claims, would the nominal interest rate rise one—to-one with +1 and the expected real interest rate thereby remain unaffected. Before proceeding, note that there is a reason that we have set up the IS and LM equations in a general nonlinear form. We want the model to allow for the empirically important feature that the different multipliers generally depend on the “state of the business cycle”. The spending multiplier, for instance, tends to be larger in a slump than in a boom. 19.5.2 The nominal interest rate as target Instead of targeting a certain level of the money supply, the central bank now maintains the nominal interest rate at a certain target level 0 This version of the model corresponds better to how central banks nowadays operate in practice. The central bank announces a target level of the nominal interest rate and through open-market operations adjusts the monetary base until the target rate is realized. In this setup is exogenous, while is endogenous along with . Instead of the upward-sloping LM curve we get a horizontal line, the line (“” for interest rate) in Fig. 19.9. The model is now recursive. Since does not enter the IS equation, is given by this equation independently of the LM equation. Indeed, the IS equation determines as an implicit function = ( − +1 ) (19.51) Comparative statics By considering the IS equation in the form (19.41), we shall find the partial derivatives of the function. For example, the partial derivatives w.r.t. the c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 751 i IS e , ,G ,D IR Yn Y Figure 19.9: A fixed interest rate implying equilibrium output close to the natural level ( +1 and given). interest rate, public spending, a demand shock, and a liquidity preference shock, respectively, are 0 = 1 − 1 = = 1 1 − = 0 (19.52) The latter derivative shows that a liquidity preference shock has no effect on equilibrium output. The shock is immediately counteracted by a change in the money supply in the same direction, so that the interest rate remains unchanged. Thus, the liquidity preference shock is “cushioned” by the monetary policy. On the other hand, a shock to output demand has a larger effect on output than in the case of money stock targeting (compare (19.52) to (19.49). This is because under money stock targeting a dampening rise in the interest rate was allowed to take place. But with a constant interest rate this financial crowding-out effect does not occur. From this kind of analysis, Poole (1970) concluded that: • a money stock targeting rule is preferable (in the sense of implying less volatility) if most shocks are output demand shocks, while c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 752 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND • an interest rate targeting rule is preferable if most shocks are liquidity preference shocks. By inserting the solution for from (19.51) into (LM), we find the money supply required to obtain the target interest rate We get = · (( ) + ) = · ((( − +1 ) ) + ) Taking the differential on both sides of (LM) yields = ( + + ) + (19.53) This implies + ) 0 + ) = ( 1 − 1 = 0 1 − = ( = 0 = 0 Since for a fixed interest rate there is no financial crowding-out, the production outcome can also be illustrated by a standard 45◦ “Keynesian cross” diagram as in Fig. 19.10. Under a constant interest rate policy the effect on of a one-unit increase in is given via the spending multiplier = 1(1 − ) 1 from (19.52). Since the fiscal tightness parameter is unchanged, the net tax revenue only rises according to the rule T = 0 ( ) which under “normal circumstances” tends to be less than This is so in spite of the fact that in view of the spending multiplier being above one, given a constant interest rate. So it is here understood that the increase in is financed by allowing a budget deficit to be larger than otherwise. This brings the issue of Ricardian equivalence into the picture. Ricardian non-equivalence The Keynesian grounds for rejecting Ricardian equivalence as an acceptable approximation are sharpest under interest rate targeting. The skepticism about Robert Barro’s portrait of the household sector as a set of infinitely lived dynasties is one thing. On top of this comes that refutation of Ricardian equivalence has stronger implications in an economy where output is determined by aggregate demand. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 753 Yd D(Y , r, ) G D 45 Yn Y Figure 19.10: Given a fixed interest rate, a “Keynesian cross” diagram is sufficient to display the equilibrium output level ( = − +1 and given). Consider the question: To what extent, if at all, will a deficit-financed increase in result in crowding out of current private consumption? As a thought experiment, let us temporarily assume that Barro’s portrait of the household sector is an acceptable approximation. Facing a deficit-financed increase in , the household dynasties thus set aside savings to fully prepare for the deficit-induced higher taxes in the future. In an economy with full capacity utilization and inelastic labor supply private consumption would fall correspondingly. In an economy with less than full capacity utilization and involuntary unemployment, however, there is no reason that private consumption should fall. On the contrary, by shifting people from unemployment to work, the higher entails both higher production and higher disposable income. So there is scope for a response involving a rise in private saving without a reduction in private consumption. And the prediction of the ISLM model is that under the interest rate targeting rule, this is exactly what will take place. How do we know? Because “the balanced budget multiplier” is at least 1, as we shall now see. The balanced budget multiplier What will be the effect on of a rise in if we require an always balanced budget? Letting the rise in be financed by a corresponding rise in the tax c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 754 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND revenue, T implies T = + 0 ( ) = There will be an automatic rise in tax revenue via 0 ( ) 0, but generally an exactly balanced budget will require a simultaneous adjustment of the fiscal tightness parameter, of size = − 0 ( ) Now, = + = + ( − 0 ( ) ) By ordering, = 1+ 0 + From (19.41) with = +1 = = = 0 we find = (1 − ) 0 Thus, the total effect on of a unit increase in under a balanced budget policy approximately equals the total derivative w.r.t. which is 1+ + 1 + = 0 = 1− 0 = 1 − + 0 1 + 1 + 1− 1 − ≥ 1 = + )0 ( ) 1 − − (+1 +1 where we have used (19.35). This is called the balanced budget multiplier. In + = 0 it equals exactly 1. This is the famous Haavelmo result case +1 +1 (Haavelmo, 1945). If the interest rate were allowed to increase, as would be the case with a constant (the -exogenous regime), then the balanced budget multiplier would be smaller because of the implied financial crowding-out effect. Back to the Ricardian equivalence issue Let us now return to the issues of crowding out and Ricardian equivalence raised above. With a constant interest rate we have under a balanced budget that ≥ = T 0 in view of the balanced budget multiplier being at least 1. Thereby, the change in disposable income is −T ≥ 0. With infinitely lived Barro-style dynasties the situation is the same if the government instead of a balanced budget policy allows government debt temporarily to rise, thereby postponing the extra taxation. Then from the raised current disposable income the households just set aside extra savings in the same amount. So in both cases, with a constant interest rate the increased generates a rise in output at c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.5. Alternative monetary policy regimes 755 least as high as the increase in and, a fortiori, not less than the increase in T This amounts to a nonnegative change in current after-tax income, − T and thereby private consumption, tends to rise, if anything. So there is no crowding out of private consumption, but possibly crowding in. As is raised and monetary policy keeps the interest rate unchanged, also investment tends to be “crowded in” rather than “crowded out”. We conclude that introducing Barro-style dynasties in a Keynesian framework will not take away the expansionary effect of the increase in It will only make it smaller than otherwise. The spending multiplier is at least one in a situation with unemployment and abundant capacity. The quantitative importance of Ricardian non-equivalence is enhanced compared with a situation with full employment and full capacity utilization as in classical theory. There is the usual effect that taxing less now and more later increases aggregate private consumption now, because the current tax cut raises aftertax income of current tax payers who are aware that the set of future tax payers will partly include new people. In addition, current private beforetax income is raised because the rise in private consumption is not offset by lower investment, but tends to raise aggregate demand and production in the economy. The paradox of thrift An instructive special case of (19.30) is: = + + + ˜ − +1 ) + + with = 0 + 1 ( − T) − 2 ( − +1 ) + ( T = + 1 where 0 0 0 1 1 2 0 0 1 1 In addition to linearizing the consumption and tax revenue functions we have assumed a negligible influence of expected future output on consumption and investment. Under the interest rate targeting rule, the equilibrium condition, = , now yields = ˜ − +1 ) + + 0 − 1 − 2 ( − +1 ) + ( 1 − 1 (1 − 1 ) (19.54) Consider a negative demand shock ( 0). This leads to lower production and higher unemployment. Suppose people respond by prudence and attempt to save more, say by reducing 0 and/or 1 This worsens the incipient recession and the attempt at increasing saving is defeated. The reason is that the decreased propensity to consume lowers aggregate demand, thereby c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 756 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND reducing production. The resulting lower income brings aggregate consumption further down and so on through the renowned Keynes-Kahn multiplier process.23 Whereas consumption is reduced, aggregate private saving is not increased, in spite of the endeavours at the individual level to increase saving. Indeed, aggregate private saving is = − T − = − − T = + + − T (19.55) ˜ and remains unchanged because = (− +1 ) is unchanged for fixed What happens is only that income is reduced exactly as much as consumption. This is Keynes’ famous paradox of thrift. It is an example of a fallacy of composition, a term used by philosophers to denote the error of concluding from what is locally valid to what is globally valid. Such inference overlooks the possibility that when many agents act at the same time, the conditions framing each agent’s actions are affected. By allowing consumption and investment to depend on +1 as before, the paradox of thrift comes through in an even stronger form. In response to a decrease in 0 and/or 1 , aggregate private saving will go down, because on the right-hand side of (19.55) will go down. Digression: the loanable funds theory of the interest rate To Keynes’ conclusions that unemployment could be a state of rest and an increased propensity to save would make things worse, many of his contemporaries objected (for instance name, year) that the interest rate would adjust so as to bring the demand for new loans, coming from investors, in line with an increased supply of new loans, coming from savers. This is called the “loanable funds theory of the interest rate” according to which the interest rate is determined by “the supply and demand for saving”. The problem with this theory is that it does not take into account that the aggregate saving depends not only on the interest rate, but also on aggregate income (that the same could be said about investment is of no help for the theory). To clarify the issue, we consider the simplest possible case where = ( ) and = () 0 1 0 0 = = − (no expectational errors) and where government spending and taxation are ignored. Let denote aggregate saving. Then in our closed economy, = − = − ( ) ≡ ( ) = 1 − 0 = − 0 Equilibrium in the economy now requires ( ) = () 23 Keynes (1936, pp. 113 ff.) c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° (19.56) 19.5. Alternative monetary policy regimes 757 which may be interpreted as supply of saving being equilibrated with demand for saving. Conditional on a given income level, , we could draw an upwardsloping supply curve and a downward-sloping demand curve in the ( ) plane. But this would not determine since the position of the supply curve will depend on the endogenous variable, At least one extra equation is needed. This is what the money market equilibrium condition, = ( ) delivers, combined with the definition = − and exogeneity of and Indeed, (19.56) is nothing but an IS equation since by adding consumption on both sides of the equation, we get = ( ) + () And whether we combine the LM equation with this or with (19.56), the solution for the pair ( ) will be the same. A liquidity trap In case of a large adverse demand shock, the IS curve may be moved so much leftward in the IS-LM diagram that whatever the money supply, output will end up smaller than the natural level, Then the economy is in a liquidity trap: conventional monetary policy can not accomplish an equilibrium close to the natural rate. It is a trap in the sense that when the central bank strives to stimulate aggregate demand by lowering the interest rate through open market operations, it is like attempting to fill a leaking bucket with water. The phenomenon is illustrated in Fig. 19.11. The background is that the nominal interest rate has a lower bound, 0. An increase in can not bring below 0. Agents would prefer holding cash at zero interest rather than short-term bonds at negative interest. That is, equilibrium in the asset markets is then consistent with the “=” in the LM equation being replaced by “≥”. When an economy is at the zero lower bound, the spending multiplier tends to be relatively large for two reasons. The first reason is the more trivial one that being in a liquidity trap is a symptom of a serious deficient aggregate demand problem and low capacity utilization so that there is no hindrance for fast expansion of production. The second reason is that there will be no financial crowding-out effect of a fiscal stimulus as long as the central bank maintains its policy of attempting an interest rate as low as possible. Note that the economy can be in a liquidity trap, as we have defined it, before the zero lower bound on the nominal interest rate has been reached. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 758 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND i LM M ISe , ,G ,D P Yn , L Y Figure 19.11: A situation where the given IS curve is such that no non-negative nominal interest rate can generate full employment ( +1 and given). 19.5.3 A counter-cyclical interest rate rule Suppose the central bank conducts stabilization policy by using the countercyclical interest rate rule = 0 + 1 1 0 (19.57) where 0 and 1 are policy parameters and 0 if negative, is not so small that the zero bound for becomes topical under “normal circumstances”. This policy rule is “counter-cyclical” in the sense of being intended to dampen the deviations of from its trend. The policy is counter-cyclical although the interest rate behaves “pro-cyclically” in the terminology of business cycle econometrics where a variable is called pro- or counter-cyclical depending on whether its correlation with output is positive or negative, respectively. If the LM curve in Fig. 19.8 is made linear and its label changed into IRR (for Interest Rate Rule), that figure covers the interest rate rule (19.57). Instead of a LM curve, we have an upward sloping IRR curve. Both and are here endogenous. The fixed interest rate target from above is a limiting case of this interest rate rule, namely the case 1 = 0. But by having 1 0 the counter-cyclical interest rate rule yields qualitative effects more in line with those of a money targeting rule. If 1 | from (19.44), the stabilizing response of to a decrease in is even stronger than under the money targeting rule. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.6. Conclusion 759 Comparative statics Inserting (19.57) into (IS) gives = ( 0 + 1 − +1 ) + + By taking the differential on both sides we find 1 +1 1 1 = ∈ (0 ) 1 − − 1 1 − = 0 1 − − 1 = − 0 1 − − 1 = = 0 We see that all multipliers become become close to 0 if the reaction coefficient 1 is large enough. In particular, undesired fluctuations due to demand shocks are damped this way. The corresponding changes in are given as = 1 for = 1 +1 and respectively. From (19.53) we find the corresponding changes in as = ( + 1 ) for = 1 , and +1 ; finally, from (19.53) we have again = 0 19.5.4 Further aspects (unfinished) Extending the model with an interest rate spread (banks’ lending rate = + ) Empirics about spending multipliers and their dependence on the state of the economy. Refutation of Say’s law for an economy with many industries. 19.6 Conclusion The IS-LM framework is based on the presumption that for short-run analysis of effects of demand shocks in an industrialized economy it makes sense, as a first approximation, to treat the nominal price level as a predetermined variable. This approach may build on the assumption that the wage level is predetermined and that the marginal cost curve is horizontal. When this is combined with constant markups due to a more or less constant price c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 760 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND elasticity of demand at firm level, a price level which is independent of output in the short run follows. An alternative - or supplementary - rationale for the presumed price insensitiveness builds on the menu cost theory: the idea that there are fixed costs (pecuniary or non-pecuniary) associated with changing prices. The main theoretical insight of the menu cost theory is that even small menu costs can be enough to prevent firms from changing their price. This is because the opportunity cost of not changing price is only of second order, i.e., “small”; this is a reflection of the envelope theorem. So, nominal prices become sticky in the short run even if marginal costs, MC, are rising. But owing to imperfect competition (price MC ), the effect on aggregate output, employment, and welfare of not changing prices is of first order, i.e., “large”. Traditionally, the IS-LM model has been seen as only one building block of the more elaborate aggregate supply-aggregate demand (AS-AD) framework of many macroeconomic textbooks. In that framework the IS-LM model describes just the demand side of a larger model where the level of nominal wages is an exogenous constant in the short run, but the price level is endogenous. In this chapter we have interpreted the IS-LM model in another way, namely as an independent model in its own right, based on the approximation that both nominal wages and prices are predetermined in the short run; “fixed” means set in advance by agents operating in imperfectly competitive markets and being hesitant with regard to frequent or large price changes. Given the pre-set wages and prices, output and employment become fully demand-determined. Not prices on goods and services, but quantities are the equilibrating factors. This is a complete upside-down compared with the long-run theory of the previous chapters where output and employment were supply-driven − with absolute and relative prices as the equilibrating factors. Both theory and empirics support the view that when aggregate production is demand determined, the level of production and employment is significantly sensitive to fiscal and monetary policy. 19.7 Literature notes (incomplete) Further examinations of the role Walras’ law and refutation of Say’s law in macroeconomics are contained in Patinkin, D., 2008, Walras’ law, The New Palgrave Dictionary of Economics, 2nd edition, and Malinvaud, E., 1998, Macroeconomic Theory, Vol. B, Elsevier. The latter text gives a thorough account of macroeconomics with quantity rationing. c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 19.7. Literature notes 761 In the vocabulary of Walrasian economics, the term equilibrium is reserved to states where all markets clear unless the price in question is zero. On this background it may be a surprise that one may talk about “Keynesian equilibrium with unemployment”. This is an established terminology within “macroeconomics with quantity rationing”; and in Section 19.2 we explained what is meant by “equilibrium” in this context. There is an alternative terminology where a state of affairs with involuntary unemployment is called a disequilibrium. See for example Leijonhufvud, A. (1968), On Keynesian Economics and the Economics of Keynes, Oxford University Press, and Herings, J. J. (1996), Static and Dynamic Aspects of General Disequilibrium Theory, Kluwer. Although terminologies may differ, contributors to this field of macroeconomics (Patinkin, Clower, Benassy, Grandmont, Younès, Dreze, Malinvaud, Roberts, Böhm) seem to agree that the important aspects of the matter are the dynamic processes triggered by clearing and non-clearing markets. In the wake of the development of the “menu cost theory” by Akerlof and Yellen (1985a, 1985b) and Mankiw (1985), a path-breaking paper by Blanchard and Kiyotaki (1987) integrated (a) ideas from the quantity rationing framework, (b) price and wage setting by market participants with market power, and (c) the existence of menu costs in a general equilibrium model with monopolistic competition. We return to this model in Chapter 22. The IS-LM model was presented in a famous article by Hicks (1937) in an attempt to summarize the analytical content of Keynes’ General Theory of Employment, Interest and Money (1936). Keynes () approved the presentation. Of course Keynes’ book contained many additional ideas and there has subsequently been controversies about “what Keynes really meant” (see, e.g., Leijonhufvud 1968). But the IS-LM model has remained a cornerstone of mainstream short-run macroeconomics. The demand side of the large macro-econometric models which governments, financial institutions, and trade unions apply to predict macroeconomic evolution in the near future is built on the IS-LM model. Empirically the IS-LM model does a quite good job (see Gali 1992 and Rudebusch and Svensson 1998). At the theoretical level the IS-LM model has been criticized for being ad hoc, i.e., not derived from “primitives” (optimizing firms and households, given technology, preferences, budget constraints, and market structure). In recent years, however, more elaborate micro-founded versions of the IS-LM model have been provided (McCallum and Nelson 1999, Sims 2000, Dubey and Geanakoplos 2003, Walsh 2003, and Woodford 2003). Some of these “modernizations” are considered in later chapters. To be added: The case with investment goods industries with monopolistic competition: c Groth, Lecture notes in macroeconomics, (mimeo) 2013. ° 762 CHAPTER 19. THE THEORY OF EFFECTIVE DEMAND Kiyotaki, QJE 1987. Keynes 1937. Comparison between Keynes (1936) and Keynes (1939). Balanced budget multiplier: Haavelmo (1945). The natural range of unemployment: McDonald. Keynes and DeLong: Say’s law vs. the treasury view. 19.8 Appendix A. The envelope theorem ENVELOPE THEOREM FOR AN UNCONSTRAINED MAXIMUM Let = ( ) be a continuously differentiable function of two variables, of which one, , is conceived as a parameter and the other, as a control variable. Let () be a value of at which ( ) = 0, i.e., ( ()) = 0. Let () ≡ ( ()). Provided () is differentiable, 0 () = ( ()) where denotes the partial derivative of ( ) w.r.t. the first argument. Proof 0 () = ( ()) + = 0 by definition of (). ¤ ( ()) 0 () = ( ()), since ( ()) That is, when calculating the total derivative of a function w.r.t. a parameter and evaluating this derivative at an interior maximum w.r.t. a control variable, the envelope theorem allows us to ignore the terms that arise from the chain rule. This is also the case if we calculate the total derivative at an interior minimum.24 B. The opportunity cost of not changing price is of second order (no text yet available) 19.9 Exercises 24 For extensions and more rigorous framing of the envelope theorem, see for example Sydsaeter et al. (2006). c Groth, Lecture notes in macroeconomics, (mimeo) 2013. °