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Transcript
Macro3 Manual Purpose of the Module This module expands on the material covered in the first two macro modules. This module differs from those in three ways. First, it incorporates “net exports” in GDP and the exchange rates that were ignored previously. Second, changes in prices and wages matter for aggregate demand and supply. This means you get to see reactions to policy changes in a more complex way, including how changes in prices and wages cause long run adjustment toward “full employment” real GDP. This module also incorporates supply and demand shocks, which can cause problems in addressing the ones in the initial conditions. Finally, you will be able to see how long run adjustment of prices and wages eventually lead to a full employment equilibrium, even without changes in policies. Nature of the Problem The basic macroeconomic problems of inflation and unemployment are no different in this module than in previous ones. However, in this module you will see that what effects your attempts to cope with those problems have on net exports and on the exchange rate (the price of the dollar in terms of the Euro). Further, you will only be able to control the nominal value of one of the policy tools, the money supply (just like the actual Federal Reserve System). This will make controlling short run fluctuations of unemployment and inflation more difficult. The Model This module is based on the Aggregate Supply-Aggregate Demand model. On the demand side, the determination of demand is discussed in terms of the four sectors of the economy, consumers, business, government, and net exports. In other words, if AD is aggregate demand, C is consumer demand, I is (business) investment demand, G is government demand for goods and services, and NX is (net) demand by foreigners: AD = C + I + G + NX To determine AD it is necessary to look at each of its components. Of course, in this module G is whatever you decide it should be. Consumption Consumer demand is affected by after tax income (real GDP minus taxes) and by the real rate of interest: C = a1 + a2 * (GDP – T) + a3 * Rate Where T is the total amount of taxes collected, Rate is the real rate of interest, a1, a2, and a3 are parameters. The underlying theory requires that a1 be non-negative (> 0) and in this module it is set at a1 = 10. Theory also requires that the response of consumption to variations in after tax in income be positive, but less that one (1 > a2 > 0) and in this module its value is set at 0.9 that is the “marginal propensity to consume”. In principle the relationship between the real rate of interest and consumer spending could be either positive or negative (or even zero), however decades of empirical research have led economists to conclude that the relationship is in fact negative. In this module the value of a3 is set at –25. Investment In reality many things affect investment behavior, but in this module the only influence is the real rate of interest. Investment demand in this module is: I = b1 + b2 * Rate Certainly b1 must be positive, and in the module b1 is set at 870. negatively related to the real rate of interest, and b2 is set at –75. Investment is Net Exports The determination of net exports involves determination of both exports and imports. In this module it is the price level that determines the level of export demand for this nations products. What is being implicitly assumed is that an increase in the nation’s price level implies a reduction in the ability of this country’s ability to compete in international markets. [If the exchange rates between this country’s currency and the currencies of its trading partners was strictly set according the model called “purchasing power parity” (PPP) a rise in the price level would always be offset by an equal drop in the exchange rate. However, in reality the PPP model does not fully explain the relationship between price levels and exchange rates, so price level changes do affect exports.] In this module imports are determined by the level of domestic GDP, the higher domestic income, the more imported goods are bought. The ratio between the change in imports and the change in income is often called the “marginal propensity to import.” With the domestic price level called “p,” in the module net exports are: NX = (c1 / p) – c2 * GDP Since c1 represents nominal exports, so c1 must be a positive number. However, real exports are c1 / p, so the higher the price level goes, the less this country will export. In the module the value of c1 is set at 10. Since the second term represents the nation’s imports, c2 is positive (higher GDP means more imports) and in the module the value of c2 is set at 0.01, so the “marginal propensity to import” is one percent. The Money Market The foregoing relationships would allow you to construct an aggregate demand curve, but one which depends only a little on the price level (just exports) and which does depend on the real rate of interest -- with no way to determine what that real rate was. In a previous module the real rate was set by the user as one of the policy tools. That is one way of viewing monetary policy. In this module the monetary policy tool is control over the nominal money supply (total number of dollars). However, the demand for money is a demand for purchasing power, so to find where the demand for money equals the supply of money, money supply has to be described in terms of purchasing power as well. If M is the nominal money supply, set by the user, the real money supply is M / p. The demand for money is affected by real income (GDP) and by the nominal rate of interest (Nrate). In this module, equilibrium in the market for money is found when: M /p = d1 + d2 * GDP + d3 * Nrate Parameter d1 is assumed to be positive (people would hold some money even if income and the nominal interest rate were zero) and in the module it is set at 15. As income rises the demand for money would also rise, since having more income means people will want to spend more (buy more) and that means -- somewhere along the line -- having the money to pay for what they buy. The module assumes that the money market is always in equilibrium, adjusting far more quickly than the markets for goods and services or the market for labor and other resources. [Warning: the demand for money is not a demand for income, economists generally assume people want unlimited incomes, but can’t get them. This is the demand for holding, at a moment in time, some of that income in the form of money -- cash, checking account balances, etc.] The relationship between income and the demand for money is described by d2, assumed to be equal to 0.025. In other words, every time income rises by $10, people want to hold another twenty-five cents in “money.” The relationship between the nominal rate of interest and the demand for money is negative. Think of the nominal rate of interest as the “opportunity cost” of holding money, instead of holding bonds or stocks or other assets that pay returns to their owners (cash obviously doesn’t pay interest, and neither do most checking accounts). The greater the opportunity cost of holding money (higher interest rates) the less money people want to hold. In the module this involves parameter d2, which is set at -0.95. Combining information from the money market with the information from the demand for goods and services, it is possible to describe aggregate demand as depending on the parameters, on government spending and taxes (fiscal policy), on the money supply (monetary policy), on the price level, and on expected inflation. Expected inflation gets into the picture because the demand for money depends on the nominal interest rate, not just the real interest rate. Real and Nominal Interest Rates The real interest rate is the increase in purchasing power you’d expect if you gave someone a loan, or the real cost to you, in terms of purchasing power, of paying back a loan if you borrowed from someone else. If you borrowed at 10% interest, so that for every $100 you borrowed you have to pay back $110 at the end of the year, your real interest rate depends on how much you expect prices to change over the year -- how much would you be able to buy with that $110 if you didn’t have to pay off the loan. If you expected prices to go up 10%, then the purchasing power of $110 at the end of the year is the same as the purchasing power of the $100 you borrowed at the start of the year -- and the real interest rate to you is 0, no cost at all. In other words the real rate is the nominal interest rate minus the expected inflation rate (0 = 10% - 10% in the example): Rate = Nominal Rate – Expected Inflation This is actually only an approximation; useful when real interest rates and expected inflation rates are relatively low. There is a more complex formula used when one or the other or both of these are high, but that more complex formula is not used in this module. Aggregate Supply Output is supplied by firms whose interests are in profits. If the prices for the goods firms sell rise compared to their costs, it will be profitable for firms to increase production. If the costs of resources rises relative to the prices of goods firms would have an incentive to reduce production. In this module the aggregate supply of goods and services is: AS = e1 – e2 * (wages / p) Wages are used in this relationship to describe the level of all resource costs (not a bad thing, since about 70% of all costs are labor costs in the US). As the price level rises toward infinity (relative to wages), the amount of goods supplied rises toward e1, which is 2500 in this module. If GDP is above the “full employment level” the value of e2 is set at 150.012, so if the wage and the price levels are equal to each other aggregate GDP supplied is e1 – e2, which is the “full employment long run equilibrium” in this module. If GDP is below the full employment level e1 and e2 have different values, so that the slope of the aggregate supply curve is much flatter for low output levels than for high output levels. The Tools Government Spending Government spending is set in real terms so the amount of goods the government gets does not depend on what happens to the price level. Since in this module the real rate of interest is not constant when you change government spending (holding taxes and the money supply constant), do not expect to see the full Keynesian multiplier effect of the spending change. There will be “crowding out” effects on investment and consumer spending. Taxes Taxes are also set in real terms, a change in the price level has no effect on the amount of purchasing power households and firms have to turn over to the government. Again, do not expect to see the full multiplier effects since real interest rates are not constant when you change taxes (holding government spending and the money supply constant). Money Supply You control the total nominal money supply, the number of dollars in the hands of the public. (This module takes no notice of the distinctions among the various types of money -- currency, checking account funds, etc.) You do not control the real money supply, which is the nominal money supply divided by the price level, because you do not control the price level. Your policy decisions do influence the price level, as they influence all the rest of the economy, but that isn’t the same as being able to simply set the price level. This distinction is one that faces monetary authorities in the real world as well, and limits their power. Aggregate Supply and Demand Graph The analysis of the model used can be done using a simple graph. Information about monetary and fiscal policy, and the behavior of consumers, investors, and international markets is summarized in the aggregate demand curve in Figure 1. The behavior of firms that produce output is summarized in the aggregate supply curve in that diagram. Figure 1 Aggregate Supply and Demand (short run) P AS P1 P0 AD1 AD0 GDP0 GDP1 GDPFE GDP In Figure 1, AD0 represents original aggregate demand (in a recession), while AD1 represents the impact of expansionary monetary and/or fiscal policy, or the impact of a non-policy expansionary shock. Both combinations (P0 and GDP0) and (P1 and GDP1) represent short run equilibrium positions. Any long run equilibrium would have to occur at the level of GDP labeled GDPFE, the full employment level of real output. Starting with either AD0 or AD1, in the long run adjustments of the real wage to its long run equilibrium level will induce shifts in the supply curve so that equilibrium will be reached at GDPFE, the only difference, in terms of this graph, will be the price level at long run equilibrium. The process of adjustment in the long run involves the way wages eventually catch up with prices. If demand increases, in the demand for goods and services prices rise relative to costs (wages) in the short run, which is why output increases. However, this increases demand for labor and, while the labor market adjusts more slowly than the market for goods and services, after awhile the increased demand for labor means that wages rise (for a given current price level). As a result the profit maximizing output for firms at the given price level decreases -- a shift to the left in the short run AS. This is illustrated in Figure 2. Figure 2 Long Run Equilibrium P AS1 P1 AS0 P0 AD1 AD0 GDPFE In Figure 2, AS0 is the aggregate supply curve that will result if for some reason aggregate demand is at AD0, while AS1 is the short run supply curve after the full adjustment to a shift in aggregate demand to AD1. With high aggregate demand (AD1), in the long run the economy winds up with a high price level P 1 (and high money wages) but with real output at GDPFE. With “low” aggregate demand (AD0) the economy winds up in the long run with a low price level P0 (and low money wages) -- and the same real GDP, GDPFE. If a disturbance caused a shift in aggregate supply the adjustment process still leads to a long run equilibrium at GDPFE, as long as the disturbance did not change the economy’s capacity to produce. Only a change in capacity causes the value of GDPFE to change, and changes the long run equilibrium in this model. The kinds of disturbances and policies used in this module cannot affect capacity, and cannot affect GDPFE. Running the Module When you begin the module you have to choose whether your economy will start off in an inflationary period or in a recession. Whichever way you start off, you will be shown the initial conditions the levels of real GDP, inflation, unemployment, etc. When you begin to control your society you can leave the values of the three tools at their initial default values and see the results, but if you do, all you will see is the initial conditions already presented. Alternatively, you can change one or more of the three tools (government spending, taxes, and the money supply) to try to fix the existing problem. Since at first you will not know how much effect each tool will have on each of the various aspects of the economy, it is best if you change only one tool at a time. For example, if the economy is in an inflation you could note the initial conditions, then cut government spending from its default level and see the results. (At this point you need to click on “No Shock” on the tool bar to get results if the economy has NOT experiences either a demand shock or a supply shock.) When you get the short run results the options on the tool bar will have changed and if you wish you can click on “No Shock Long Run” to see the long run effects of your policies. Then try “new policy” – which resets everything – and leave government spending at its default value while increasing taxes. Finally, try “new policy” again and, leaving government spending and taxes at their default values, reduce the money supply. To see what the long run equilibrium is like, click on “long run” and you will get the values the economy will eventually arrive at without your help. Then you can try to get it to similar values without waiting for the long run to arrive (the long run does assume the default values for government spending and taxes, so if you change those you can’t get exactly the same results for all aspects of the economy). Once you have explored these aspects of the module, you can see what happens to your initial conditions when the economy is further disturbed by a “shock.” A shock is an unpredicted disturbance that shifts either AD or AS and in this module you can choose to either cause a shock to demand or to supply. (Click on “Demand Shock” or “Supply Shock.”) In the real world there are many possible sources of shocks to both sides of the market, in this module there is one type of shock to each. On the demand side, the shock is a sudden change in the expected rate of inflation. In the basic model people expect an inflation rate of 0.01% (in other words, virtually no inflation. If you pick the demand shock, there will be a significant change in that expectation and you can see what effect that has by clicking on “results.” After you see the immediate effects of the shock you may want to click on the new option “Demand Shock Long Run” to see the eventual effects of the shock and of your policies. On the supply side the shock changes the parameter e2 (an example of this type of shock would be a change in the tax code so that employers no longer pay a Social Security tax - though other taxes have to be raised so total tax collections don’t change). Again, to see the impact of this type of shift in the short term, click on “results.” To see the long run effects, click on “long run.” Mathematical Model Short Run Most of the underlying equations for this module were shown in the “model” section, with explanations of the parameters and their meanings. Those equations will just be repeated here, beginning with the ones related to aggregate demand: 1) AD = GDP = C + I + G + NX 2) C = a1 + a2 * (GDP – T) + a3 * Rate 3) I = b1 + b2 * Rate 4) NX = (c1 / p) + c2 * GDP Combining equations (1) through (4), and solving for GDP: Let: 5) AA1 = {[(a1 + b1 + (c1/p)] / [1 – a2 – c2]} AA2 = {[a3 + b2] / [1 – a2 + c2]} AA3 = {1 / [1 - a2 + c2]} GDP = AA1 + AA2 * Rate + AA3 * [G – a2 * T] Since (5) depends on the real interest rate we need to combine it with the money market information in (6): 6) M / p = d1 + d2* GDP + d3 * Nrate Since the nominal rate is the real rate plus expected inflation, (6) can be re-written (EDP is the expected rate of inflation) as: a) M / p = d1 + d2 * GDP + d3 * [Rate + EDP] Combining (5) and (6a) and solving for the real interest rate: 7) Rate = aa1 + (aa2 * M / p) + (aa3 * EDP) + (aa4 * (G - (a2 * T))) + (aa5 / p) Where: den = (((b2 + a3) / (1 - a2 + c2)) + (d3 / d2)) aa1 = - ((d1 / d2) + ((a1 + b1 + cc1/p) / (1 - a2 + c2))) / den aa2 = (1 / d2) / den aa3 = - (d3 / d2) / den aa4 = (-1 / (1 - a2 + c2)) / den aa5 = c1 * aa4 Equation (7) does not depend on anything except the parameters of the original equations, the policy tools you enter, and the price level. Taking the solution for Rate in (7) and using it to substitute for Rate in (5), then simplifying: 8) GDP = bb1 + bb2 * M/p + bb3 * EDP + bb4 * (G – a2* T) + bb5 * (1/p) Where: bb1 = - ((d1 / d2) + ((d3 / d2) * aa1)) bb2 = (1 / d2) * ((b2 + a3) / (1 - a2 + c2)) / den bb3 = - (d3 / d2) * ((b2 + a3) / (1 - a2 + c2)) / den bb4 = (d3 / d2) * (1 / (1 - a2 + c2)) / den bb5 = - (d3 / d2) * aa5 Equation (8) has GDP (demanded) depending on parameters, the expected inflation rate, the policy tools you control, and the price level. The aggregate supply equation in this module is: 9) AS = GDP = e1 - e2 * (wage / p) In (9) e1 (at or above full employment) is 2500, e2 is 150.012, so if the real wage (wage/p) is 1, GDP supplied is about 2350. In this module that is full employment output. (Having p = 1 and wage = 1 means you are at the original equilibrium, wage and price values are measured relative to the original equilibrium values—these are wage and price indices not dollar values.) Note that because of the minus sign in front of e2, the higher the price level compared to the wage rate, the higher the level of GDP supplied. As the real wage falls toward zero, output rises toward 2500 that is its maximum value (not its equilibrium value—long or short run). The AS equation has GDP (supplied) depending on the parameters, the wage rate, and the price level. In equilibrium AS must equal AD, so if we equate GDP from (8) with GDP from (9) we can solve for the (short term) equilibrium price level as a function of the parameters, the current wage rate, expected inflation, and the policy tools: 10) p = [bb2 * M – e2 * wage + bb5] / [(e1 – bb1) – (bb3 * EDP) – (bb4 * (G – a2 * T)] In the short run the price level is determined by (10) because the wage rate stays constant in the short run. Substituting (10) for the price level in (9) gives a solution for (short run) equilibrium GDP: 11) GDP = e1 + (e2 * wage) / [bb2 * M – e2 * wage + bb5] / [(e1–bb1) – (bb3 * EDP) – (bb4 * (G – a2 * T)] Since (11), (10), and (7) in combination determine everything that goes into the consumption, investment, and net export values, the components of GDP can be obtained by using these equilibrium values and substituting into (2), (3) and (4) respectively. All that is left for the short run is to determine the unemployment, inflation and exchange rates. The inflation rate is quite simple to obtain. The price level starts at 1, of course, the new price level is obtained from (10) and the inflation rate is: 12) Inflation = (p0 – p1) / p0 Where p0 is the original price level (1) and p1 is the price level obtained in (10). The unemployment rate is determined by an equation adapted from Okun’s law, so in this module the unemployment rate is: 13) Unemployment = 0.05 - (0.001 * (GDP - 2350.37)) If GDP is at its long run equilibrium value (full employment), then the unemployment rate is at 0.05, or 5%. The exchange rate is determined by supply and demand for the nations currency. In other words this is a perfectly flexible exchange rate system, with no direct government intervention in the exchange market. In this module part of the market is derived from the balance of trade (Net exports) that depends on the domestic price level and on domestic GDP. [Purely foreign influences, such as foreign GDP, are held constant.] The exchange market also depends on international capital flows, so (other things constant) it depends on the level of domestic interest rates compared to foreign rates. Strictly, the exchange rate would depend on the differences between domestic and foreign interest rates and on the comparison between domestic and foreign price levels. However, only the domestic values are variable in this module. 14) Exchange = (0.9 + (0.02 * (Rate - 4.237))) / p If the domestic interest rate equals the foreign rate (4.237%) and the price level is at its original value of 1, the exchange rate is 0.9 Euros equals $1. Long Run The difference between the long and short run in this model is that in the long run the wage rate changes if the economy is not at the long run equilibrium. Over time the wage will adjust in response to price level changes, and if productivity conditions meant that there was a long run equilibrium with the wage price ratio equal to 1, the new wage price ratio will return to 1 in the long run. If the price level rose in the short run, encouraging output supplied at the original wage to rise, in the long run the wage rises by an equal proportion, returning the ratio to 1. That means long run output is determined by the supply equation (9). Meanwhile the price level can be determined from (10) with the added information that the wage level is equal to the price level. The revised long run price equation is: 15) p = [bb2 * M + bb5] / [e2 + (e1 – bb1) – (bb3 * EDP) – (bb4 * (G – a2 * T)] Given the statement about the equality of the wage and price levels in the long run equilibrium, (15) also determined the wage rate. The real rate of interest (Rate) can be determined from (7), then the components of GDP can be resolved from their original equations (2), (3), and (4). The long run equilibrium in this module is similar to the one predicted by the quantity equation: p* real GDP = v * M where v is the velocity of money. In the long run real GDP is at its equilibrium full employment value, if the velocity of money is back to its original equilibrium value, the price level changes by the same proportion as any change in the money supply. Indeed, for any given change in the money supply, with government spending and taxes constant, there is an equi-proportional change in the price level and the money supply. However, since the demand for money depends on interest rates, and government spending and taxes can affect interest rates even in the long run, changes in fiscal variables can affect the price level in the long run. The long run value of real GDP cannot be affected by these variables because they do not affect aggregate supply, in the long run the changes in prices are offset by the changes in money wages, so long run output cannot depend on these aspects of demand.