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Micro-based Dynamic Macroeconomic Models
14.12.2009.
Lecture note C
Christian Groth
A brief history of macroeconomics.
The menu cost theory
This lecture note contains a sketch of the history of macroeconomics since Keynes
and a sketch of one of the important microfoundations for the Keynesian assumption of
nominal price stickiness, the menu cost theory.
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From Keynes to new classicals to new Keynesians
John Maynard Keynes’ General Theory (1936) came out in the midst of the Great Depression. It was an attempt to come to grips with this economic catastrophe. And to
find out policies for its cure and prevention in the future. On the one hand Keynes’ book
revolutionized the way economists thought about the economy as a whole. On the other
hand, in many respects the analytical content of the book was incomplete.
Keynes’ American followers, such as Paul Samuelson, Lawrence Klein, Franco Modigliani,
Robert Solow, and James Tobin, were pragmatic and policy-oriented. Apart from incorporating a Phillips curve (linking price changes to the level of economic activity), they
seemed satisfied with the basic logic of Keynes’ theory. They viewed it as the relevant
point of departure for the study of the short run, in particular when excess capacity and
involuntary unemployment prevail (considered the normal state of affairs). The classical
(pre-Keynesian) theory, relying on market clearing through flexible prices, was conceived
applicable for the study of the long run or a state with sustained full employment. This
way of reconciling Keynes and the classics became known as the “neoclassical synthesis”
or the “neoclassical-Keynesian” synthesis. We stick to the last label, since nowadays “neoclassical” usually refers to supply-determined models with optimizing agents and flexible
prices.
The monetarists, lead by Milton Friedman, attacked the policy activism of Keynesianism on the grounds of time lags in implementation, uncertainty about the relevant
intervention, or mere government incompetence. The monetarists shared the notion that
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nominal rigidities are of importance for short run mechanisms, although in their view the
“short run” was shorter than believed by Keynesians. Of lasting influence was Friedman’s
emphatic claim that while there is usually a short-run trade-off between inflation and unemployment, there is no long-run trade-off.1 The reason is the endogeneity of inflation
expectations − in the long run it is impossible to fool rational people.
The new classical counter-revolution, started by Robert Lucas, Thomas Sargent, and
Neil Wallace in the early 1970s and later joined by Robert Barro and Edward Prescott,
rejected Keynesian thinking altogether and started afresh. Or rather, they revived the
classical or Walrasian line of thinking, emphasizing the equilibrating role of flexible prices
under perfect competition not only as long-run theory, but also as short-run theory. Lucas’
epoch-making contribution was the systematic incorporation of uncertainty and rational
expectations into macroeconomics. When combined with the hypothesis of market clearing by price adjustment, this gave rise to the “policy-ineffectiveness proposition” claiming
that systematic monetary policy designed to stabilize the economy is doomed to failure.
Regarding the explanation of business cycle fluctuations, there were two different strands
in this new classical approach. Lucas’ monetary misperception theory (Lucas 1972 and
1975) emphasized shocks to the money supply as the primary driving force. In contrast,
the real business cycle theory of Kydland and Prescott (1982) and Prescott (1986) views
economic fluctuations as primarily caused by shocks to real factors, “productivity shocks”.
Yet, the two strands were developed within the same type of stochastic modeling approach
with a Walrasian foundation.
Partly in response to the challenges from this new classical Macroeconomics, partly
independently, other economists in the 1970s and the 1980s took a different line of attack.
Their general conception was that the Keynesian approach, when extended by some sort of
an expectations-augmented Phillips curve, performed well empirically; money neutrality
seemed a good approximation to the long-run issues, but not to short-run issues, where
instead refinements of the Keynesian theory along several dimensions were in great need.
At the same time such refinements were now possible due to new analytical tools from
microeconomic general equilibrium theory and the rational expectations methodology.
We are here talking about a quite heterogeneous group of economists who are called new
Keynesians. Their endeavour became known as the new Keynesian reconstruction effort.
This and the next chapters describe key elements in this reconstruction.
The limitations of the old Keynesian theory addressed by the new Keynesians can be
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Friedman (1968). Almost simultaneously the same point had been made by the more Keynesian
oriented Edmund Phelps (1967, 1968).
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summarized in four points:
(1) It is not encompassed that nominal prices and wages do in fact change somewhat
over time in response to events in the economy.
(2) It is not made clear why nominal prices and wages change only sluggishly.
(3) The underlying microeconomics is not elucidated. What are the budget constraints
faced by the economic agents? How are demand and supply determined when some
agents have market power and are price setters? If markets do not clear by instantaneous adjustment of perfectly flexible prices, how do they then “clear” (reach
a state of balance)? What kind of general equilibrium arises under these circumstances, taking into account the spillovers across the different markets?
(4) The integration of forward-looking rational (unbiased) expectations into the theory
is only halfway. Shocks are treated in a peculiar (almost self-contradictory) way:
they can occur, but only as a complete surprise and a once-for-all event. Agents’
expectations never incorporates that new shocks can arrive.
Problem (3) was in fact taken up first, namely by the American economists Robert
Barro and Herschel Grossman (1971) and the French economists Jean-Pascal Benassy
(1975) and Edmond Malinvaud (1977). These contributions became known as “macroeconomics with quantity rationing”.2 With prices and wages predetermined in the short
run, the short side of the market determines the actual amount of transactions. This
is called the minimum transaction rule. And with price-setting firms and wage-setting
workers (or trade unions) facing downward-sloping demand curves, prices and wages are
generally set above the marginal cost of production and the marginal disutility of labor,
respectively. Thus, given the prevailing prices and wages, firms and workers are actually
happy to produce and sell more than expected. In this way aggregate output tends to be
demand-determined. At the same time the consumption demand by workers depends not
only on wages, prices, and initial resources, as in the Walrasian microeconomic theory,
but also on how much of their labor supply actually gets employed. In this way also
“quantity signals” play a role and in contrast to the Walrasian demand function we get a
so-called effective demand function.
In the first wave of “macroeconomics with quantity rationing” wages and prices were
treated as exogenous, which is of course not satisfactory. But a path-breaking paper
2
Barro later shifted to the new classical camp. His reasons are given in Barro (1979).
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on general equilibrium with monopolistic competition by Blanchard and Kiyotaki (1987)
made it possible to integrate the quantity rationing framework with price setting behavior.
At about the same time Akerlof and Yellen (1985) and Mankiw (1985) developed the
“menu cost theory”. Sluggishness in price adjustment caused by small “menu costs” can
at the aggregate level have large real effects. This became an important element in the
new Keynesian theory of nominal rigidities.
2
Menu costs
The classical theory of perfectly flexible wages and prices and neutrality of money seems
contradicted by overwhelming empirical evidence. At the theoretical level the theory
ignores that the dominant market form is not perfect competition. Wages and prices
are usually set by agents with market power. And there may be costs associated with
changing prices and wages. Here we consider such costs.
2.1
Two types of 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 convex adjustment costs, where the marginal price adjustment
cost is increasing in the size of the price change.
The most obvious examples of menu costs are of course costs associated with
1. remarking commodities with new price labels,
2. reprinting price lists and catalogues.
But the term menu costs should be interpreted in a much broader sense, including costs
of:
3. information-gathering,
4. recomputing optimal prices,
5. conveying the new directives to the sales force,
6. offending customers by frequent price changes,
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7. search for new customers willing to pay a higher price,
8. renegotiations.
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 7 and 8, may be
relevant also in the different labor markets.
When convex price adjustment costs are present, the situation is somewhat different.
Suppose, the price change cost for firm i is cit = αi (Pit − Pit−1 )2 , αi > 0. Then the firm
will want 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 on 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.3
Below we describe the role of the first kind of price adjustment costs, menu costs, in
more detail.
2.2
The menu cost theory
The menu cost theory originated almost simultaneously in Akerlof and Yellen (1985) and
Mankiw (1985). It is one of the microfoundations provided by new Keynesians for the
presumption that nominal prices and wages are sticky in the short run. For simplicity, here
we shall talk mostly about prices and price-setting firms. To summarize the important
theoretical insight of the menu cost theory: there are menu costs associated with changing
prices. Even small menu costs can be enough to prevent firms from changing their price
in response to a change in demand. 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 (see
Appendix). 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”.
2.2.1
Point of departure: imperfect competition with price setters
To understand what determines prices and their sometimes slow movement over time, we
need a theory with agents that set prices and decide when to change them and by how
3
For details in a macro context, see McDonald (1990).
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much. This brings agents with market power into the picture.4 That is why imperfect
competition is a key ingredient in new Keynesian economics. The challenge is to explain
the behavior of price-setting suppliers on the basis of their objectives and constraints.
We assume a market structure with monopolistic competition:
1. There is a given large number, n, of firms and equally many (horizontally) differentiated consumption goods.
2. Each firm supplies its own good on which it has a monopoly and which is an imperfect substitute for the other goods.
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, facing
a downward-sloping demand curve, chooses a price which maximizes the firm’s profits,
and then the firm adjusts output to the demand at that price. Or equivalently, facing a
downward-sloping demand curve, each firm chooses an output level which maximizes the
firm’s profits and then the firm sets its price accordingly. There is no elaborate strategic
interaction between the firms, and in that respect monopolistic competition is different
from oligopoly.
Sometimes a fourth property is included in the definition of monopolistic competition,
namely that each firm makes no profit. The interpretation is that there is a large set
of as yet unexploited possible differentiated goods, and that there is free entry and exit.
But here we consider entry and exit as costly and time consuming. In the short run the
number of active firms is thus given.
With respect to asset markets our framework corresponds to “The World’s Smallest
Macroeconomic Model” in Krugman (1999) in the sense that there are no bank-created
money and no other assets than base money, the supply of which at the beginning of
the current period is M. Thus, changes in the money supply can not be brought about
through open market operations since there are no other financial assets for the central
bank to buy or sell. Instead we have to imagine that a change in M occurs in the form
of a lump-sum “helicopter drop” at the beginning of the period.
4
Under perfect competition, nobody sets prices. (This is in fact a sign of a logical difficulty within
perfect competition theory. To assign the price setting role to abstract “market forces” or an abstract
omnipotent “Walrasian auctioneer” is not of much help.)
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2.2.2
A price setting firm i
Firm i has the production function
yi =
where
i
α
i,
0 < α < 1,
is labor input (physical capital is ignored). Thus,
the firm’s output is perceived by the firm as given by
µ ¶−ε e
Y
Pi
Pi
d
yi =
≡ D̃( , Y e ),
P
n
P
1/α
i
= yi . The demand, yid , for
(1)
ε > 1,
where Pi is the price set by the firm, P is the general price level, Y e is the expected level of
aggregate demand, and ε is the (absolute) price elasticity of demand. The interpretation
is that the firm faces a downward sloping demand curve the position of which is given by
the general level of demand.
Firm i chooses Pi with a view to the maximization of profit. The profit maximizing
quantity and price corresponds to the point where MR = MC, i.e., where marginal revenue
equals marginal cost. Symmetry is assumed and so, if firm i chooses its price Pi equal to
the “average” price, P, the firm expects its sales to equal the average real spending per
consumption good, Y e /n.
We assume there are no expectational errors and so Y e = Y, where Y is the actual level
of aggregate demand. As in “The World’s Smallest Macroeconomic Model” by Krugman
(1999), aggregate demand is proportional to the real money supply, i.e.,
Y e = γM/P,
where γ > 0 is a parameter reflecting consumers’ impatience. So (1) can be written
µ ¶−ε
Pi M
Pi
M
d
≡ D( , ),
ε > 1,
(2)
γ
yi =
P
nP
P P
cf. Fig. 1. (Note that along the vertical axis we have the relative price, Pi /P, and both
MR and MC are measured in real terms, i.e., relative to the general price level P.)
2.2.3
Even small menu costs can be operative
The nominal profit of firm i is
1/α
Πi = Pi yi − W yi
= Pi
µ
Pi
P
¶−ε
≡ Π(Pi , P, W, M ),
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M
−W
γ
nP
õ
Pi
P
¶−ε
M
γ
nP
!1/α
Pi
P
M
M'
and
given
P
P
i
1
W 1 /α
Yi
P
i
⎛ Pi M ' ⎞
,
⎟
⎝P P ⎠
D⎜
D ⎛⎜
Pi M ⎞
, ⎟
⎝P P ⎠
i
MC
MR
0
Y
i
Figure 1:
Suppose that initially, Pi = Pi∗ , where Pi∗ is the price that maximizes Πi , given P, W, and
M. Thus, maximum profit is
Π(Pi∗ , P, W, M ) ≡ Π∗i ,
Let the money supply shift to the new level M 0 > M through a lump-sum “helicopter
drop” at the beginning of the period. Suppose no other agents respond by changing price,
neither price setters nor wage setters. Will firm i in this situation have an incentive to
change its price? Not necessarily. The reason is that the menu cost may exceed the
opportunity cost associated with not changing price.
The opportunity cost to firm i of not changing price tends to be small because we have
dΠ ∗
∂Π ∗
∂Pi
∂Π ∗
(Pi , P, W, M)
(Pi , P, W, M ) =
+
(P , P, W, M)
dM
∂Pi
∂M ∂M i
∂Π ∗
=0+
(P , P, W, M ).
∂M i
(3)
The first term on the right-hand side of (3) vanishes at the profit maximum because
∂Π
(Pi∗ , P, W, M )
∂Pi
= 0, i.e., the profit curve is flat at the maximizing price Pi∗ . An illus-
tration is shown in Fig. 2. Moreover, since our thought experiment is one where P and
W remain unchanged, there in no indirect effect of the rise in M via P or W . Thus, only
the direct effect through the fourth argument of the profit function is left.
The result reflects a general principle, called the envelope theorem: in an interior
optimum, the total derivative of a maximized function wrt. a parameter is equal to the
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Πi Π( Pi , P,W , M ') Πi * Π(Pi , P,W , M ) Pi * Pi *' Pi Figure 2: The profit curve is flat at the top (P and W are fixed, M shifts to M 0 > M).
partial derivative wrt. that parameter;5 the relevant parameter here is the aggregate
money supply, M. Hence, the effect of a change in M 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 M, the profit of firm i is the same
whether or not the firm adjusts its price in response to the change in M.
For finite changes in M this is so only approximately. Indeed, given a finite change,
∆M, the opportunity cost of not changing price can be shown to be of “second order”,
i.e., proportional to (∆M/M)2 . This is a very small number, when |∆M/M| is small.
Therefore, in view of the menu cost, say c, it may be advantageous not to change price.
Indeed, the net gain (= c − 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
no change in the general price level in this equilibrium, a higher output level results.
2.2.4
A closer look at the labor market
The considerations above presuppose that workers do not immediately increase their wage
demands in response to the increased demand for labor. This assumption can be rationalized in two different ways. Either one can 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 an increase in
5
See Appendix.
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labor demand need not have any effect on the wage claims.
There is an alternative way of rationalizing absence of no immediate upward wage
pressure which is more apt in our case. This is because we have treated labor as homogeneous so that there is no basis for existence of many different craft unions. Instead we
simply assume there is involuntary unemployment in the labor market. By definition this
means that there are people around without a job but willing to take a job at the going
wage or even a lower wage. Such a situation is in fact what several labor market theories
tell us we should expect to often be present. Both efficiency wage theory, insider-outsider
theory, and collective bargaining theory imply that wages tend to be above the individual
reservation wage. Thus involuntary unemployment arises, hence employment can easily
change with negligible effect on the wage level in the short run.
2.2.5
Menu costs in action
We have thus seen that 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.
Let us return to Fig. 1 where this point is illustrated. For fixed M and P, the demand
curve faced by firm i is shown as the solid downward-sloping curve D(Pi /P, M/P ) to
which corresponds the marginal revenue curve, MR. For fixed P and W, the marginal
costs faced by the firm are shown as the upward-sloping marginal cost curve, MC (as
mentioned, MR and MC are measured in real terms, i.e., relative to the general price
level P ). Suppose that initially all prices are set optimally in accordance with the MR
= MC rule. Hence, MR = MC and Pi /P = 1 initially.
Consider a moderate shift in the money supply from M to M 0 > M. If there were no
menu costs, prices would increase and leave real money supply and output unchanged.
But when menu costs exist, it is possible that neither prices nor wages change. Then, the
higher nominal money supply translates into higher real money supply and the demand
curve is shifted to the right. As still Pi /P > MC, the firm willingly produces and sells
the extra output corresponding to the higher demand. The extra profit obtained this way
is marked by the hatched area in Fig. 1. In the other production lines the firms are in
the same situation and willingly increase output. As a result, aggregate output increases
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which translates into higher employment. The final outcome is higher 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 |∆M/M| .
In the real world, nominal aggregate demand (here proportional to money supply)
fluctuates up and down around some expected level. Sometimes the 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 (positively correlated with the money change) because the opportunity costs
by not adjusting prices are only of second order.
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Appendix
ENVELOPE THEOREM Let y = f (a, x) be a continuously differentiable function of two
variables, of which one, a, is conceived as a parameter. Let g(a) be a value of x at which
∂f
(a, x)
∂x
= 0, i.e.,
∂f
(a, g(a))
∂x
= 0. Let F (a) ≡ f (a, g(a)). Provided F (a) is differentiable,
F 0 (a) =
∂f
(a, g(a)),
∂a
where ∂f /∂a denotes the partial derivative of f (·) wrt. the first argument.
Proof
F 0 (a) =
∂f
(a, g(a))
∂a
+
∂f
(a, g(a))g 0 (a)
∂x
=
∂f
(a, g(a)),
∂a
since
∂f
(a, g(a))
∂x
= 0 by
definition of g(a). ¤
That is, when calculating the total derivative of a function at an interior maximum
wrt. a parameter, 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.6
6
For extensions and more rigorous framing of the envelope theorem, see for example Sydsaeter et al.
(2006).
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