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Chapter 12
New Keynesian Economics
The two current leading views of business cycles are Real Business Cycle (RBC) Theory
and New Keynesian Economics. Each of these schools of thought has a rich history
marked by frequent vigorous debate between them. While a terse summary of their
general views does not do them justice, we first briefly highlight the main difference
between the two points of view. RBC Theory views periodic expansions and recessions
as natural, indeed efficient, responses of the economy to the ups and downs of the state of
“technology” of the economy.72 As such, recessions are not dire events for the economy,
but rather natural slowdowns which are preceded by an expansion and which will again
be followed by future expansions. In terms familiar from microeconomics, pure RBC
Theory maintains that the aggregate economy operates perfectly competitively on both
the demand side and the supply side. 73 An important implication of RBC Theory,
therefore, is that the government has no role to play in the macroeconomy – that is,
neither fiscal policy nor monetary policy can be used to improve the macroeconomic
condition. In contrast, New Keynesian Economics adopts the point of view that there are
fundamental market failures in the aggregate economy which render business cycle
fluctuations, specifically periods of lower-than-potential GDP, inefficient. 74 The
important implication of this point of view is that the government may indeed have a role
to play in improving macroeconomic conditions.
Here we will consider just one strand of New Keynesian theory. As we will see,
microeconomic analysis is at the heart of New Keynesian theory. Unlike most of our
discussion of representative-agent macroeconomics, however, the focus of New
Keynesian theory is not on the microeconomics of consumer behavior but rather on the
microeconomics of firm behavior.
72
“Technology” here is broadly defined – specifically, the Solow Residual (on which we will have more to
say when we study RBC theory) is the most often-used measure of technology.
73
Even the most ardent RBC macroeconomist does not literally believe the economy is perfectly
competitive in the pure textbook sense, but rather that in aggregate market failures tend not to be so
catastrophic as to make perfect competition a terrible approximation.
74
The notion of “efficiency” you should have in mind throughout our discussion here is exactly that from
microeconomics: a market (in our case, the entire macroeconomy) is operating efficiently if there is no
deadweight loss, which means that no trades between suppliers and demanders which could increase
overall utility go unconsummated. Another familiar characterization of economic efficiency is that price
equals marginal cost.
Spring 2014 | © Sanjay K. Chugh
163
Differentiated Goods and the Consumption Aggregator
In our study of the representative consumer, we supposed that there was only one object
(i.e., “all stuff”) which the consumer purchased in order to obtain utility. This was true in
both the consumption-leisure model (in which there was literally only one object called
“all stuff” which the consumer could purchase) as well as the consumption-savings model
(in which there was one object called “all stuff” in each of the two periods of the
economy which the consumer could purchase).
The use of a single consumption good is obviously a theoretical simplification. In reality,
consumers purchase a vast number of goods and services from which they obtain utility.
And in reality, these goods are somewhat substitutable for each other. For example,
when making your decision about where to spend your Saturday evening, you may decide
to go to the movies or go to a Mets game. Both options are forms of entertainment, but
clearly they are not perfect substitutes for each other. Even if you decide to go to the
movies, you will have to choose between the latest Harry Potter movie and the newest
action thriller – clearly these two movies are also imperfect substitutes for each other.
If we believe that there are a great many options for consumption, each of which is at
least a little different from every other option, available, then one way to reconcile our
previous use of a single consumption good with this fact is to suppose that “all stuff” is
composed of these great many differentiated goods. Specifically, we will now suppose
that our usual notion of “all stuff” consumption is a function,
c ? c ? c1 , c 2 , c3 ,…, c N ?
(2)
where c denotes the type-1 consumption good (perhaps a movie), c denotes the type-2
3
consumption good (perhaps a Mets game), c is the type-3 consumption good (perhaps
dinner at a fancy restaurant), etc. If there are N different goods, then we have that “all
stuff” consumption is a function of the N different types of consumption goods.
1
2
Note that we have written this function – formally called the consumption aggregator
function – in abstract form. Especially note that we do not necessarily mean the simple
1
2
3
N
sum c ? c ? c ? c ? … ? c . In fact, in theoretical New Keynesian models, the function
c ? ? ? is usually assumed to satisfy the following two properties: the first partial
derivative with respect to consumption of good type i satisfies
? ? ?0
?c ?
(3)
?ci
and the second partial derivative with respect to consumption of good type i satisfies
Spring 2014 | © Sanjay K. Chugh
164
? ? ?0
?2c ?
? ?
? ci
(4).
2
These two conditions state, respectively, that total consumption c is an increasing
function of consumption of type i and that total consumption c increases at an everdecreasing rate as consumption of type i increases. Think of this simply as (if you’re a
movie-buff) the more movies you see, the more total consumption (not just of movies but
of “all stuff”) you enjoy – but the more and more movies you see, the less and less extra
total consumption you gain. These properties should remind you of the general
properties we imposed on the representative consumer’s utility function – note well,
however, that the consumption aggregator function is not a utility function. Indeed, the
utility function still takes total consumption c as an argument and continues to have the
usual properties we have discussed at length. It is still utility, and not consumption, that
is the maximization goal of the representative consumer. A very common functional
form assumed for the consumption aggregator in New Keynesian models is
?
1/ ?
1/ ?
1/ ?
1/ ?
c(c1, c2 , c3 ,…, c N ) ? ??? c1 ? ? ? c2 ? ? ? c3 ? ? … ? ? c N ? ?? ,
?
?
(5)
where ? ? 1 . The value ? (the Greek letter “epsilon”) has very important economic
meaning in these kinds of New Keynesian models. It governs how substitutable, from the
point of view of the consumer, the different goods are for each other. At one extreme is
the value ? ? 1 , which, when substituted into the above expression, yields the simple sum
c1 ? c2 ? c3 ? … ? cN . With ? ? 1 , each consumption good is just as good as any other
from the point of view of the representative consumer – that is, the goods are perfect
substitutes for each other. With ? ? 1 , however, goods are only imperfect substitutes for
each other, meaning that they are differentiated to a degree depending on the exact value
of ? . A basis for all of New Keynesian economics is the assumption that ? ? 1 .
Monopolistically Competitive Firms
The heart of New Keynesian Economics lies not in the representative consumer, but
rather with firms. Each of the N differentiated goods is assumed to be produced by a
distinct monopolistically competitive firm. Recall from basic microeconomics that a
fundamental feature of monopolistic competition is that goods are similar to each other
but not completely identical. Continuing the example from above, movies and baseball
games are similar goods (forms of entertainment) but obviously not identical.
Spring 2014 | © Sanjay K. Chugh
165
Pi
Also recall from basic microeconomics that a firm that produces a differentiated good
possesses market power. In terms of analysis that should be familiar, this market power
manifests itself in the fact that the firm faces a downward-sloping demand curve and
hence a marginal revenue curve that lies strictly below its demand curve. This in turn
implies that the firm’s profit-maximizing choice features price greater than marginal cost
i
i
– algebraically, P ? MC , where P i denotes the nominal profit-maximizing price of the
i
firm that produces good i and MC is the nominal marginal cost at the profitmaximizing quantity. These features are summarized in Figure 58.
MC
MR
Demand
for good i
ci
Figure 58. A monopolistically competitive firm faces a downward-sloping demand curve for its product.
The marginal revenue curve thus lies strictly below the demand curve, and the firm’s profit-maximizing
choice of output occurs where MR = MC. At this optimal quantity, price exceeds marginal cost.
Recall from expression (5) above that ? ? 1 in the consumption aggregator implies that
the goods are perfect substitutes for each other. The implication for firms of ? ? 1 is that
they do not have any market power (and thus face perfectly elastic demand curves).
Thus, setting ? ? 1 (in New Keynesian models that use this channel to introduce market
failures) is one way of “shutting off” the New Keynesian elements of a New Keynesian
model.
For the remainder of our discussion, we will assume that N ? 2 for simplicity, so that the
representative consumer’s total consumption is a function of two differentiated goods,
each of which is produced by a distinct firm. Also, we assume ? ? 1 (strictly), except
where noted to highlight some issues, so that the model we are considering is indeed a
New Keynesian model.
Spring 2014 | © Sanjay K. Chugh
166
The Aggregate Price Level
In our simple models which featured only one homogenous consumption good, the
nominal price level of the economy was a simple object – it was just the nominal price of
the single consumption good. In our New Keynesian model here, however, even
specializing to the case of just N ? 2 differentiated goods renders the nominal price level
of the economy a somewhat more complicated notion to consider. Clearly the aggregate
price level, which we will denote by P , should depend somehow on the nominal prices
of the two distinct goods, which we denote by P 1 and P 2 . That is, P is some function
of P 1 and P 2 . There are many possible ways of aggregating the individual prices into a
single measure of the price level of the economy. We will refrain from putting a
particular functional form on this price-level aggregator (even though New Keynesian
models offer a great many from which to choose) and simply use the abstract function
P ? P( P1 , P 2 ) .
(6)
To re-emphasize, the unsuperscripted P denotes the nominal price level of the economy
(the price of a “market basket” of goods) while P 1 and P 2 denote, respectively, the
nominal prices of good type 1 and good type 2. For our purposes the important feature of
this function is that P is strictly increasing in each of its arguments. In calculus notation,
this means
?P ? ? ?
?0
?P1
(7)
?P ? ? ?
? 0.
?P 2
(8)
and
The assumption that the price level P is strictly increasing in each of the individual
prices should strike you as reasonable. To draw an analogy with the Consumer Price
Index (CPI), if the price of any of the goods in the CPI basket rises, the aggregate price
level rises even though the relationship between the CPI and the individual price is
usually not a straightforward one. Similarly here in our New Keynesian model, the
functional relationship between the price of any individual good and the aggregate price
level is in general a complicated one, but the aggregate price level depends positively on
each individual price in the basket.
Spring 2014 | © Sanjay K. Chugh
167
Aggregate Consumption Demand
Each of the two firms (in our case where we have specialized to N ? 2 ) faces a
downward-sloping demand curve for its product. Because there is more than one good,
we now need to define aggregate consumption demand. A simple definition of aggregate
consumption demand may seem to be that aggregate consumption demand is the sum of
the demands for each of the differentiated products. Graphically, this latter would mean
that aggregate consumption demand is the “horizontal summation” of each individual
good’s demand curve. 75 However, such a procedure would be incorrect in our New
Keynesian model.
Horizontal summation of demand curves is incorrect here because goods that are different
cannot be summed. For example if we have 20 apples and 10 bananas, we have – well,
20 apples and 10 bananas. That is, they inherently cannot be summed because they are
different objects. 76 More fundamentally, such a procedure turns out to approach the
problem of constructing the aggregate consumption demand from the wrong point of
view. Recall in our study of the consumption-leisure model that we derived the
(aggregate) consumption demand function. This consumption demand function remains
the correct notion of consumption demand, because it is total consumption, which in turn
is the consumption aggregator, which still is the direct argument of the representative
consumer’s utility function.
P
P2
P1
The consumption aggregator then shows the relationship between aggregate consumption
demand and demand for each of the differentiated goods. Recall from above that total
consumption (the “all stuff” object) is an increasing function of each type of
differentiated consumption good. This fact is all we need to conclude that there is a
positive relationship between total consumption and consumption of each differentiated
good. We thus diagram the relationship between the demand for the two goods and
aggregate consumption demand in Figure 59.
MC
MR
MC
Demand
for good 1
c1
MR
Demand
for good 2
c2
Aggregate
Consumption
Demand
c
75
This notion of horizontally summing demand curves should be familiar to you from microeconomics.
We could then define the term “fruit” to be either a banana or an apple, and assume the conversion one
apple = one fruit and one banana = one fruit. With these assumptions (which notice probably come very
naturally to you as you think about this example), we would then say we have 30 pieces of fruit.
76
Spring 2014 | © Sanjay K. Chugh
168
Figure 59. There is a positive relationship between aggregate consumption demand and demand for each
differentiated good. Aggregate consumption demand is derived by using the consumption-leisure model.
The way we will interpret the relationship depicted in Figure 59 is the following: when
some event (the usual events are preference shocks and government policy) shifts the
consumption demand function, the demand functions facing the two individual firms also
shift in the same direction. Because the individual firms’ demand functions shift, the
associated marginal revenue functions shift as well, implying a new profit-maximizing
choice of price and quantity for each individual firm.77
To preview the comparison of New Keynesian theory and RBC theory we will make after
studying both points of view, notice that the exogenous event – that is, the “unexplained”
event, or shock – that begins the thought experiment is a shift in a component of demand
(here, consumption). New Keynesian theory holds that “demand shocks,” coupled with
the rest of the theoretical apparatus we are describing in this chapter, are the predominant
factor that causes macroeconomic fluctuations. In contrast, RBC theory holds that it is
“supply shocks” that are the predominant source of macroeconomic fluctuations.
Staggered Price-Setting
Consider the case in which the consumption demand function shifts outwards for some
reason. As just described, this event in turn causes the demand functions, and hence the
associated marginal revenue functions, facing each individual firm to shift outwards as
well. Assuming the marginal cost functions do not shift, these events imply new profitmaximizing choices of price and quantity for each of the two firms in Figure 59. In
i
particular, both quantity c and price P i rise.78 Because the price of each good rises,
clearly the aggregate price level P rises because of the properties of the price-level
aggregator we described above.
However, suppose instead that only one of the two firms can change its price at the time
of the event that shifts the aggregate consumption demand curve. Let’s suppose it is firm
2
2 (the firm that produces consumption good c ) that has the ability to change price. Firm
1
1 (the firm that produces consumption good c ), on the other hand, cannot change its
price at all. The situation facing firm 1 is illustrated in Figure 60.
77
78
Convince yourself of this last point by diagramming it.
Again, diagram it to convince yourself.
Spring 2014 | © Sanjay K. Chugh
169
P1
Optimal P1 if no price
stickiness
MC
Initial optimal P1
Initial
MR
New
MR
Initial
demand
for good 1
New
demand
for good 1
c1
Initial
optimal c1
c1 with price
stickiness
Figure 60. After a shift outwards of the consumption demand function, the demand function facing firm 1
and hence firm 1’s marginal revenue function both shift outwards. If firm 1 could change its price, it
would raise both its price and quantity produced because the new MR function intersects the MC function
at a higher quantity. Associated with such a price increase is a rise in the quantity produced. However, if
firm 1 continues with its initial optimal price, then the quantity of good 1 that it produces rises by even
more, as can be read off the new demand function.
Figure 60 shows the events facing firm 1 following a rise in consumption demand. Firm
1’s demand function and marginal revenue function both shift outwards. If Firm 1 were
to change its price, it would choose the price labeled “optimal P 1 if no price stickiness”
because that price yields the quantity at which marginal cost equals marginal revenue.
We can see from the diagram that quantity produced would rise. However, if firm 1 does
not change its price and is forced to continue using the initial optimal P 1 , then its
quantity produced will rise by even more, as can be read off the new demand function.
Firm 2 is assumed to be able to change its price immediately. It thus faces a similar
situation as firm 1, except it will raise its price P 2 . Consequently, its quantity produced
also rises, but by less than it would if were also unable to change its price.
Spring 2014 | © Sanjay K. Chugh
170
Implications for Government Policy
Now we consider how the macroeconomic effects of policy differ depending on whether
or not firm 1 is able to change its price. First consider the case where firm 1 can change
its price. We can conclude that the aggregate price level P rises because the aggregate
price level is an increasing function of both P 1 and P 2 . Because both P 1 and P 2 rise,
P clearly rises. On the other hand, suppose firm 2 can raise its price but firm 1 does not
raise its price. In this case, P 2 still rises by the same amount as in the case that firm 1
could change its price because firm 2’s decisions do not depend on firm 1’s actions.79
However, because P 1 does not change, the aggregate price level P does not rise by as
much as in the case that firm 1 did change its price. Simultaneously, overall consumption
c rises by more with firm 1’s price held constant because c1 rises by more in this case.
In the preceding conclusion lies the important implications of New Keynesian theory for
government policy. In the presence of staggered price-setting, government policy that
raises aggregate consumption demand generates less inflation and a larger increase in
production than the same government policy in the absence of staggered price-setting.
Thus, staggered price-setting gives economic policy-makers leverage over real quantities
in the economy, more leverage than they would have if all firms could adjust prices
simultaneously.
Critique of New Keynesian Theory
A long-standing criticism of the strand of New Keynesian Theory that we have developed
is the assumption of staggered price-setting. In particular, we have offered no
explanation why some subset of firms cannot or does not change its price in the face of
an increase in its demand while some other subset does change its price.
One common justification given for staggered price-setting is the presence of
asynchronous menu costs. Recall that menu costs are the costs incurred by a firm simply
by the act of changing prices.80 If different sectors of the economy experience menus
costs of different magnitudes at different times during the business cycle, then staggered
price-setting may arise. For example, perhaps it is easier (i.e., less costly) for militaryequipment producers to raise their prices during war time than it is for producers of
entertainment simply because of the political and/or cultural environment of the time.
This example suggests that “menu costs” need not be interpreted as only direct costs of
changing prices but also can include more intangible costs such as lost goodwill, etc.
While there is little empirical evidence suggesting the magnitude of these intangible
menu costs, it is at least a plausible story.
79
That is, there are no game-theoretic interactions here.
The terminology itself implies its meaning: a restaurant that wants to change its prices must print new
menus, which itself has a cost associated with it.
80
Spring 2014 | © Sanjay K. Chugh
171
At a more realistic level, it does seem true that firms do not all change prices
simultaneously. If we accept this, then staggered price-setting seems less strange of an
assumption and perhaps we can accept not having a stronger microeconomic foundation
for it.
Finally, strong empirical support for the New Keynesian view comes from data that
suggest that government policy, both fiscal and monetary, does have important short-run
effects on output. Data generally support the view that government policy is more
effective than real business cycle (RBC) theory predicts. This last observation alone may
be enough justification for studying New Keynesian theory – and indeed, the debate
between the RBC view and the New Keynesian view has been one of the most vigorous
areas of debate in macroeconomics over the past few years.
Spring 2014 | © Sanjay K. Chugh
172
Appendix: Theories of Price Stickiness
During the normal ups and downs of the economy (termed “business cycles,” a topic
which is usually in the domain of macroeconomics), demand tends to fluctuate – even
demand for broadly-defined categories of goods. In terms of a supply and demand
diagram, this means the demand curve shifts in and out during the “normal” course of
economic events. We will consider “good economic times” to be periods of relatively
high economy-wide income and “bad economic times” to be periods of relatively low
economy-wide income. If we further adopt the simplifying assumption that all goods are
normal goods, this means that in good economic times demand curves tend to shift out,
while in bad economic times demand curves tend to shift in. With an unshifting supply
curve, these shifts of the demand curve imply fluctuations of equilibrium price.
At the other extreme, price fluctuations could arise solely due to changes in costs for
firms, holding the demand function constant. Indeed, many industries are subject to such
cost “shocks” from time to time. For example, the production costs of manufacturing
firms, whose output makes up a sizable fraction of the U.S. economy, generally rise when
the price of steel rises.81 When the general wage level in the economy rises, as occurred
during much of the 1990’s in the U.S., all firms’ costs rise. Profit maximization by firms
implies that firms would try to pass along most if not all of any increase in production
costs to consumers in the form of higher prices.
Thinking then of our usual downward-sloping demand curves and upward-sloping supply
curves, these fluctuations in demand and costs should imply that (equilibrium) prices
fluctuate a fair amount during the course of business cycles. But much empirical
evidence has shown that prices do not in fact fluctuate very much over short periods of
time. The phenomenon that prices do not fluctuate as much as standard economic theory
predicts is known in academic circles as “price stickiness.”
Here we will consider five simple theories of price stickiness and also visit some of the
real-world evidence surrounding these theories. The discussion here follows the basic
structure presented by Blinder and his coauthors in Asking About Prices (1998), a very
interesting exploration of the origins of price stickiness that proceeds, rather than by
simply presenting economic theories in a vacuum, by asking managers of businesses in
various industries about the relative importance of various postulated theories of price
stickiness.
Theory I: Constant Marginal Cost of Production
Suppose markets are perfectly competitive and that all firms have constant marginal cost
(MC) curves over the relevant range of outputs. That is, for a single firm, if the “normal”
range of output is between 100 units and 500 units, suppose the MC curve is perfectly
81
As occurred, for example, when the Bush Administration passed a set of steel tariffs in March 2002.
Spring 2014 | © Sanjay K. Chugh
173
horizontal over this range. A constant MC schedule is not so difficult to rationalize. For
example, if a firm has a machine that makes between 100 and 500 units of output and the
electricity, water, etc. necessary to operate the machine has constant per-unit cost
(perhaps because the firm has a contract with the utility company), then over the range
100-500 units, the extra total cost incurred in producing one more unit could be constant
– that is, MC is constant. Because the market supply curve is simply the horizontal sum
of individual firms’ marginal cost curves, this implies that the market supply curve in
such an industry is perfectly elastic.
P
Figure 61 illustrates how prices can be constant despite fluctuations in the demand
schedule during the course of the business cycle. Thus, constant marginal cost is one
reason why prices may be sticky.
QS
P*
QD1
QD2
Q
Figure 61. If all firms in a perfectly competitive industry have constant marginal cost, then the market
supply curve is perfectly elastic, which in turn implies that fluctuations in the demand curve leave prices
unchanged.
Evidence about marginal cost curves in U.S. industries provides surprisingly more
support for constant marginal cost than many economists may think. According to
interview data compiled by Blinder et al (1998), 40% of U.S. goods and services are
produced by firms that report that they have constant marginal cost over “usual” ranges
of production. Only 11% report rising marginal cost over “usual” ranges of production,
while 33% report declining marginal costs over “usual” ranges of production (but here
there seems to be reason to suspect that respondents were confusing marginal cost with
average total cost).82 This evidence seems at odds with the usual textbook assumption
that marginal costs rise as output expands.
82
Recall that it is possible for marginal cost to be rising even as average total cost is falling – this is true
when the MC curve is below the ATC curve.
Spring 2014 | © Sanjay K. Chugh
174
Theory II: Variable Elasticity of Demand
P, MR, MC
Instead of considering perfectly competitive industries, let us think of monopolistically
competitive industries. Recall that in monopolistically competitive industries, each firm,
because it produces a slightly different good than every other firm in the industry, faces a
downward-sloping demand curve.83 Here we will suppose that each individual firm’s
MC curve has the usual upward slope. Profit maximization by the individual firm
implies choosing the quantity such that marginal revenue equals marginal cost (MR =
MC), as shown in Figure 62, in which q* is the profit-maximizing quantity and P* the
associated profit-maximizing price.
MC
P*1
MR1
q*1
QD1
Q
Figure 62. A monopolistically competitive firm faces a downward-sloping demand curve, and profit
maximization implies producing that quantity that equates marginal revenue to marginal cost.
In good economic times, when incomes are relatively high, the demand curve, and hence
the marginal revenue curve, in Figure 62 would shift outwards. If this shift out is a
parallel shift, the new profit-maximizing quantity and price are as shown in Figure 63.
The profit-maximizing price rises due to the increase in demand.
The shift out in the demand curve may not be a parallel shift, however. Figure 64 shows
a shift out of the demand curve in which the entire demand curve becomes more elastic
(that is, flatter) as economy-wide income rises. Demand curve Q2D is shifted out relative
to demand curve Q1D but is flatter than Q1D . At high prices, the demand curve has shifted
out by less than at lower prices. Such a nonparallel shift may seem r

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