Download CHAPTER 3 The Economy in the Long Run: The Classical Market

CHAPTER 3
THE ECONOMY IN THE LONG RUN: THE CLASSICAL MARKET CLEARING MODEL
Chapter Outline
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The Supply of Goods and Services: The Production Function and the Labour Market
The General Form of the Production Function
The Production Function in the Long Run: Fixed Capital and Technology
The Marginal Product of Labour and Labour Demand
The Supply of Labour
Equilibrium on the Labour Market
The Classical Aggregate Supply Curve
The Demand for Goods and Services
Consumption and Savings
Investment
Government and Net Export Spending
The Effects of Fiscal Policy Since the Mid-1970s
The Money Stock, the Price Level and the Inflation Rate
Money
Money Growth and Inflation
The Quantity Theory of Money in Canada
The Real Interest Rate in the Long Run
Working With Data
Changes from the Previous Edition
As this was a completely new chapter in the 6th edition, there are no major changes in this edition.
We have made some minor changes. Box 3-1 on factor productivity is new, and previous Box 3-3 has
been edited to become the Policy in Action feature for this chapter.
Learning Objectives
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Students should understand that the difference between the long run (this chapter) and the very long
run (Chapter 4, Growth) involves the assumption that, in the long run, the capital stock and
technology are assumed to be fixed.
Students should understand that over the long run we assume that all factors of production are fully
employed and all prices in all markets are completely flexible.
Students should understand that a very simple classical model assumes that the supply of goods and
services is based on the production function, with technology and capital assumed to be fixed.
Therefore, equilibrium output depends on equilibrium labour use.
Students should understand that labour demand comes from the production function, based on the
diminishing marginal product of labour, and that labour supply comes from the choice of work versus
leisure, based on the real wage.
Students should understand how consumption and savings are related to the rate of time preference
and the real interest rate, and the increased savings is a desire for increased consumption possibilities
in the future, based on a larger capital stock.
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Students should understand that the demand for goods and services is based on the allocation of
income amongst spending by consumers, the business sector, the government, and the foreign sector.
Students should understand that in a long run classical world, the price level is determined by the
level of the money supply and the inflation rate is determined by the rate of growth of the money
supply.
ing that capital and technology are fixed. The time frame for analysis here is ten to fifteen years, which
we have labeled the long run (as opposed to the very long run where we study growth theory). Since the
capital stock and technology are assumed to be fixed, there is a one to one correspondence between
equilibrium labour and equilibrium output. This is used to derive the Classical vertical AS curve. The
demand side of the economy is summarized by the investment savings model, where the real rate of
interest is determined. The nominal side of the economy obeys the quantity theory of money.
Accomplishing the Objectives
In this chapter the students are asked to work with a model where prices are completely flexible
and all markets clear at all times. This chapter builds on the production function that was introduced in
Chapter 2, and allows students to do some empirical work with the Cobb-Douglas form, assuming that
capital and labour’s shares are 0.3 and 0.7 respectively. For the remainder of the chapter we use the
general form of the long run production function.
Y  F( K , N )
(5)
Where the term A has been dropped as technology is assumed to be fixed, and capital is written as K , as
it is assumed to be fixed also. The diminishing marginal product of labour is used to derive the demand
for labour curve. Students are informally introduced to the income leisure choice model of deriving the
supply of labour curve. Equilibrium labour use is denoted by N * , which, given fixed technology and
capital, leads to Y * , which is full employment output. Students are then shown how this relates to the
Classical vertical AS curve.
The Classical investment savings model is then developed. Students are again shown how choice
plays a role in this model, as the consumption savings choice is informally modeled. The concept of the
rate of time preference is treated in Box 3-1.
The final section deals with the nominal side of the economy. The quantity theory of money is
presented in static (price level) and dynamic (inflation rate) form. The final section concludes with a
discussion of the Fisher effect, the assumed long run relationship between the nominal interest rate and
the inflation rate.
Suggestions and Pitfalls
It is a good idea to bring up several key points at the beginning. First, the long run is
distinguished from the very long run by the assumption of fixed capital and technology. Instructors may
want to refer back to Chapter 1: in the long run the AS curve is vertical but not moving, and in the very
long run (growth theory) the vertical AS curve is shifting out by a approximately 2% per year (see Figure
1-2). Second, instructors should also emphasize that savings, which is foregone consumption, leads to an
increase in the capital stock, but we will not discuss these ramifications until the next chapter (growth
theory). Given this, the capital stock is not really rigidly fixed, but rather, given the size of the capital
stock, net additions (net investment) are small enough that, over the period of time under consideration
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(ten to fifteen years), they can be ignored. Third, this is a market clearing model, so that all prices are
assumed to move infinitely quickly to ensure continuous market equilibrium.
It may also be helpful at the outset to give an overview of how the model works: the production
function and the labour market determine the level of output; the savings investment model determines
the allocation of this level of output; the price level and the nominal wage are determined by the quantity
theory of money.
Throughout this chapter there is no rigorous mathematical treatment of the underlying choices
faced by individual agents in various situations. The details of indifference curves, budget constraints and
tangencies have deliberately been left omitted (they are treated in Chapter 14), so that the student can see
the big picture. However, instructors who want the details now can easily borrow them from the material
in Chapter 14.
When deriving the supply of labour curve, instructors could discuss the concept of leisure as a
valid alternative to working, based on the level of the real wage. This will help later when discussing
why, at N * , there can be no unemployment (See Discussion Question #1). Also when discussing the
consumption savings choice, students should be made aware of the role of the rate of time preference, and
how this motivates individuals to make various choices concerning current and future consumption.
When discussing the savings investment model, it is important that students understand the role
of the real rate of interest. For instance, a shock, which shifts out the investment curve, will increase the
real rate of interest in equilibrium. However, students tend to think of higher real rates of interest as bad.
It can be pointed out that the higher real interest rate is a Pareto optimal equilibrium. This will help when
discussing the Fisher effect later in the chapter. In situations where the Fisher effect does not hold, the
real rate of interest can be thought of as a disequilibrium rate, which is what students probably have in
mind when they say that high real rates of interest are bad (see Discussion Question #6).
Students may benefit from a discussion of the relationship between the quantity theory of money
and the Classical aggregate supply curve. This relationship can be developed using the following two
diagrams:
Classical AS
N S ( P1 )
W
P
N S ( P0 )
W1
M 1  P1
W0
M 0  P0
N D ( P1 )
N D ( P0 )
N*
Y*
N
Y
In the above diagrams, W is the nominal wage and P is the price level. Notice that we are still assuming
that labour supply and demand are a function of the real wage. However, we have nominal wage on the
vertical axis, and the price level is a shift parameter on the supply and demand curves. Notice that if the
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price level is a shift parameter on these curve, then we are assuming that the price level is exogenous to
the money market. This has to be true in a classical model, as the price level is determined in the money
market by the quantity theory of money. The initial equilibrium is at nominal wage W0 and equilibrium
labour use N * . With N * labour use, and the assumption that the capital stock is quasi-fixed, then
equilibrium output is Y * through the production function. In the right hand diagram, the equilibrium
price level, P0 , is determined by the equilibrium nominal money stock, assumed to be M 0 . Therefore, in
the initial equilibrium, P0 ,Y * is one point on the aggregate supply curve. Now we ask the question, what
would happened to real output if the price level were to increase. The only way that the price level can
increase is if the nominal money stock increases. Therefore, we assume that there is a positive money
shock, and the new money stock is M 1 . Through the quantity theory of money, this increases the price
level to P1 . In the labour market, this shifts the labour demand curve outwards and the labour supply
upwards by the change in the price level. Therefore, the nominal wage increases to W1 . Notice that the
increase in the nominal wage W1  W0 is exactly equal to the increase in the price level P1  P0 .
Therefore the real wage W1 P1  W0 P0 . Equilibrium labour use N * has not changed, therefore,
equilibrium real output Y * has not changed. Therefore, the Classical labour supply curve is vertical.
Many instructors encounter the fact that students are skeptical of any quantity theory
relationships. Therefore, you may want to spend some time on Figures 3-12 and 3-13. A very nice
stylized story can be told about inflation and money growth with Figure 3-12. Start at 1950, when
inflation and money growth are low, then discuss how money growth increases in 1960 but inflation
remains low. There are considerable long lags in the quantity theory relation. By 1970 inflation has
caught up with money growth. In 1975 the Bank of Canada began monetary targeting, but it did not
substantially reduce the inflation rate until the 1990s. Therefore, it took a long time for inflation to
increase and a long time for it to decrease. This would also be a good time to discuss the Policy in Action
feature on the monetarist experiment.
Solutions to Problems in the Textbook
Discussion Questions
1. The Classical model is a market clearing model. Therefore, at the equilibrium N * , all individuals
who choose to work are working. Underneath the model is the assumption that labour makes a work
leisure choice based on the real wage. Those who are not working are not in the labour force, because
the real wage is too low. This implies that they have chosen leisure over work and are not counted as
being unemployed. Therefore, the model cannot be used to discuss unemployment.
2. The production function assumes that the capital stock and technology are fixed. Therefore, adding
labour to a fixed amount of capital and technology produces diminishing marginal product of labour.
The intuitive manner in which to see this is to think about a company that has 4 machines and 3
workers. Hiring another worker allows the fourth machine to be used. However, hiring a fifth
worker means that there is no machine for this worker, and he/she will have to share. Output will go
up, but not by as much as it would if this worker had his/her own machine.
3. This question is designed to get students to think about the choices involved in economic decisions.
What is important here, although it was not covered in the text (see above, under Suggestions for
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Lecturing) are the concepts of income and substitution effects of a price change. Here the choice is
between consumption today and consumption in the future (savings). The income effect is that an
increase in the real rate of interest gives you more consumption possibilities in the future for any
given amount of savings. The substitution effect is that the price of current consumption has
changed. It is quite possible for the income effect to dominate, and the savings curve to be downward
sloping. Empirically, there is not a lot of support for an upward sloping savings curve.
4. Figure 3-10 was derived under the assumption that private savings would not change when the
government ran a budget deficit. If private savings changed in the same direction, the results would
still hold. However, a change in private savings could shift the curve the other way, so that total
savings could stay the same or even go up. Ultimately, this would be an empirical matter.
5. This question is designed to get students to see that if real money demand grows, because real income
is growing, then the money supply can grow by this amount without being inflationary. Equation
(22) can be altered by adding real income growth:
% M  % Y  % P
(22(a))
Therefore, if nominal money were growing at the same rate that real income was growing (growth in
real money supply equals growth in real money demand), then inflation would be zero, even though
there is a positive growth in the nominal money supply. Good students will recognize that the income
elasticity of money demand is assumed to be unity in this equation.
6. The Fisher effect is a long run proposition that says that the nominal interest rate and inflation should
be related over the long run. However, as we mentioned in Chapter 1, and we will be explicit about
in Parts 3 and 4 of the book, the price level (and the inflation rate) may be sluggish in periods shorter
than the long run. Monetary policy can change the course of the nominal interest rate in the short run,
and this does not necessarily have to be related to the inflation rate. Also, it is quite possible that, in
the short run, agent’s expectations of the inflation rate may be incorrect.
Application Questions:
1. The graph over the period 1968-1970, monthly, should look like this:
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Inflation Rate
5
4
3
2
1
0
0
5
10
Rate of Growth of Money
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15
20
There is basically no relationship between these variables.
2. Here is what the recalculated table looks like:
Y K
Billions
1975 480.3
1976 506.7
1977 524.2
1978 545.6
1979 568.5
1980 576.4
1981 594.1
1982 576.7
1983 592.7
1984 626.4
1985 660.3
1986 677.8
1987 705.7
1988 740.6
1989 759.8
1990 762.4
1991 747.9
1992 754.8
1993 772.5
1994 810.0
1995 832.1
1996 845.2
1997 882.7
1998 919.0
1999 967.6
2000 1013.1
2001 1026.9
2002 1053.1
N
A
Billions Millions
390.8 10.0
16.0
407.2 10.5
19.3
422.1 10.8
19.4
436.3 11.1
19.6
455.1 11.5
19.7
477.7 11.9
19.3
507.4 12.2
19.1
525.1 12.3
18.3
537.5 12.5
18.5
550.8 12.7
19.2
566.9 13.0
19.8
585.6 13.3
19.8
607.9 13.5
20.2
636.8 13.8
20.6
667.3 14.0
20.6
692.3 14.2
20.3
709.9 14.3
19.7
724.1 14.4
19.7
735.5 14.5
20.0
750.4 14.6
20.7
766.4 14.8
21.0
785.7 14.9
21.0
817.4 15.2
21.5
849.8 15.4
21.9
887.8 15.7
22.5
928.8 16.0
22.9
963.7 16.2
22.8
994.9 16.4
23.0
20.9
0.7
0.7
0.5
-2.0
-0.7
-4.2
0.8
3.7
3.1
0.3
1.7
2.2
-0.1
-1.6
-3.0
0.3
1.2
3.7
1.5
0.2
2.1
1.8
2.6
2.2
-0.7
0.9
This does not appear to make an appreciable difference.
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Output, Y (Billions of 1997
Dollars)
3. New Figure 3-1 looks like this:
1200.0
900.0
664.1
600.0
408.8
300.0
0.0
0
2.5
5
7.5
10
12.5
15
17.5
Labour, N (Millions)
4(a). 10,9,7,4
4.(b) at $18.00, N=2; at $8, N=4.
4.(c)
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Real Wage
10
8
6
4
2
0
1
2
3
4
Labour
Additional Problems
1. Explain how we can make the assumption that the capital stock is fixed, yet in the savings
investment portion of the Classical model, net investment is positive, and, therefore, the capital
stock must be growing.
The capital stock grows by 1-2% per year, so that the ratio I/K is quite small in any one year. It takes a
long period of time for these changes in the capital stock to be felt in an economy. Over a period of 10-15
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years, we generally analyze the economy in a situation where we can ignore the effects of this growth in
the capital stock. Thus, the capital stock is not really fixed, but rather it is a convenient modeling
assumption for the time frame for the long run.
2. Suppose that the economy has a production function of the following form:
Y  0.1( K  3 N )
Suppose that capital is fixed at K=10. Calculate output and MPN for N=1 to N=10.
K
10
10
10
10
10
10
10
10
10
10
N
1
2
3
4
5
6
7
8
9
10
Y
3.90
4.27
4.56
4.80
5.01
5.20
5.38
5.55
5.70
5.85
MPN
0.373
0.286
0.241
0.212
0.192
0.177
0.164
0.154
0.146
3. Suppose that for a real wage up to $10.00 per hour, labour finds it more attractive to give up an
hour of leisure for each additional dollar of real wage, but for a real wage above $10.00 per
hour, labour feels that they can consume more leisure for each additional dollar increase in the
real wage. What would the labour supply curve look like? Can you provide an explanation for
this labour supply curve?
This scenario would give rise to a backward bending labour supply curve. Technically, this is a situation
where, for a real wage in excess of $10.00 per hour, the income effect outweighs the substitution effect.
Intuitively, labour may have a preference function such that, at lower real wages they feel that they must
work more, and, as the real wage gets higher, labour feels that they can afford to consume more leisure.
4. In Figure 3-5, if N * is the full employment level of labour use, and, therefore, there is no
unemployment, where are the workers on the labour supply curve above the equilibrium real
wage w* ?
Because labour supply is based on the choice between income and leisure, the individuals who are not
working at the current equilibrium are not in the workforce. The have chosen to consume leisure rather
than work, because the real wage is too low to induce them to give up leisure. Therefore, they cannot be
counted as unemployed.
5. Explain why individuals with high rates of time preference are spenders and individuals with
low rates of time preference are savers.
A rate of time preference measures how much you discount the future. Alternatively, and equivalently, it
measures how much you need to be compensated for giving up current consumption. If you have a high
rate of time preference, it means that you discount the future substantially. Therefore, in this situation,
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you must receive a large reward, a high real rate of interest, for giving up current consumption.
Therefore, ceteris peribus, individuals with a high rate of time preference choose current consumption
over savings.
6. Suppose that businesses all had an increase in expectations concerning future profitability, so
that for every dollar that they wish to borrow, they are willing to pay a higher real rate of
interest. Analyze the effects of this change on the savings investment equilibrium.
This is an exogenous change, which would cause the investment curve to shift outwards. At the initial
equilibrium real rate of interest, there would be excess demand for loadable funds. This would cause the
real rate of interest to increase, moving savers up the savings curve and moving borrowers up the new
investment curve. In the new equilibrium, there would be a higher real rate of interest, and higher savings
and investment. In the model of this chapter, current consumption would be lower, and real income
would not change. Therefore, the allocation of the level of real income would be different (more savings
and investment, less current consumption).
7. Comment on the following statement:
"Government budget deficits crowd out private sector investment. "
This is the analysis that surrounds Figure 3-10. However, in order for this conclusion to be correct, when
savings decreases (budget deficit), private sector savings does not change. However, total savings could
be unaltered in the face of a government budget deficit, if private sector savings increased when
government savings decreased. In spite of this possibility, Figure 3-11 seems to suggest that budget
deficits are indeed consistent with higher real rates of interest.
8. You are given the following information. The very long run rate of growth of real income is 2%
per year, and the income elasticity of real money demand is 0.5. If the Bank of Canada wished
to maintain an inflation rate of 2%, what is the required growth rate of nominal money?
In this situation, real money demand will be growing by 1% per year (=0.5*2%). In equilibrium, the
growth of real money demand must equal the growth of real money supply. Assuming that the change in
velocity is zero, this equilibrium condition can be written as
% M  % P  0.5 * % Y
This is just a version of equation (22) in the text. If the target rate of inflation ( %P ) is 2%, then
rearrange and substitute:
% M  ( 0.5 * 2 )  2
=3
Therefore, the required rate of growth of nominal money is 3% per year.
9. Comment on the following statement:
"If the government would just give us all one million dollars, we would all be better off."
One answer to this statement is “if this is true, why are we not all better off?” Money is virtually costless
to print, therefore, we would all be getting something for nothing. The quantity theory of money tells us
that doing this would simply lead to inflation. By printing more money, the government has not used any
resources to produce any good that can be consumed. That is, there is more money, but there are not
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more goods to buy. If this could be done, then the scarcity constraint would be violated, and there would
be no economic problem.
10. True or False? Why?
"Since the real wage is calculated as the nominal wage divided by the price level, the real
interest rate must be calculated by dividing the nominal interest rate by the price level."
False. The real wage is a measure of wages at a point in time, and the price level measures the cost of
buying a market basket of consumer goods at a point in time. However, the nominal interest rate measures
the change in the value of a financial asset between two periods, therefore, it does not make any sense to
divide it by the price level. The real interest rate measures the change in your ability to purchase goods,
given that you have purchased a financial asset. Therefore, the real rate of interest is the difference
between the extra amount of money that you have, measured by the nominal interest rate, and the change
in the purchasing power of money, measured by the inflation rate.
11. True or false? Why?
"The Classical aggregate supply curve is vertical because there is no more labour available
beyond N * ."
Uncertain – depending on how it is answered. It is true that there is no more labour available beyond
N * , at the level of the equilibrium real wage, w* . It is not true that there is no more labour available as
some sort of a physical constraint. N * is the total amount of labour that is wiling to work given that the
real wage is w* . More labour is available if the real wage increases.
12. Assume a government bond pays you a fixed interest rate of 5.5% per year and the average
annual rate of inflation is 4.2%. What is your real rate of return? How would this real rate of
return change if inflation increased to 6.8%?
The real interest rate is defined as the nominal interest rate minus the inflation rate, that is,
r=i-
Therefore your real rate of return is
r = 5.5% - 4.2% = 1.3%
if the inflation rate is 4.2%. But if the inflation rate increases to 6.8%, then your real rate of return will be
negative, that is,
r = 5.5% - 6.8% = - 1.3%.
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