Download Chapter 5

Using the
ClosedEconomy
One-Period
Model
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Outline
• Introduce graphical tools to illustrate
Competitive Equilibria and Pareto Optimal
allocations
• Run experiments: Increases in government
spending and total factor productivity.
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Competitive Equilibrium
• Representative consumer optimizes given
market prices (i.e. real wage w)
• Representative firm optimizes given market
prices
• The government budget constraint holds: G = T
• All markets clear
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Graphic Analysis
• Want to combine everything on one diagram
• Start with production function:
• In equilibrium, N = h – l, so
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Figure 1 The Production Function (as a
function of N)
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Figure 2 The Production Function (as a
function of l)
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Graphic Analysis, c’td
• Now, need to get to (C, l) plane from (Y, l)
• Take the consumption market clearing:
• And rearrange as:
C = Y − G = zF(K, h − l) − G
• Turn the production function into the
Production Possibilities Frontier (PPF)
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Figure 3 The Production Function and the
Production Possibilities Frontier
All the blue points are feasible for the economy
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Marginal Rate of Transformation
• Slope of the PPF is −MPN, marginal product of
labor, but it has another name:
• The (negative of the) slope of the PPF is also
called the marginal rate of transformation
(MRT):
– the rate at which one good can be converted
technologically into another.
• So here MRTl,C = MPN
• Also, in CE, MPN = w (firm’s optimization)
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Figure 4 Consumer’s Diagram
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Consumer’s Problem
• Line ABD is the budget constraint, has slope w
• I1 is the indifference curve, has slope MRSl,C
• At the optimal point, I1 is tangent to the budget
line ABD, hence they have the same slopes:
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Key Properties of a Competitive
Equilibrium
•
•
•
•
Now we combine all conditions in one place:
We have: MRTl,C = MPN = w
And also:
So the key condition that has to hold in
equilibrium is:
• And we can plot all parts in one picture
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Figure 5
Competitive Equilibrium
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Social Planner’s Problem
• Computing CE is long and tedious even in the
simplest models such as ours
• We can work around this issue by solving the
Social Planner’s Problem (SPP)
• The welfare theorems tell us that we will arrive
at the same allocation
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First and Second Welfare
Theorems
• These theorems apply to any macroeconomic
model
• First Welfare Theorem: Under certain
conditions, a competitive equilibrium allocation
is Pareto Optimal.
• Second Welfare Theorem: Under certain
conditions, any Pareto Optimal allocation is also
a Competitive Equilibrium allocation
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What Social Planner Does, 1
• He acts like a benevolent dictator whose
objective is to maximize the utility of the
consumer, given the conditions of the economy.
• Since he is a dictator, he doesn’t care about
prices!
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What Social Planner Does, 2
• In particular, he is able to:
1. Order the firm to hire Nd = N hours of labor and
produce Y units of output.
2. Order the consumer to work Ns = N hours.
3. Take an amount G of output and give the remainder
to the consumer.
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What Social Planner Does, 3
• Hence the planner’s problem is to choose
C and l, given technological constraints,
to maximize the utility of the consumer.
• Formally, he solves:
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Key Properties of a
Pareto Optimum
• In this model, the competitive equilibrium and
the Pareto optimum are identical (there is only
one consumer), so
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Figure 6 Pareto Optimality
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Figure 7 Using the SWT to Recover
the Competitive Equilibrium
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Asking Questions to the Model
• Now we can finally ask our model some
questions
• We will conduct two experiments:
1. What will happen if the value of government
expenditures G goes up (i.e. what will happen if the
stimulus bill gets through)?
2. What will happen if the total factor productivity z in
the economy suddenly goes up?
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Figure 8 Equilibrium Effects of an
Increase in Government Spending
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Effects of an Increase in G
• Essentially a pure income effect
• C decreases, l decreases, Y increases, w falls
• Does it agree with our business cycle facts?
– (i.e. can we conclude changes in G are the major
cause of the business cycles?)
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Table 1 Summary of Business
Cycle Facts
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Effects of an Increase in G
• Essentially a pure income effect
• C decreases, l decreases, Y increases, w falls
• Does it agree with our business cycle facts?
– (i.e. can we conclude changes in G are the major
cause of the business cycles?)
• Apparently, NO (consumption should not be
countercyclical)
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World War II Increase in G
• Very large increase in G
• Y increases, C decreases by a small amount
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Figure 9 GDP, Consumption, and
Government Expenditures
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Figure 10 Increase in Total Factor
Productivity
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Figure 11 Competitive Equilibrium
Effects of an Increase in Total Factor
Productivity
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Effects of an Increase in z
• PPF shifts out, and becomes steeper – income
and substitution effects are involved.
• C increases, l may increase or decrease, Y
increases, w increases
– Usually assume l will decrease, i.e. substitution
effect is stronger
– Here these effects cancel out each other
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Effects of an Increase in z
• C increases, l may increase or decrease, Y
increases, w increases
• Does it agree with our business cycle facts?
– (i.e. can we conclude changes in z are the major
cause of the business cycles?)
• Apparently, YES (if l falls and hence N goes up)
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Digression: How to Measure z
• Employ the concept of the Solow Residual
• Fitting Cobb-Douglas production function to
U.S. data gives:
• The Solow Residual is computed as:
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Figure 12 The Solow Residual for
the United States
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Figure 13 Deviations from Trend in
Real GDP and the Solow Residual
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