Chapter 5
A ClosedEconomy
One-Period
Macroeconomic
Model
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Chapter 5 Topics
• Introduce the government.
• Construct closed-economy one-period macroeconomic
model, which has: (i) representative consumer; (ii)
representative firm; (iii) government.
• Economic efficiency and Pareto optimality.
• Experiments: Increases in government spending and
total factor productivity.
• Consider a distorting tax on wage income and study
the Laffer curve.
• Public goods: How large should the government be?
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Closed-Economy One-Period Macro
Model
•
•
•
•
Representative Consumer
Representative Firm
Competitive Equilibrium
Experiments: What does the model tell us are the
effects of changes in government spending and in total
factor productivity?
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Figure 5.1
A Model Takes Exogenous Variables
and Determines Endogenous Variables
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Competitive Equilibrium
•
•
•
•
Representative consumer optimizes given market prices.
Representative firm optimizes given market prices.
The labor market clears.
The government budget constraint is satisfied, or G = T.
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Income-Expenditure Identity
In a competitive equilibrium, the income-expenditure
identity is satisfied, so
Y  C G
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The Production Function
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Figure 5.2
The Production Function and the Production
Possibilities Frontier
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Figure 5.3
Competitive Equilibrium
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Key Properties of a Competitive
Equilibrium
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Figure 5.4
Pareto Optimality
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Key Properties of a Pareto Optimum
• In this model, the competitive equilibrium and the Pareto
optimum are identical.
• We know this as, at the Pareto optimum,
MRS l ,C  MRTl ,C  MPN
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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 is Pareto optimal.
• Second Welfare Theorem: Under certain conditions, a
Pareto optimum is a competitive equilibrium.
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Figure 5.5
Using the Second Welfare Theorem to
Determine a Competitive Equilibrium
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Effects of an Increase in G
• Essentially a pure income effect
• C decreases, l decreases, Y increases, w falls
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Figure 5.6
Equilibrium Effects of an Increase in
Government Spending
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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 5.7
GDP, Consumption, and Government Expenditures
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Effects of an Increase in z (or an increase in K)
• PPF shifts out, and becomes steeper – income and
substitution effects are involved.
• C increases, l may increase or decrease, Y increases, w
increases.
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Figure 5.8
Increase in Total Factor Productivity
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Figure 5.9
Competitive Equilibrium Effects of an Increase in
Total Factor Productivity
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Figure 5.10
Income and Substitution Effects of an Increase
in Total Factor Productivity
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Figure 5.11
Deviations from Trend in GDP and the
Solow Residual
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Figure 5.12
The Relative Price of Energy
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Figure 5.13
Government Expenditures as a Percentage of GDP
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Figure 5.14
Total Government Outlays as a Percentage of GDP
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A Simplifed Model with a Proportional Income
Tax
• Use the model to study the incentive effects of the
income tax, and to derive the “Laffer curve.”
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Production Function Without Capital
• Labor is the only input, but there is still constant
returns to scale (linear production function).
Y  zN
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Production Possibilities Frontier
C  z (h  l )  G
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Consumer’s Budget Constraint
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Profits for the Firm
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The Consumer’s Budget Constraint in
Equilibrium
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Figure 5.15
The Production Possibilities Frontier in the
Simplified Model
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Revenue for the Government Given the Tax Rate t
REV  tz[h  l (t )]
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Figure 5.16
The Labor Demand Curve in the Simplified Model
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Figure 5.17
Competitive Equilibrium in the Simplified Model with
a Proportional Tax on Labor Income
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Figure 5.18
A Laffer Curve
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A Model of Public Goods: How Large Should the
Government Be?
• To this point, we have assumed that government
spending is to acquire goods that are thrown away.
• Economically, defense spending works like this –
defense may make us better off, but it diverts
resources from other uses.
• What if we allow for public goods – e.g. parks, public
transportation, health services – that provide direct
benefits to the private sector.
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A Model of Public Goods
• Representative consumer’s budget constraint:
C T  Y
• Production possibilities frontier:
G
C Y 
q
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The Optimal Choice of Government Spending
• The government chooses G to make the representative
consumer as well off as possible.
• G chosen so that the marginal rate of substitution of
private for public goods equals the marginal rate of
transformation.
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Figure 5.19
There Can Be Two Competitive Equilibria
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Figure 5.20
The Optimal Choice of Government Spending
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What Happens to the Optimal Choice of G when Y
increases?
• This works like a pure income effect.
• Private consumption and government spending both
increase.
• Wealthier countries choose to have larger governments
– but not clear whether G/Y increases or decreases. Is
G a luxury good or an inferior good?
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Figure 5.21
The Effects of an Increase in GDP
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Figure 5.22
The Effects of an Increase in Government
Efficiency
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What Happens if the Government Becomes More
Efficient?
• q increases – can produce more G for a given input of
private goods.
• Income and substitution effects.
• G increases, but private consumption may increase or
decrease.
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