Download Chapter 5

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.
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Closed-Economy One-Period
Macroeconomic 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 incomeexpenditure identity is satisfied.
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Equation 5.2
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Equation 5.3
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Equation 5.4: The Production
Function
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Equation 5.5
• In equilibrium, N = h – l, so
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Figure 5.2A The Production Function
and the Production Possibilities Frontier
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Figure 5.2B The Production Function
and the Production Possibilities Frontier
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Figure 5.2C The Production Function
and the Production Possibilities Frontier
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Figure 5.3 Competitive
Equilibrium
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Equation 5.6: Key Properties of
a Competitive Equilibrium
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Figure 5.4 Pareto Optimality
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Equation 5.6: Key Properties of
a Pareto Optimum
• In this model, the competitive equilibrium and
the Pareto optimum are identical, as
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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
Real GDP and the Solow Residual
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Figure 5.12 The Relative Price of
Energy
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A Simplified 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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Equation 5.7: Production
function without capital
• Labor is the only input, but there is still constant
returns to scale (linear production function).
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Equation 5.8: Production
Possibilities Frontier
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Equation 5.9: Consumer’s
budget constraint
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Equation 5.10: Profits for the
firm
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Equation 5.11: The consumer’s
budget constraint in equilibrium
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Figure 5.13 The Production Possibilities
Frontier in the Simplified Model
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Equation 5.12: Revenue for the
government given the tax rate, t
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Figure 5.14 The Labor Demand
Curve in the Simplified Model
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Figure 5.15 Competitive Equilibrium in
the Simplified Model with a Proportional
Tax on Labor Income
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Figure 5.16 A Laffer Curve
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Figure 5.17 There Can Be Two
Competitive Equilibria
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Figure 5.18 Federal Personal
Taxes as a Percentage of GDP
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