Chapter 5

A Closed- Economy

One-Period Macro-

economic 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 5.1A 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 5.2The Production Function and the Production Possibilities Frontier

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Figure 5.3Competitive Equilibrium

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Key Properties of a Competitive Equilibrium

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Figure 5.4Pareto 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,

NClCl MPMRTMRS ,,

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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 5.5Using 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 5.6Equilibrium 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 5.7GDP, 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 5.8Increase in Total Factor Productivity

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Figure 5.9Competitive Equilibrium Effects of an Increase in Total Factor Productivity

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Figure 5.10Income and Substitution Effects of an Increase in Total Factor Productivity

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Figure 5.11Deviations from Trend in GDP and the Solow Residual