1. A Closed- Economy One-Period Macro-economic Model
Chapter 5
A Closed- Economy One-Period Macro-economic Model
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2. 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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3. 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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4. Figure 5.1 A Model Takes Exogenous Variables and Determines Endogenous Variables
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5. 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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6. Income-Expenditure Identity
In a competitive equilibrium, the income-expenditure identity is satisfied, so
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7. The Production Function
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8. Figure 5.2 The Production Function and the Production Possibilities Frontier
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9. Figure 5.3 Competitive Equilibrium
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10. Key Properties of a Competitive Equilibrium
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11. Figure 5.4 Pareto Optimality
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12. 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,
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13. 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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14. Figure 5.5 Using the Second Welfare Theorem to Determine a Competitive Equilibrium
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15. Effects of an Increase in G
Essentially a pure income effect
C decreases, l decreases, Y increases, w falls
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16. Figure 5.6 Equilibrium Effects of an Increase in Government Spending
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17. World War II Increase in G
Very large increase in G.
Y increases, C decreases by a small amount.
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18. Figure 5.7 GDP, Consumption, and Government Expenditures
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19. 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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20. Figure 5.8 Increase in Total Factor Productivity
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21. Figure 5.9 Competitive Equilibrium Effects of an Increase in Total Factor Productivity
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22. Figure 5.10 Income and Substitution Effects of an Increase in Total Factor Productivity
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23. Figure 5.11 Deviations from Trend in GDP and the Solow Residual
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24. Figure 5.12 The Relative Price of Energy
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25. Figure 5.13 Government Expenditures as a Percentage of GDP
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26. Figure 5.14 Total Government Outlays as a Percentage of GDP
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27. 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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28. Production Function Without Capital
Labor is the only input, but there is still constant returns to scale (linear production function).
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29. Production Possibilities Frontier
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30. Consumer’s Budget Constraint
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31. Profits for the Firm
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32. The Consumer’s Budget Constraint in Equilibrium
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33. Figure 5.15 The Production Possibilities Frontier in the Simplified Model
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34. Revenue for the Government Given the Tax Rate t
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35. Figure 5.16 The Labor Demand Curve in the Simplified Model
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36. Figure 5.17 Competitive Equilibrium in the Simplified Model with a Proportional Tax on Labor Income
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37. Figure 5.18 A Laffer Curve
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38. 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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39. Representative consumer’s budget constraint:
A Model of Public Goods
Representative consumer’s budget constraint:
Production possibilities frontier:
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40. 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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41. Figure 5.19 There Can Be Two Competitive Equilibria
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42. Figure 5.20 The Optimal Choice of Government Spending
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43. 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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44. Figure 5.21 The Effects of an Increase in GDP
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45. Figure 5.22 The Effects of an Increase in Government Efficiency
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46. 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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