A Closed- Economy One-Period Macro-economic Model Chapter 5 A Closed- Economy One-Period Macro-economic Model Copyright © 2014 Pearson Education, Inc.

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? © 2014 Pearson Education, Inc.

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? © 2014 Pearson Education, Inc.

Figure 5.1 A Model Takes Exogenous Variables and Determines Endogenous Variables © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

Income-Expenditure Identity In a competitive equilibrium, the income-expenditure identity is satisfied, so © 2014 Pearson Education, Inc.v

The Production Function © 2014 Pearson Education, Inc.

Figure 5.2 The Production Function and the Production Possibilities Frontier © 2014 Pearson Education, Inc.

Figure 5.3 Competitive Equilibrium © 2014 Pearson Education, Inc.

Key Properties of a Competitive Equilibrium © 2014 Pearson Education, Inc.

Figure 5.4 Pareto Optimality © 2014 Pearson Education, Inc.

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, © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

Figure 5.5 Using the Second Welfare Theorem to Determine a Competitive Equilibrium © 2014 Pearson Education, Inc.

Effects of an Increase in G Essentially a pure income effect C decreases, l decreases, Y increases, w falls © 2014 Pearson Education, Inc.

Figure 5.6 Equilibrium Effects of an Increase in Government Spending © 2014 Pearson Education, Inc.

World War II Increase in G Very large increase in G. Y increases, C decreases by a small amount. © 2014 Pearson Education, Inc.

Figure 5.7 GDP, Consumption, and Government Expenditures © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

Figure 5.8 Increase in Total Factor Productivity © 2014 Pearson Education, Inc.

Figure 5.9 Competitive Equilibrium Effects of an Increase in Total Factor Productivity © 2014 Pearson Education, Inc.

Figure 5.10 Income and Substitution Effects of an Increase in Total Factor Productivity © 2014 Pearson Education, Inc.

Figure 5.11 Deviations from Trend in GDP and the Solow Residual © 2014 Pearson Education, Inc.

Figure 5.12 The Relative Price of Energy © 2014 Pearson Education, Inc.

Figure 5.13 Government Expenditures as a Percentage of GDP © 2014 Pearson Education, Inc.

Figure 5.14 Total Government Outlays as a Percentage of GDP © 2014 Pearson Education, Inc.

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.” © 2014 Pearson Education, Inc.

Production Function Without Capital Labor is the only input, but there is still constant returns to scale (linear production function). © 2014 Pearson Education, Inc.

Production Possibilities Frontier © 2014 Pearson Education, Inc.

Consumer’s Budget Constraint © 2014 Pearson Education, Inc.

Profits for the Firm © 2014 Pearson Education, Inc.

The Consumer’s Budget Constraint in Equilibrium © 2014 Pearson Education, Inc.

Figure 5.15 The Production Possibilities Frontier in the Simplified Model © 2014 Pearson Education, Inc.

Revenue for the Government Given the Tax Rate t © 2014 Pearson Education, Inc.

Figure 5.16 The Labor Demand Curve in the Simplified Model © 2014 Pearson Education, Inc.

Figure 5.17 Competitive Equilibrium in the Simplified Model with a Proportional Tax on Labor Income © 2014 Pearson Education, Inc.

Figure 5.18 A Laffer Curve © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

Representative consumer’s budget constraint: A Model of Public Goods Representative consumer’s budget constraint: Production possibilities frontier: © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.

Figure 5.19 There Can Be Two Competitive Equilibria © 2014 Pearson Education, Inc.

Figure 5.20 The Optimal Choice of Government Spending © 2014 Pearson Education, Inc.

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? © 2014 Pearson Education, Inc.

Figure 5.21 The Effects of an Increase in GDP © 2014 Pearson Education, Inc.

Figure 5.22 The Effects of an Increase in Government Efficiency © 2014 Pearson Education, Inc.

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. © 2014 Pearson Education, Inc.