Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 5 A Closed- Economy One-Period Macroeconomic Model
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-2 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.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-3 Government Provide public goods, G, financed by lump-sum taxes, T, on consumers or firms. Government budget is balanced (no deficits). –G = T
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-4 Closed-Economy One-Period Macroeconomic Model Representative Consumer Representative Firm Government Competitive Equilibrium Experiments: What does the model tell us are the effects of changes in government spending and in total factor productivity?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-5 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.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-6 Income-Expenditure Identity In a competitive equilibrium, the income- expenditure identity is satisfied.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-7 Equation 5.2
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-8 Equation 5.3
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-9 Figure 5.2A The Production Function and the Production Possibilities Frontier Y = z F (K, N)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 5.2B The Production Function and the Production Possibilities Frontier
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 5.2C The Production Function and the Production Possibilities Frontier
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Production Possibility Frontier Describe what the technological possibilities are for the economy as a whole, in terms of the production of C goods and l, given z, G, h. Points in the shaded area and on PPF are technologically feasible for the economy. Points on AB are not feasible since all consumption goods produced are taken away by government, nothing left to private consumption. Captures the tradeoff between C and l that the available production technology makes available to the representative consumers in economy.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved PPF - continued The slope of PPF = MRT l, C MRT l, C : marginal rate of transformation of leisure into consumption, the rate at which leisure can be converted technologically into consumption goods through work. MRT l, C = - MP N = w
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 5.3 Competitive Equilibrium
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 5.6: Key Properties of a Competitive Equilibrium At equilibrium, facing the same market price, the rate at which the consumers are willing to trade l for C is the same as the rate at which the firms are willing to convert l into C by using production technology.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Pareto Optimality A competitive equilibrium is pareto optimal if there is no way to rearrange production or to reallocate goods so that someone is made better off without making someone else worse off. Q: suppose there exists a social planner, who care about welfare of consumers, firms, and government in total, whether the CE obtained before is also socially optimal?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Solve for the PO A social planner chooses C and l, given production technology for converting l into C, to make consumers as well off as possible. That is, he chooses consumption bundle on or within PPF and that is on the highest possible IC for consumers.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 5.4 Pareto Optimality PO allocation is point B, where IC is tangent to PPF. Slope of IC = -MRS l, C Slope of PPF = -MRT l, C
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 5.6: Key Properties of a Pareto Optimum In this model, the competitive equilibrium and the Pareto optimum are identical, as
Copyright © 2008 Pearson Addison-Wesley. All rights reserved First and Second Welfare Theorems 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. Application: if CE is also PO, solve for the market outcomes could be an easy way to solve social planner’s problem.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Effects of an Increase in G Essentially a pure income effect C decreases, l decreases, Y increases, w falls
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 5.6 Equilibrium Effects of an Increase in Government Spending