1. Chapter 5
A Closed-Economy One-Period Macroeconomic Model

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.
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3. Government
Provide public goods, G, financed by lump-sum taxes, T, on consumers or firms.
Government budget is balanced (no deficits).
G = T
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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?
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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. Definition of Competitive Equilibrium
Competitive equilibrium is a set of endogenous quantities (c*, Ns*, Nd*, T*, Y*, π*) and endogenous price w* such that
Given w, π, and T, (c*, l*) solves consumer’s utility max. problem, and Ns* is the labor supply.
Given w, Nd* solves the firm’s profit max. problem, and Y*, π* are the respective output, and profit.
The labor market clears: Ns*=Nd*
The government budget constraint binds: G=T*
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7. Income-Expenditure Identity
In a competitive equilibrium, the income-expenditure identity is satisfied.
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8. Equation 5.2
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9. Equation 5.3
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10. Figure 5.2A The Production Function and the Production Possibilities Frontier
Y = z F (K, N)
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11. Figure 5.2B The Production Function and the Production Possibilities Frontier
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12. Figure 5.2C The Production Function and the Production Possibilities Frontier
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13. 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.
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14. 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 = - MPN = w
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15. Figure 5.3 Competitive Equilibrium
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16. 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.
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17. 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?
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18. 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.
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19. 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
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20. 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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21. 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.
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22. Effects of an Increase in G
Essentially a pure income effect
C decreases, l decreases, Y increases, w falls
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23. Figure 5.6 Equilibrium Effects of an Increase in Government Spending
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