Chapter 5: A Closed-Economy One-Period Macroeconomic Model 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.
Closed-Economy One-Period Macroeconomic Model Representative Consumer Representative Firm Competitive Equilibrium Experiments: What does the model tell us about the effects of changes in government spending and in total factor productivity?
A Model Takes Exogenous Variables and Determines Endogenous Variables Exogenous variables are determined outside a macroeconomic model. Given the exogenous variables, the model determines the endogenous variables. In experiments, we are interested in how the endogenous variables change when there are changes in exogenous variables.
Let s first look at the competitive equilibrium
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.
Competitive Equilibrium Recall that representative consumer s optimal consumption problem involved a graph with consumption and leisure
Competitive Equilibrium Recall that representative consumer s optimal consumption problem involved a graph with consumption and leisure representative firm s profit maximization problem involved a graph with labor and output
Competitive Equilibrium Recall that representative consumer s optimal consumption problem involved a graph with consumption and leisure representative firm s profit maximization problem involved a graph with labor and output We want to be able to put these two problems in one graph transform output into consumption transform labor into leisure
Resource Constraint In a competitive equilibrium, the incomeexpenditure identity is satisfied.
Derivation of RC This can be verified from the consumer s budget constraint.
The Production Function In equilibrium, N = h l, so This allows us to look output as a function of leisure
Production Function
Output as a Function of Leisure
Consumption as a Function of Leisure C = Y - G
Production Possibilities Frontier Production Possibilities Frontier (PPF): the technological relationship between consumption and leisure Marginal Rate of Transformation (MRT): slope of PPF, rate at which leisure can be converted in the economy into consumption goods through work Then MRT = MPN
Production Possibilities Frontier An increase in G shifts PPF downwards AB is infeasible as consumption is negative
Competitive Equilibrium Now we can put the representative consumer s optimal consumption problem and the representative firm s profit maximization problem in the same graph to find the competitive equilibrium
Competitive Equilibrium Slope = This figure brings together the representative consumer s preferences and the representative firm s production technology to determine a competitive equilibrium. AD: budget constraint DB: non-labor income
Key Properties of a Competitive Equilibrium = w MRS: slope of indifference curve MRT, MPN: slope of PPF w: slope of budget constraint
Now let s discuss the optimality of the competitive equilibrium
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. The Pareto optimum is the allocation that a social planner would choose. The social planner s problem is to maximize consumer welfare given the technology and the resource constraints
Pareto Optimality
Key Properties of a Pareto Optimum In this model, the competitive equilibrium and the Pareto optimum are identical, as
First and Second Welfare Theorems These theorems apply to many macroeconomic models 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.
When might competitive equilibria fail to be Pareto Optimal? Externalities Pollution (negative), fine architecture (positive) Distorting taxes Income tax, sales tax, property taxes are all distortionary (e.g. MRS < MPN = MRT) Price setters Monopolistic firms are not price takers
Now let s discuss how the competitive equilibrium changes in response to exogenous changes
Effects of an Increase in G Essentially a pure income effect T increases C decreases, l decreases Y increases, w falls
Equilibrium Effects of an Increase in Government Spending PPF shifts down by the increase in G Since we assume G=T, increase in T reduces consumer disposable income Consumption and leisure fall, employment and output rises
GDP, Consumption, and Government Expenditures The model correctly predicts that a large increase in G leads to an increase in output and a decrease in consumption
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
Increase in Total Factor Productivity Increase in z increase in MPN increase in w Income effect Consumption, leisure increase Substitution effect Substitute away from leisure
Effects of an Increase in Total Factor Productivity An increase in z leads to an increase in output and consumption. Labor may increase or decrease depending on the size of substitution vs. income effects
Deviations from Trend in Real GDP and the Solow Residual The model correctly predicts that an increase in z leads to an increase in output and consumption. It can also be consistent with procyclical labor and real wages if the subsitution effect is greater than the income effect of real wages.
Distortionary Taxes Let s extend the concept of competitive equilibrium to include distortionary taxes. Let s consider the example of labor income taxes. The household budget constraint is then C = w 1 t N S + π where t is the labor income tax rate. The firm s problem is unchanged.
Tax distorted Competitive Equilibrium (TDCE) The TDCE is where MRS l,c = w 1 t < w = MRT = MP N TDCE Not Pareto optimal Consumption goes down (income and substitution effects!) Leisure goes up (if substitution effect is larger than income effect)
Any questions? We are now ready to look at handout 3!