A Closed-Economy One-Period Macroeconomic Model

Transcription

1 A Closed-Economy One-Period Macroeconomic Model Economics Intermediate Macroeconomics Aaron Hedlund University of Missouri Fall 2015 Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

2 Government Previously addressed consumer and firm optimization. Remaining sector: government. For now, exogenous government purchases G of consumption goods financed by lump sum tax T. No public goods yet. Balanced budget assumption: G = T This setup allows for basic analysis of the effects of fiscal policy. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

3 Competitive Equilibrium Now we define a competitive equilibrium for a closed economy, i.e. an economy with no external trade, given exogenous G = T and K. A competitive equilibrium in this economy consists of a wage w and allocations C, N s, and N d such that: 1 C and N s satisfy the consumer s optimization problem. 2 N d satisfies the firm s profit maximization problem, giving π = zf (K, N d ) wn d. 3 The labor market clears: N d = N s. 4 The goods market clears: zf (K, N d ) = C + G. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

4 Equilibrium Conditions and Walras Law Walras law: conditions (1) (3) (4). Substitute G = T, π = zf (K, N d ) wn d, and N d = N s N into C = wn s + π T. The equilibrium equations are w = U l(c, h N) U C (C, h N) C = wn + π G w = zf N (K, N) π = zf (K, N) wn After some substitutions we get U l (zf (K, N) G, h N) U C (zf (K, N) G, h N) = zf N(K, N) MRS l,c = MRT l,c = MP N. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

5 Optimality and the Social Planner Problem An allocation is Pareto optimal if there are no other allocations that make someone better off without making someone else worse off. Only one representative agent, so a Pareto optimum solves the following social planner problem: Solution conditions: max U(C, h N) such that C + G = zf (K, N) C,N U l (C, h N) U C (C, h N) = zf N(K, N) C + G = zf (K, N) U l(zf (K, N) G, h N) U C (zf (K, N) G, h N) = zf N(K, N) Same as the competitive equilibrium! Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

6 Fundamental Welfare Theorems First welfare theorem: under certain conditions, a competitive equilibrium is Pareto optimal. A formal statement of the magic of the invisible hand. Second welfare theorem: under certain conditions, a Pareto optimum can be decentralized as a competitive equilibrium. Sources of social inefficiencies: 1 Externalities: activities for which an individual does not account for the costs/benefits imposed on others. E.g. factory pollution. No property rights/markets for pollution. 2 Distortionary taxation: causes MRS l,c < MP N labor wedge. 3 Market power: lack of competition. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

7 The Effects of Government Spending - Theory What are the effects of an increase in G? Comparative statics: C G = U ll + zf NN U C zf N U Cl < 0 l G = N G = U Cl + zf N U CC < 0 w G = zf N NN G < 0 Y G = zf N N G > 0 where z 2 F 2 N U CC + 2zF N U Cl U ll zf NN U C > 0 Y and N but C (crowding out). Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

8 Do Business Cycles Result from Government Spending? WWII: sharp increase in G, smaller increase in Y, and small decrease in C. Model predictions consistent with procyclical Y and N. Model predictions inconsistent with procyclical C and w. Result: government spending shocks unlikely to be the main cause of business cycles. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

9 The Effects of TFP Changes - Theory What are the effects of an increase in z? Comparative statics: C z = F (U ll + zf NN U C zf N U Cl ) + FNzU 2 C l z = F NU C + F (U Cl zf N U CC ) where > 0 z 2 FNU 2 CC + 2zF N U Cl U ll zf NN U C > 0 l Income and substitution effects: z subst = F NU C < 0 and l z inc = l z l z subst > 0. Overall labor/leisure effect ambiguous. Real wage increases: w z > 0. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

10 The Effects of TFP Changes - Data Model consistent with long run increases in Y, C, w, and approximately constant N. Employment procyclical in the short run substitution effect must dominate. RBC theory: business cycles driven primarily by shocks to z. How to reconcile long run and short run evidence on labor supply? Intertemporal substitution. Big debate over micro and macro elasticity of labor. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

11 What are TFP Shocks? TFP is share of output not accounted for by capital and labor inputs. Shocks to TFP include technological innovation, weather changes, changes in government regulations, energy price fluctuations, etc. Other important factors in recessions: monetary policy, credit crises, geopolitical turmoil. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

12 The Recession and Stimulus Spending ARRA (stimulus bill) passed in 2009 increased spending by $787 billion = 5.5% of GDP. However, includes $288 billion in tax cuts, $209 billion in transfers, and $290 billion in G a 10.1% increase. Goal is to increase GDP during recession, possibly caused by a decrease in z. Why? Competitive equilibrium is Pareto optimal, so economy optimally responds to z shocks. G is wasteful in the model, causing increases in Y but decreases in C and welfare. Missing elements in the model? Keynesians believe that the economy can sometimes be inside the PPF and increasing G can put the economy closer to potential. Later we will compare RBC and Keynesian business cycle theories. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

13 Government Expenditures and Transfers Government expenditures G have been decreasing relative to GDP (left) while transfers have been increasing over time, causing increases in total government outlays (right). Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

14 Distortionary Taxation A Simplified Model Production function Y = zn. Profits π = zn d wn d = (z w)n d. Proportional labor income tax t. Balanced budget: G = twn d. Equilibrium conditions: w = z w(1 t) = U l(c, h N) U C (C, h N) C = w(1 t)n and G = twn After some substitutions we get z(1 t) = U l(z(1 t)n, h N) U C (z(1 t)n, h N) The equilibrium is not Pareto optimal. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15

15 Tax Revenue and the Laffer Curve Tax revenue REV (t) = tzn(t) = rate base. REV (t) first increases, then decreases the Laffer curve. Maximum revenue REV = t zn(t ). For any G < REV, there are two rates t 1 and t 2 that can finance it. Econ 4353 (University of Missouri) Static Equilibrium Fall / 15