Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
One-Period Macro Model Households & Firms Competitive Equilibrium Effects of Productivity Shocks Government Sector Households • Chooses: Labor Supply (Ns), leisure (l = 1- Ns), and consumption (c) to max u (c, l ) subject to c wN s a N l 1 s given w = real wage rate and a = household wealth (exogenous). • Optimal values of {c*,l*}, given w and a, solves: ul (c*, l*) MRS c ,i w uc (c*, l*) c* w (1 l*) a • Implications (i) Changes in wealth creates a pure income effect: dc*/da > 0 dl*/da > 0 and dN*/da < 0 (ii) Changes in real wages creates both an income and substitution effect: dc*/dw > 0 and dN*/dw = ?? Figure 4.12 Real Wage in the United States, 1980–2003 Figure 4.13 Average Weekly Hours in the United States, 1980–2003 The workweek and real GDP per person in 36 countries: 1980s Firms • Chooses labor demand (Nd) and output Y to maximize profits (P): max{ P Y wN } d subject to Y zF ( K , N ) d d d Y zF ( N ) f ( N ) Assume capital stock K fixed z = Productivity/Technology Shock (“Solow Residual”) Figure 4.20 The Solow Residual for the United States • Optimal values of {N*,Y*}, given w, solves MPN f N ( N ) w d Y* f (N ) d • Implications: (i) dN*/dw < 0 (ii) dN*/dz > 0 (Labor Demand Curve) (Productivity Shock) Competitive Equilibrium (CE) • • • • • • Sometimes called “general equilibrium” There are many identical “representative” households and firms. Households {c*,Ns} given a and w. Firms {Y*,Nd} given w. Households are the owners of firms and takes profits as given: a = P Y – wN Market-Clearing: Nd = Ns = N* = 1-l* (labor mkt) Y* = c* (Goods Mkt) • A competitive equilibrium is {c*,N*,Y*,w*} solving: ul ( c *,l *) uc ( c *,l *) w* f N ( N *) w * (utility max) (profit max) Y * f ( N *) (prod function) Y* c * (market-clearing) Where l* = 1 – N* Pareto Optimality • An allocation is Pareto Optimal if no other feasible allocation can improve the welfare of one without reducing the welfare of another. • PO is a statement about efficiency not necessarily fairness or equality. • The Welfare Theorem: The competitive equilibrium (CE) is Pareto Optimal (PO). • Verify – The Social Planner’s (SP) Objective is to choose allocations {c*=Y*, l*} which solves: max u (c, l ) subject to c Y zF ( K , N ) zf ( N ) and N l 1 Solution – Identical to the CE. • The Welfare Theorem is basically Adam Smith’s Invisible Hand. • Social planning is difficult to implement. Competitive equilibrium (market system) is easy. • Exceptions to the theorem: (i) Externalities not internalized by markets (ii) Non-competitive markets. (iii) Government policies (tax distortions). Productivity Shocks • Productivity shocks (z): Changes the efficiency of capital and labor (technology, weather, cost of energy, government regulations, ect) • An increase in z: Income effect (+) C and (+) l Substitution Effect (+) C and (-) l Hence dc*/dz > 0 and dN*/dz = ?? • In the case where both effects are roughly equal, Y and w increases.. Figure 5.11 Deviations from Trend in Real GDP and the Solow Residual Figure 5.12 The Relative Price of Energy • Why dN*/dz = ?? Intuition: (i) (+) z (+) MPN (+) ND (+) w (+) NS (Substitution Effect) (ii) (+) z (+) firm profits (+) non-labor income (a) (-) NS (Income Effect) • Consistent with empirical evidence? One Period CE Model with Government • Government sector (i) Collects revenues from taxes (T). (ii) Purchases goods and services (G) • Assume balanced budget (G = T) • Household wealth (a) = P T Goods Market Clearing: Y = C + G Labor market Clearing: Nd = Ns CE Model with Government • • • • • Households {c*,Ns} given a and w. Firms {Y*,Nd} given w. Government Sets G = T Households are the owners of firms and takes profits as given: a = PT Market-Clearing: Nd = Ns = N* = 1-l* (labor mkt) Y* = c*+G (Goods Mkt) • A competitive equilibrium given G is {c*,N*,Y*,w*} solving: ul ( c *,l *) uc ( c *,l *) w* f N ( N *) w * Y * f ( N *) Y * c * G Effects of Government Purchases • Negative Income Effect: dc*/dG < 0 dl*/dG < 0 dN*/dG and dY*/dG > 0 du(c*,l*)/dG < 0 • G = 0 would maximize welfare. Effects of Government Purchases • Stabilization Policy: The government can use government purchases to stabilize output from productivity shocks (dG/dz > 0) but it will lead to a further decrease in economic welfare. The Growth Rate of U.S. Real Gross Domestic Product since 1870 Figure 5.7 GDP, Consumption, and Government Expenditures Comparison with IS Model (Simple Income Determination) • CE vs IS: (i) Both Predict dY/dG > 0. Government purchases can be used to stabilize GDP and business cycles. (ii) Increase in G alone, then dY/dG > 0 and dy/dC > 0 “welfare” increases. (iii) If G = T, then dY/dG = 1 and dY/dC = 0. dC/dG = 0 “welfare” constant. (iv) CE dC/dG < 0 and welfare decreases! Comparison with IS-LM • CE vs IS-LM: Not entirely comparable since no saving/interest rate in CE model. (i) Both Predict dY/dG > 0. Government purchases can be used to stabilize GDP and business cycles. (ii) Increase in G alone, then dY/dG > 0 and dy/dC might be > 0, so “welfare” ambiguous. (iii) CE dC/dG < 0 and d (welfare)/dG < 0! • In basic model the need for government expenditures (G) is exogenous (no direct benefits to private sector). • Modifications: (i) Substitutability of public & private consumption: CT c G, 0 1 (ii) Productive Government expenditures: z z0 G, where 0 Proportional (Marginal) Taxes • Most individual taxes in US are collected via marginal income taxes: (i) Wealth: a=P (ii) Consumer’s BC: c w (1 t ) N P s (iii)Government’s BC: G T twN s • Competitive Equilibrium w/ proportional taxes is {c*,N*,Y*} and w* solving MRS c ,l ul w * (1 t ) uc f N ( N *) w * Y * f ( N *) c * G N * N d N s (1 l*) Where T = tw*N* = G • Graphical example - Effect of tax rate: dc*/dt < 0 dl*/dt > 0 dN*/dt < 0 • CE w/ proportional taxes is NOT Pareto Optimal MRS c ,l ul w * (1 t ) MPN MRT uc • Laffer Curve: The non-monotonic relationship between tax rates t and tax revenue REV = twN. Supply Side Economics d(REV)/dt < 0. • Evidence: (i) Economic Recovery Act of 1981 * Highest Income Tax Bracket cut from 70% to 50% * Lowest cut from 14% to 11% (ii) G.W. Bush Tax Cuts of 2001 * 40%35% 36%33% 31%28% 28%25% Figure 5.18 Federal Personal Taxes as a Percentage of GDP