1. One-Period Macro Model Households & Firms Competitive Equilibrium Effects of Productivity Shocks Government Sector

2. Households Chooses: Labor Supply (N s ), leisure (l = 1- N s ), and consumption (c) to subject to given  = real wage rate and a = household wealth (exogenous).

3. Optimal values of {c*,l*}, given  and a, solves:

4. 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*/d  > 0 and dN*/d  = ??

5. Figure 4.12 Real Wage in the United States, 1980–2003

6. Figure 4.13 Average Weekly Hours in the United States, 1980–2003

7. The workweek and real GDP per person in 36 countries: 1980s

8. Firms Chooses labor demand (N d ) and output Y to maximize profits  )  subject to Assume capital stock K fixed  z = Productivity/Technology Shock (“Solow Residual”)

9. Figure 4.20 The Solow Residual for the United States

10. Optimal values of {N*,Y*}, given , solves Implications: (i)dN*/d  < 0(Labor Demand Curve) (ii)dN*/dz > 0(Productivity Shock)

11. Competitive Equilibrium (CE) Sometimes called “general equilibrium” There are many identical “representative” households and firms. Households  {c*,N s } given a and  Firms  {Y*,N d } given . Households are the owners of firms and takes profits as given: a =  Y –  N Market-Clearing: N d = N s = N* = 1-l*(labor mkt) Y* = c*(Goods Mkt)

12. A competitive equilibrium is {c*,N*,Y*  solving: (utility max) (profit max) (prod function) (market-clearing) Where l* = 1 – N*

13. 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).

14. Verify – The Social Planner’s (SP) Objective is to choose allocations {c*=Y*, l*} which solves: subject to and Solution – Identical to the CE.

15. 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).

16. 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  increases..

17. Figure 5.11 Deviations from Trend in Real GDP and the Solow Residual

18. Figure 5.12 The Relative Price of Energy

19. Why dN*/dz = ?? Intuition: (i)(+) z  (+) MPN  (+) ND  (+)   (+) NS (Substitution Effect) (ii)(+) z  (+) firm profits  (+) non-labor income (a)  (-) NS (Income Effect) Consistent with empirical evidence?

20. 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) =  Goods Market Clearing: Y = C + G Labor market Clearing:N d = N s

21. CE Model with Government Households  {c*,N s } given a and  Firms  {Y*,N d } given . Government  Sets G = T Households are the owners of firms and takes profits as given: a =  Market-Clearing: N d = N s = N* = 1-l*(labor mkt) Y* = c*+G(Goods Mkt)

22. A competitive equilibrium given G is {c*,N*,Y*  solving:

23. Effects of Government Purchases Negative Income Effect: dc*/dG < 0 dl*/dG 0 du(c*,l*)/dG < 0 G = 0 would maximize welfare.

24. 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.

25. The Growth Rate of U.S. Real Gross Domestic Product since 1870

26. Figure 5.7 GDP, Consumption, and Government Expenditures

27. 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!

28. 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!

29. In basic model the need for government expenditures (G) is exogenous (no direct benefits to private sector). Modifications: (i)Substitutability of public & private consumption: (ii)Productive Government expenditures:

30. Proportional (Marginal) Taxes Most individual taxes in US are collected via marginal income taxes: (i)Wealth: a =  (ii)Consumer’s BC: (iii)Government’s BC:

31. Competitive Equilibrium w/ proportional taxes is {c*,N*,Y*} and  solving Where T = t  N* = G

32. Graphical example - Effect of tax rate: dc*/dt < 0 dl*/dt > 0  dN*/dt < 0 CE w/ proportional taxes is NOT Pareto Optimal Laffer Curve: The non-monotonic relationship between tax rates t and tax revenue REV = t  N. Supply Side Economics  d(REV)/dt < 0.

33. 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%

34. Figure 5.18 Federal Personal Taxes as a Percentage of GDP