(1) Numerical Problem 5, Chapter 3, page 101 for 8th edition, pages 104 for 9th edition, page 108 for the 10th edition.Consider an economy in which the marginal product of labor MPN is MPN = 309 – 2N, where N is the amount of labor used. The amount of labor supplied, NS, is given by NS = 22 + 12w + 27,where w is the real wage and T is a lump-sum tax levied on individuals. a. Use the concepts of income effect and substitution effect to explain why an increase in lump-sum taxes will increase the amount of labor supplied. b. Suppose that T = 35. What are the equilibrium values of employment and the real wage? c. With T remaining equal to 35, the government passes minimum-wage legislation that requires firms to pay a real wage greater than or equal to 7. What are the resulting values of employment and the real wage? Note: In the 8th, 10th editions, the MPN is MPN = 309 – 2N while in the 9th edition, the MPN is MPN = 3095 – 2N. I will treat either expression as correct when I mark your homework.However, I believe that the expression in the 8th edition makes more sense given the rest of the problem. (2) Numerical Problem 7, Chapter 4, pages 148-149 for 8th edition, pages 152 for 9th edition, page 156 for the 10th edition.Suppose that the economy wide expected future marginal product of capital is M PKf = 20–0.02K,where K is the future capital stock. The depreciation rate of capital, d, is 20% per period. The current capital stock is 900 units of capital. The price of a unit of capital is 1 unit of output.Firms pay taxes equal to 15% of their output. The consumption function in the economy is C =100+0.5Y – 200r, where C is consumption, Y is output, and r is the real interest rate. Government purchases equal 200, and full-employment output is 1000. a. Suppose that the real interest rate is 10% per period. What are the values of the tax-adjusted user cost of capital, the desired future capital stock, and the desired level of investment? b. Now consider the real interest rate determined by goods market equilibrium. This part of the problem will guide you to this interest rate. i. Write the tax-adjusted user cost of capital as a function of the real interest rate r. Also write the desired future capital stock and desired investment as functions of r. ii. Use the investment function derived in Part (i) along with the consumption function and government purchases, to calculate the real interest rate that clears the goods market.What are the goods market-clearing values of consumption, saving, and investment? What are the tax-adjusted user cost of capital and the desired capital stock in this equilibrium?

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