chapter4 - Chapter 4 Numerical Problems 1. General...

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Chapter 4 Numerical Problems 1. General formulation of the problem: With income of Y1 in the first year and Y2 in the second year, the consumer saves S1=Y1 - C1 in the first year and S2=Y2 - C2 in the second year, where C1, C2 are the consumption amounts. Saving in the first year earns interest at rate r, where r is the real interest rate. And the consumer needs to accumulate just enough after two years to pay for college tuition, in the amount T. As S2 =0 and W3=0, C2+T=Y2+(W1+S1)(1+r) where W1 is the level of wealth at the beginning of this period, W2=W1(1+r) will be the level of assets at the beginning of next period. So C2+T=Y2+(W1+Y1-C1)(1+r) or C1+ C2(1+r)+T= Y2+(W1+Y1)(1+r) or C1/(1+r)+C2+T/(1+r)= Y2/(1+r)+W1+Y1 As C2=C1=C we have C+ C (1+r)= Y2+(W1+Y1)(1+r)-T So C= (Y2+(W1+Y1)(1+r)-T)/(2+R) and S1=Y1-C a. Y1 = Y2= $50,000 r = 10 %, T = $12,600. C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C= $44,000. And then S1 = Y1 - C = $50,000 - $44,000 = $6000. b. C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C = $46,200. S1 = Y1 - C = $54,200 - $46,200 = $8000. This illustrates that a rise in current income increases savings. c. Y2 = $54,200. C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C = $46,000. S1 = Y1 - C = $50,000 - $46,000 = $4000. This illustrates that a rise in future income decreases savings. d. With the increase in wealth of W1, the total amount invested for the second period is W1 + Y1 - C, C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C = $44,550. S1 = Y1-C =$50,000 - $44,550 = $5450. This illustrates that a rise in wealth decreases savings. e. T = $14,700. C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C = $43,000. Then S1 =Y1 - C = $50,000 - $43,000 = $7000. The rise in targeted wealth needed in the future raises current saving. f. r = 25%. C= (Y2+(W1+Y1)(1+r)-T)/(2+R) implies C = $44,400. Then S1 = Y1 - C = $50,000 - $44,400 = $5600. The rise in the real interest rate, with a given wealth target, reduces current saving. 2. a.
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This chart shows the MPK f as the increase in output from adding another unit of fabricator: # Fabricators Output MPK f 0 0 - 1 100 100 2 150 50 3 180 30 4 195 15 5 205 10 6 210 5 b. uc = (r + d)p k =(0.12 + 0.20)$100 = $32. The firm should buy two fabricators, since for the second fabricator MPK f =50 > 32 = uc. But for the third fabricators, MPK f = 30 < 32 = uc. You want to add fabricators only if the future marginal product of capital (the benefit of adding a fabricator) exceeds the user cost of capital (the cost of adding the fabricator). The MPK f of the third fabricator is less than its user cost, so it should not be added. C. When r = 0.08, uc =(0.08 + 0.20)$100 = $28. Now they should buy three fabricators, since MPK f = 30 > 28= uc for the third fabricator and MPK f = 15 < 28 = uc for the fourth fabricator. d.
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This note was uploaded on 07/24/2008 for the course ECON 360 taught by Professor Wang during the Fall '06 term at SUNY Buffalo.

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chapter4 - Chapter 4 Numerical Problems 1. General...

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