chapter4

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

This preview shows pages 1–3. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 11

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online