answerstohomework4spring2007

answerstohomework4spring2007 - Economics 302 Spring 2007...

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Economics 302 Spring 2007 Homework #4 Due Tuesday, March 27 Homework will be graded for content as well as neatness. Sloppy or illegible work will not receive full credit. 1. You live in country “I-love-spring-and-gosh-I-wish-I-could-go-outside-now” (ILSAG, for short). ILSAG has a Cobb Douglass production function Y=K 1/2 L 1/2 . The hard- working citizens of ILSAG save 20% of their incomes and the depreciation rate in the economy is 10%. a. According to the Solow model, what should be the steady-state level of capital per worker? k ss = 4. b. What would be the “golden rule” level of capital per worker? y=k 1/2 , so MPK=1/(2*k^1/2), as in the book, (see pg203). Setting MPK= δ , gives k gold =25. c. What savings rate would give rise to the golden rule level of capital? The golden rule steady state level of capital would be achieved if citizens saved 50% of their income. d. Suppose you are the almighty ruler of ILSAG and your dutiful citizens do everything you tell them. If you care only about your citizens long-run happiness (read: consumption) what fraction of their savings should you have your citizens save? The gold rule level! So, 50% e. Given your last answer, suppose that you tell your people to switch their initial savings rate from what it was initially to the rate that would make them happiest in the long-run. What will be the dynamics of the capital stock in the short run? The capital stock will increase in the short-run, eventually converging to a higher steady- state f. What will be the dynamics of the capital stock in the long run?
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