Question

h different quanti- d saves 32 percent 5. Two countries, Richland and Poorland described by the Solow growth model. The the same Cobb-Douglas production functi F(KL) = A KL, but with different ties of capital and labor. Richland saves 32 of its income, while Poorland saves 10 perce Richland has population growth of 1 percent year, while Poorland has population growth of 3 percent. (The numbers in this problem are che sen to be approximately realistic descriptions of rich and poor nations.) Both nations have tech- nological progress at a rate of 2 percent per year and depreciation at a rate of 5 percent per year. a. What is the per-worker production function f(k)? b. Solve for the ratio of Richland's steady-state income per worker to Poorland's. (Hint: The parameter a will play a role in your answer.) c. If the Cobb-Douglas parameter a takes the conventional value of about 1/3, how much higher should income per worker be in Richland compared to Poorland? d. Income per worker in Richland is actually 16 times income per worker in Poorland. Can you explain this fact by changing to value of the parameter a? What must it Can you think of any way of justifying a value for this parameter? How else you explain the large difference in inc between Richland and Poorland? 1 person must it be? justifying such ow else might

Answer 1

Answer a Given that, F(k, () = Akdelah Bichodes saues 32 percent of its income · Poodland saves lo percent of its income. Richard population growth of Ipercent of per year. Roodland population growth of 3 percent. technological progress at a sate a percent per year depreciation at a sate 5 procent per year. a) . Pes- uložked poduction Fonction fees fck) = ? ped-wlooked production & Akald / L= Akd . © solve Richestens steady-state. steady-state, Dk = Spek) - (8+n+g]k=0 hence, SAI= cst neg)k, plogging into pez. nelošleed pčoduction yout= Arta li mited skicksand cr Spielen op de 's Last nrichland +9 I poodland | Spoorland L3n poodland to

- from Cineren data. . If Alpha cavalls / theon Richland should bc 4". * tlete, two times fiches than poorland.. when the natura = 16, then, it must be the case that 6 2 2 = 2, . which in toon requires that alpha cavals 2/3. & hence, if the cobb- Douglas production function putsal t of the weight on capital and only / on laboo, a then, we can explain of 16- fold differsonce in levels of I income ped worked. 1 * one way to Castify this to might be to think about capital more broadly to include homon- Capitala which meest also be accommulated thaough uvestment much in the way one accumlates physical - capital