课程名称：总体经济学 课程性质：商院选修 课程范围：成长理论、Golden-rule 开课教师：赵世伟 开课学院：商学院 开课系级： 考试日期(年月日)：2011/04/22 考试时限(Mins)：9:10AM~11:30AM(140分钟) 附注： 试题本文： Note:The full score is 100 points. Any violation of academic integrity is NOT allowed ----------------------------------------------------------------------------- 1.Consider the production funtion Y=K^α(AL)^(1-α) where 0<α<1,K is capital input, L is labor input, and A is technology level. (a) (10%) Let y=Y/AL and k=K/AL. Derive the expression of dk/k. (hint:Recall that dK=sY-δK, where s is saving rate and δ is the rate of capital depresiation. In addition, the population growth rate of technological progress is g.) (b) (10%) Solve for the steady-state value y* and c*, where c=C/AL and C is consumption. (c) (5%) Solve for the golden-rule value k*. (d) (5%) What saving rate is needed to yield the golden-rule level of capital. 2.To explain sustainable economic growth, some economists proposed the "Ak" model,ie.the production funtion is Y=AK. (a) (10%) Let y=Y/L and k=K/L. Derive the growth rate of output per worker dy/y. (b) (10%) Why this model might be able to explain sustainable growth？ Use your result in (a) to constitute your arguments. 3.Consider a representative agent in a static economy with the preference U(C,l), where C is consumption and l is hours of leisure. His decision and leisure is subject to the following constraints: l+L=1, C =V+(1-T)wL, where L is hours of work, w is real wage rate, V is transfer payment(from the government) and T is labor income tax rate. (a) (10%) Derive the equilibrium condition for this decsion problem. (b) (5%) Analyze how consumption and labor will change due to a rise in real wage rate w. (c) (5%) Analyze how consumption and labor will change due to a rise in labor income tax rate T. 4.(10%) Consider the production funtion Y=AK^αL^(1-α) where 0<α<1,K is capitalinput, L is labor input, and A is technology level. Use growth accounting todemonstrate how you would infer the techology growth rate dA/A. 5.Consider a two-period endowment economy (i.e. no production) discussed in class. Suppose that an earthquake hits the economy at the beginning of the first period. Both real interest rate and life-time wealth are negatively affected. (a)(10%) Analyze how current and future choices of consumption will change due to this one-time shock. (b)(10%) Dose the mechanism of temporary shock explain the fluctuation of consumption well？ If yes, elaborate why this mechanism work；if no, explain how this mechanism should be modified. --

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