高宏1期中考试试卷

lump-sum transfers. How does the tax affect the c = 0 loces and the k = 0 locus. How does the economy respond to the adoption of the tax at time 0? What are the dynamics after time 0? How do the values of c and k on the new balanced growth path compare with their values on the old balanced growth path? (b) If the government does not rebate the revenue from the tax but instead uses it to make government purchases. How does the tax affect the c = 0 loces and the k = 0 locus. How do the values of c and k on the new balanced growth path compare with (a)? 5、 Consider a Diamond economy where g=0, production is C-D, and utility is logarithmic. Suppose the government taxes each young individuals an amount T and uses the proceeds to pay benefits to old individuals, thus each old person receives (1+n)T. (a) How, if at all, does this change affect the optimal consumption (C1,t , C2,t+1 )? (b) How, if at all, does this change affect the balanced-growth-path value of k? (c) If the economy is initially on a balanced growth path that is dynamically inefficient, how does a marginal increase in T affect the welfare of current and future generations?

∂F ∂K
− δ.
U e t e nt ln c(t )dt
0
Where, c (t ) denotes the per capita consumption denotes the rate of time preference for utility, 0 (Positive value means that the later the utility obtained, the lower is its value), n denotes the population growth rate, n<ρ. Flow budget constraint for household consumption is
1、 Consider a Solow economy that is on its balanced growth path。Suppose that the production function is Cobb-Douglas，n denotes the population growth rate，δ denotes the depreciation rate，g denotes the rate of technological progress. （a） Find expressions for k ∗ and y ∗ as function of the parameters of the model. （b） Now suppose that the rate of population growth rises. What happens to the balanced-growth-path values of capital per worker ， output per worker and consumption per worker？ Sketch the paths of these variables as the economy moves to its new balanced growth path. （c） What is the golden-rule of k and what saving rate is needed to yield the golden-rate capital stock？ 2、 Suppose that the production function F（K，AL）is Cobb-Douglas. Assume both labor and capital are paid their marginal products. Let w denotes ∂F/ ∂L and r denotes (a) Show that r = f ′ k − δ. (b) Show that w=A[f(k)-kf ′ (k)]. (c) Show that under constant returns, wL+rK=F(K,AL)- δK (d) Suppose the economy begins with a level of k more than k*. As k moves towards k*, is r growing at a rate greater than, less than, or equal to its growth rate in the balanced growth path? What about w? Please explain. 3、 Assume there is an infinitely lived household in the market economy. Assume that the household’s utility function is:
assets, r denotes interest income for the household, δ denotes the depreciation rate. k 0 0 is the household's initial assets constraints and it`s given. Try to use the optimal control method to solve the model and derive the optimal consumption path. 4、 Consider a RCK economy that is on its balanced growth path. Suppose at time 0, the government switches to a policy of taxing investment income at rate τ. Thus the real interest rate that households face is now given by r(t)=(1-τ) f ′ (k(t)). Assume that this change in tax policy is unanticipated (a) Assume that the government returns the revenue it collects from this tax through
k (t ) rk (t ) c(t ) nk (t ) k (t ) k
0 1
dk / dt denotes per capita household asset growth, k denotes per capita household where k