Question

宏观经济学一题（英文），中英文回答皆可，谢谢！

Consider a household with a horizon of two periods and whose income is 4000 today
and 8.000 tomorrow.

(a) Suppose the real interest rate is r=0.03. What is the household’s wealth in terms of
today’s consumption? What is the household’s wealth in terms of tomorrow’s
consumption? What is the household’s permanent income?

(b) If today’s income unexpectedly increases with 100, what is the change in
permanent income compared to (a)?

(c) If income goes up by 200 permanently, what is the change in permanent income
compared to (a)?

(d) Suppose that the utility function of the household is given by U = A^0.5 * B^0.5 = where
A is today’s consumption and B is tomorrow’s consumption. Calculate optimal
consumption today and tomorrow if r=0.06, income today is 4000, and income
tomorrow is 8.000. Check that the intertemporal budget constraint holds.
详细并正确的答案可以增加悬赏分。

Answer 1

a. 按今天来记： 4000+[8000/（1+0.03]=?
按明天来算： 4000*（1+0.03）+8000=？
b. The permanent income won't change.
c. today: 4200+[8200/（1+0.03]=?
tomorrow: 4200*（1+0.03）+8200=？
d. 最优消费选择在 MRS=1+r=1.06=MUa/MUb=1=B/A (*)

所以有B=A*1.06 跨时际消费约束下，
s.t. A+[1/(1+0.06)]B=4000+[8000/（1+0.06]=?
把（*）中 B=A*1.06代入上式
就可以算出A=？和B=？了，
这个A和B也是最优的消费。（按今天来计）
得数楼主自己去算吧，我只写出式子来。:-）
不知道我的这个做法对楼主有帮助没？本题主要考察了阿伦'费雪的实际选择。

Answer 2

是算持久收入假说吗，我自己也对利息有点搞不清楚，做个记号，还是等下面的人来答吧。