跨時求算利率 94中正國經 麻煩大家幫我看看 - 經濟

來源: 94中正國經

科目:總經

問題:
Consider an economy consisting of 100 two-period-lived-agents.Agent h receives
exogenous real income in both periods as follows:

|-(2,1),h=2,4,...,100(the even)
(y1,y2)=|
|-(1,1),h=1,3,...,99 (the odd)

Assume there is no technology for converting the current period good into the
feture period good,and the good is perishable.
Agents can borrow or lend. Each agent has the same utility function

U(c1,c2)=lnC1+lnC2.

1.Find the competitive equilibrium value of the real net interest rate r

2.Find the future period consumption for the borrowers c2

我的想法:
MAX U(c1,c2)=lnC1+lnC2.

st C1 + C2/1+r = y1 + y2/1+r

MRSc1c2= C2/C1=1+r ===> c2=(1+r)c1

帶回st c1 = 0.5*{y1 + y2/1+r}

均衡時 社會總合儲蓄為零

所以 50*0.5*{y1 + y2/1+r} + 50*0.5*{y1 + y2/1+r} =50*2+50*1
第一類消費者 第二類消費者

將條件帶入得
2 + 1/(1+r) + 1 + 1/(1+r) = 6

r = -1/3

請問利率求算出來有可能是負的嗎 還是我解的過程有哪邊錯

麻煩大家幫我看一下 想很久都想不通

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