Molly拥有柯布-道格拉斯效用函数U(c1，cz)=c1c°，其中0＜a＜1，c和C2分别是她在时期1和时期2的消费。我们前面已经看到，如果效用函数的形式是U(x1，x2)=xfx ，并且预算约束的形式是“标准”形式pix1+pzxz=m，那么商品的需求函数就是xi=am/p1和x2=(1-a)m/pz。 (a)假设Molly时期1的收入是m1，时期2的收入是mz。写出她以现值表示的预算约束。 (b)我们想要对这一预算约束与标准形式的预算约束进行比较。对于Molly的预算 约束，pi是什么？ p2是什么？ m是什么？ (c)如果a=0.2，解出Molly每期消费的需求函数，她每期的消费都是m1、mz和r 的函数。时期1消费的需求函数是C1= 。时期 2消费的需求 函数是C2= (d)利率的上升将会使她时期1的消费 。利率上升将 她时期2的消费， 她时期1的储蓄。

(a) Molly以现值表示的预算约束是：c1 + c2/(1+r) <= (m1 + m2/(1+r)), 其中r是时期1到时期2的折现率。

(b) 对于Molly的预算约束，pi是时期1商品的价格，p2是时期2商品的价格，m是时期1和时期2的现值收入之和。

(c) 当a=0.2时，Molly每期消费的需求函数为：C1=0.2(m1 + m2/(1+r))/p1，C2=0.8(m1 + m2/(1+r))/p2。

(d) 利率的上升将会使Molly减少时期1的消费，增加时期2的消费，以增加她的储蓄。具体来说，如果利率上升，她将更愿意将一部分收入储蓄到时期2，以获得更高的回报。因此，她会减少时期1的消费，增加时期2的消费，以便储蓄更多的资金。

相关问题

1. ―Thanks for your tips. ―___________________ A. No， thanks. B. It' s my pleasure. C. Yes， please. [答案] B 2. ―Hi， Molly， are you free this afternoon? ―___________________ A. Yeah， no plans yet. B. Let' s see something special. C. That' s a good idea. [答案] A 3. ―Where have you been these days? ―___________________ A. Yes， I have. B. Actually， I have moved to the country. C. You are wanted on the telephone. [答案] B 4. ―Molly， look at this. The newspaper says we should sort trash. ―___________________ A. That would be great! B. No problem. C. It is obvious. [答案] A 5. ―I' ve got a bad cold today.

以下是去重后的题目：

1. ―Thanks for your tips. ―___________________ A. No， thanks. B. It' s my pleasure. C. Yes， please. [答案] B
2. ―Hi， Molly， are you free this afternoon? ―___________________ A. Yeah， no plans yet. B. Let' s see something special. C. That' s a good idea. [答案] A
3. ―Where have you been these days? ―___________________ A. Yes， I have. B. Actually， I have moved to the country. C. You are wanted on the telephone. [答案] B
4. ―Molly， look at this. The newspaper says we should sort trash. ―___________________ A. That would be great! B. No problem. C. It is obvious. [答案] A
5. ―I' ve got a bad cold today.

以下数据给我一个去重正则表达式：1. ―Thanks for your tips. ―___________________ A. No， thanks. B. It' s my pleasure. C. Yes， please. [答案] B 2. ―Hi， Molly， are you free this afternoon? ―___________________ A. Yeah， no plans yet. B. Let' s see something special. C. That' s a good idea. [答案] A 3. ―Where have you been these days? ―___________________ A. Yes， I have. B. Actually， I have moved to the country. C. You are wanted on the telephone. [答案] B 4. ―Molly， look at this. The newspaper says we should sort trash. ―___________________ A. That would be great! B. No problem. C. It is obvious. [答案] A 5. ―I' ve got a bad cold today.

如果你想对这些数据进行去重，可以使用以下正则表达式：

pattern = r'―.+―'

这个正则表达式可以匹配所有以"―"开头和结尾的字符串，其中"."可以匹配任意字符，"+"表示匹配前面的字符一次或多次。使用这个正则表达式可以得到以下结果：

1. ―Thanks for your tips. ―
2. ―Hi， Molly， are you free this afternoon? ―
3. ―Where have you been these days? ―
4. ―Molly， look at this. The newspaper says we should sort trash. ―
5. ―I' ve got a bad cold today.

这些结果已经去重，可以直接使用。