[求助]4道效用题

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<p>Charlei has the utility function U(x<sub>1</sub>,x<sub>2</sub>)=X<sub>1</sub>X<sub>2</sub>.His indifference curve passing through 10 apples and 30 bananas will also pass through the point where he consumes 2 apples and ( )</p><p>a.25bananas    b.50bananas   c.152 bananas    d.158bananas   e.150 bananas</p><p>Ambrose's utility function is 4x<sub>1</sub>^(1/2)+x<sub>2</sub> where x<sub>1</sub> represents the units of nuts and x<sub>2 </sub>represents the units of berries. If the price of nuts is 1, the price of berries is 4, and his income is 100, how many units of berries will Ambrose choose?</p><p>a.65      b.9    c.18    d.8   e.12</p><p>If charlis'sutility function is x<sub>1</sub><sup>4</sup>x<sub>2</sub>, the price of apples is p<sub>1</sub>,the price of bananas is p<sub>2</sub>,and his income is m ,then Charlie's demand ofr apples is()</p><p>patience has a utility function u(c<sub>1</sub>,c<sub>2</sub>)=c<sub>1</sub>+0.83c<sub>2</sub>,where c1 is her consumption in period 1 and c<sub>2</sub> is her consumption in period 2. Her income in period 1 is 2 times as large as her income in period 2. at what interest rate will she chooose to consume the same amount in period 1 as in period?( )</p><p></p>

[此贴子已经被作者于2009-3-5 0:39:48编辑过]

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关键词：Indifference consumption represents difference represent

1，e;

2,X1+4X2=100.U=4X1^(1/2)+X2 ,用啦格朗日函数求最大值。

3，同理按照2的方法求。

4，设利率为r,预算线的斜率的绝对值等于1+r.

求： u(c1,c2)=c1+0.83c2的最大值，预算约束是

C2+C(1+r)=+2M1(1+r)+M1(1+r).

能给出详细解题过程吗？我是初学者

nlm0402’s answer to question 1,2,3 is correct!But I can not accept the answers 4 becouse of the function of Budget Constraints.

assumption Patience's income in period 2 is M, under the condition that consume the same amount in period 1 as period 2 the function of Budget constraints should be:

C1+C2=1.5M+0.5(1+r)M+M

[此贴子已经被作者于2009-3-5 12:59:19编辑过]

I think the complementary of the "incomparable " is necessary.
but it should be rethink cautionly.

最头疼的就是英语，还碰上用英语辩论的了，呵呵。

顺便一提，这个题目由于第一期的收入高一倍，所以没有考虑到贷款利息的问题，

如果有存贷利率差，各位认为应该怎么做？

如果是即时复利计算呢？