科目：個體經濟學一
教授：鄭秀玲
試別：93上第二次期中考
時間：2004年12月09日
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以下各題均需寫出詳細推導過程（繪圖或數學式），才予給分。

1. (10分) Mr. Wang's utility of income function is U=log(M+1), where M
   represents income. From this information you would say that he is _________
   (either risk neutral, risk lover, or risk averter).（需加以證明，才予給分）

2. (10分) Every consumer who has ever lived in country Z on the planet
   Hyperion consumes only two goods, X and Y, and has the utility function
   U(X,Y)=XY. The currency in this country is the fragel. In 1900, the price
   of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita
   income was 72 fragels. In 2000, the price of good 1 was 5 fragels and the
   prices of good 2 was 2 fragels. What is the Laspeyres price index for the
   price level in 2000 relative to the price level in 1900?

3. (10分) A consumer's behavior was observed in three situations with
   different prices and incomes. In situation 1, she chose a bundle that
   cost $1600. In situation 2, she chose a bundle that cost $2500. In
   situation 3, she chose a bundle that cost $3100. The bundle purchased in
   situation 2 would cost $1200 at situation 1 prices. The bundle purchased
   in situation 3 would cost $2000 at situation 2 prices. This consumer's
   behavior is known to satisfy the strong axiom of revealed preferences.
   Therefore,
(a) The bundle purchased in situation 1 must cost less than $3100 at situation
    3 prices.
(b) The bundle purchased in situaiton 3 must cost at least $3100 at
      situation 1 prices.
   (c)The bundle purchased in situation 1 can not cost less than $3100 at
      situation 3 prices.
   (d)The bundle purchased in situation 2 must cost at least $3100 at
      situation 1 prices.

   上述(a)~(d)，何者的敘述是對的？請說明詳細推導過程。

4.（15分）Suppose that apples are a normal good and Miss Chen is currently
   consuming 10 apples at a price of 50 cents each.
   (a)Her ordinary demand curve going through this point is steeper than her
      Slutsky compensated demand curve.
   (b)Her Slutsky compensated demand curve going through this point is steeper
      than her ordinary demand curve.
   (c)Her ordinary demand curve is steeper to the left and her Slutsky
      compensated demand curve is steeper to the right of this point.

   以上(a)~(c)，請選出一正確答案，並請繪圖說明才予給分。

5.（20分）Mary's preferences can be represented by U(X,Y)=min{X,Y}, where X is
   bottles of milk and Y is dollars to spend on other things. She faces prices
   (Px,Py)=(2,1) and her income 12. When the price of a bottle of milk goes up
   to $3, what is the maximum amount that Mary would pay to avoid the price
   increase? In prder to be as well-of as she wae with her original bundle,
   by what amount would Mary's original income have to rise?

6.（20分）John has an income of $1000 this year, and he expects an income of
   $1100 next year. He can borrow and lend money at an interest rate of 10%.
   Consumption goods cost $1 per unit this year and there is no inflation.
   (a)What is the present value of his endowment?
   (b)John has the utility function U(C1,C2)=C1C2. Solve for John's optimal
      choice when the interest rate is 10%.
   (c)When the interest rate is 20%, will he borrow or save in the first
      period? How much?

7.（15分）Upon graduation, you are offered three jobs, as follows:
    Company   Salary    Bonus   Probability of Receiving Bonus
       A     $100,000  $20,000                 0.9
       B     $100,000  $30,000                 0.7
       C     $110,000   -----                 -----

   If you are risk-neutral, which company do you go to work for?


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