科目：個體經濟學一
教授：鄭秀玲
試別：93上第一次期中考
時間：2004年10月21日
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1. (10分) Mr. Wang has a utility function U(X,Y)=(X+3)(Y+4). The price of X
   is $1 and the price of Y is $1. When he maximizes his utility subject to
   his budget constraint, he consumes positive amounts of both goods. How
   many  units of X and Y will he consume respectively?

2. (15分) John consumes only goods 1 and 2. His utility function is
   U(X1,X2) = X1+X2+min{X1,X2}. Please draw a set of his indifference curves
   precisely and discuss the characteristics of these curves.

3. (15分)Mary consumes goods X and Y. Her indifference curves are described
   by the formila Y=K/(X+7). Higher values of K correspond to better
   indifference curves. Please draw a set of her indifference curves precisely
   and discuss the characteristics of these curves.

4. (15分) 請分別就下面兩函數，求 dy/dx

(1) y = x/(x-1)^(1/2)


(2) y = ln{e^x*(2x+1)}

5. (15分) 請分別就下列效用函數，求其邊際效用，即MU1和MU2

(1) U(X1,X2) = 10 ( X1^2 + 2X1X2^2 + X2 ) - 50
(2) U(X1.X2) = X1X2 ( 1 - X1X2 )

6. (10分) Mr. Chen's utility function is 3X+Y, where X is his consumption of
   berries and Y is his consumption of apples. If the total cost of X units is
   X^2, the price of apple is $10, and Chen's income is $260, how many units of
   berries will he consume?

7. (20分) Please calculate the demand functions and draw the inverse demand
   curves for good 1 in the following utility functions respectively:

(1) U(X1,X2) = X1+X2
(2) U(X1,X2) = lnX1+X2

where the prices of good 1 and good 2 are P1 and P2; m is the consumer's income

∮完卷∮