科目：個體經濟學一
教授：鄭秀玲
試別：92學年度上學期第一次期中考
時間：2003年10月23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)，才與給分。
1. (10分) Shirley's preferences between two commodities ( X and Y) can be
represented by U(X,Y)=X+2Y.
(a) Would U(X,Y)=100X+200Y represent Shirley's preferences?
(b) Would U(X,Y)=(5X+10Y)^2 represent Shirley's preferences?
(c) Would U(X,Y)=1/X+2Y represent Shirley's preferences?
2. (16分，其中(d)為12分) John's utility function is U(X,Y)=min{X,Y^2}.
(a) If John consumes 4 units of X and 3 units of Y, what is his utility
level?
(b) If John consumes 4 units of X and 2 units of Y, what is his utility
level?
(c) If John consumes 5 units of X and 2 units of Y, what is his utility
level?
(d) Please draw a set of John;s indifference curves precisely.
3. (10分) Please draw a budget line for each case,
(a) P1=0, P2=1, and m=10
(b) P1=P2, m=15P1
(P1, P2 are the prices for good 1 and good 2 respectively, m is income)
4. (12分) Jack's utility function is U(X1,X2)=(4X1)^1/2+(X2). If the price of
good 1 is $1, the price of good 2 is $6, and his income is $264,
how many units of good 1 and good 2 will Jack choose to maximize
his utility?
5. (16分)請分別求下列效用函數之MRS及MRS的變化率，
(a) U(X1, X2)=lnX1+X2
(b) u(X1, X2)=[(X1)^c]*[(X2)^d]
6. (15分) David has the utility function U(X,Y)= X+3Y,
(a) Please draw the indifference curve connecting bundles that give David
a utility of 6.
(b) If the price of X is 4, the price of Y is 2 and his income is 8,
what bundle does David choose?
(c) If the price of X is 1, the price of Y is 4 and his income is 8,
what bundle does David choose?
7. (21分)請求下列各函數的導數，即dy/dx:
(a) y=ln[(1-e^x)/(1+e^x)]
(b) y=x^5+x^(3/4)-2*x^(1/2)
(c) y=(x+1)*(2-3x)^(1/3)
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※ 編輯: TINTINH 來自: 59.121.216.39 (10/13 17:40)