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 --------------------------------------------------------------------- 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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