科目：個體經濟學一 教授：鄭秀玲 試別：92學年度上學期第二次期中考 時間：2003年12月18日 --------------------------------------------------------------------- 以下課題均需寫出詳細求解過程，否則不予計分。 1. David's utility function is XA*XB, where XA is the quantity of apples and XB is the quantity of bananas. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $1.50 and the price of bananas fell to $1.75, then in order to be able to just afford his old bundle, David would have to have a daily income of_________. (10 points) 2. Jack's utility function is XA*XB, where XA is the quantity of apples and XB is the quantity of bananas. The price of apples used to be $1 per unit, the price of bananas used to be $2 per unit and his income used to be $40. If the price of apples increased to $5 and the price of bananas stayed constant, the Slutsky substitution effect on Jack's consumption would reduce his consumption by ________ apples. (10 points) 3. John has a utility function U(X1,X2)=(X1)^2+1.5*X1*X2+30*X2. The price are P1=$1 and P2=$1. His income is $m. What is the Engel curve for good 2? (10 points) 4. At prices (P1,P2)=($4,$2), Ivan buys the bundle (X1,X2)=(8,20). At prices (P1',P2')=($2,$4), he buys the bundle (X1',X2')=(10,13). At prices (P1",P2"), he buys the bundle (X1",X2")=(14,11). If his preference satisgy the strong axiom of revealed preference, then if must be that a. 8P1>2P2 b. 6P1"<9P2" c. 6P1"<8P2 d. P1"=P2" e. None of the above (Please choose only one answer and must show how you get the answer.) (10 points) 5. Susan bought 30CDs and 600 pounds of food in 2000 when CDs cost $18 each and food cost $4 per pound. In 2001, the price of CDs rises to $24 each and the price of food rises to $5 per pound. a. Compute the Laspeyres price index for Susan for the year 2001, using 2000 as the base year. b. In 2001, Susan's income changes and she buys 35 CDs and 500 pounds of food. Compute the Paasche price index for Susan for 2001 using 2000 as the base year. c. Can we say for sure if Susan was better off in 2000 or 2001? (10 points) 6. Mary has income $400 in period 1 and income $600 in period 2. Her utility function is [c1^a*c2^(1-a)], where a=0.40 and the interest rate is 0.20. If her income is period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would increase by $_________. (10 points) 7. Buzz is a chicken farmer. His earnings will be $100 this year and $100 next year. He can lend money at the interest rate of 20%. Because of a subsidized loan program for chicken farmers, he can borrow money at the interest rate of 10%. No matter what he borrows of lends, his earnings will still be $100 each year. Draw a graph showing his budget between consumption this year and consumption next year (Put numerical labels on the vertical and horizontal intercepts of the budget set). (6 points) 8. Yang's expected utility function is p*c1^(1/2)+(1-p)c2^(1/2), where p is the probability that he consumes c1 and (1-p) is the probability he consumes c2. He is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2,500 with probability 0.3 and $3,600 with probability 0.7. He will choose: a. the sure payment if Z>3,249 and the lottery if Z<3,249 b. the sure payment if Z>2,874.50 and the lottery if Z<2,874.50 c. the sure payment if Z>3,600 and the lottery if Z<3,600 d. the sure payment if Z>3,424 and the lottery if Z<3,424.50 e. the sure payment if Z>3,270 and the lottery if Z<3,270 (Please choose only one answer and must show how you get the answer) (6 points) 9. Suppose that Mike's utility function is given by U(W)=W^2 represents total wealth in thousands of dollars. Is Mike risk-averse, risk-loving, or risk-neutral? (需用數學或圖形加以證明，才予以計分) (6 points) 10. 請用數學或圖形證明 "For the case of quasilinear utility, the compensating and equivalent variation are the same." (10 points) 11. 假設x商品對消費者王先生而言是季芬財(Giffen goods)， 請繪出王先生對x商品之"the standard demand curve", "the Slutsky demant curve", 和 "the Hicks demand curve"。 (12 points) --

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