课程名称︰个体经济学 课程性质︰经济系必修 课程教师︰黄贞颖 开课学院：社科院 开课系所︰经济系 考试日期（年月日）︰2011年11月14日 考试时限（分钟）：2:20-4:50(自由延长至5:20) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. Consider the utility function: u(x1,x2) = min {2x1+x2, x1+2x2} (a) (10 points) Draw the indifference curve for u(x1,x2)=20. Shade the area where u(x1,x2)≧20 (b) (10 points) Draw several indifference curves. Draw the income offer curve for the following five cases separately: P1/P2>2, P1/P2=2, 2>P1/P2>1/2, P1/P2=1/2, 1/2>P1/P2 where P1 is the price of X1 and P2 that of X2. (c) (10 points) A consumer with this preference has income of 20. Suppose P1=P2+1. Solve for his optimal consumption bundle. Explain, in terms of the relationship between the MRS and the slope of the budget line, whe the optimal consumption bundle you find is optimal. (d) (10 points) A consumer with this preference has income of 20. The price of X2,P2, is 1. Draw his demand curve for X1. 2. You are given the following partial information about a consumer's purchases. He consumes only two goods: Year 1 Year 2 Quantity Price Quantity Price Good 1 100 100 120 100 Good 2 100 100 ? 80 Over what range of quantities of good2 consumed in year 2 would you conclude: (a) (10 points) That his behavior satisfies the weak axiom of revealed preference? (b) (7 points) That the consumer's consumption bundle in year 1 is revealed preferred to that in year 2? (c) (7 points) That the consumer's consumption bundle in year 2 is revealed preferred to that in year 1? 3. Rachel only consumes two goods: books (b) and video games (v). Her preference is lexicographic. That is, for any two consumption bundles of books and video games (b1,v1), (b2,v2)m she weakly prefers (b1,v1) to (b2,v2) if either b1>b2 or b1=b2 but v1≧v2. In all your diagrams, label books on the x axis and label video games on the y axis. (a) (8 points) Draw Rachel's indifference curve. (b) (8 points) Show that Rachel's preference is homothetic. (c) (10 points) Suppose the price of books is 1 and that of video games is also 1. Derive Rachel's income offer curve and Engel curve of video games. (d) (10 points) Suppose Rachel's income is 100 and the price of video games is 1. Derive Rachel's demand curve of books. --

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