课程名称︰ 个体经济学 课程性质︰ 经济系大二必修 课程教师︰ 黄贞颖 开课学院： 社会科学院 开课系所︰ 经济系 考试日期（年月日）︰ 2009 1 13 考试时限（分钟）： 两小时以上 是否需发放奖励金： 需要 （如未明确表示，则不予发放） 试题 : 1.Consumer's surplus: A consumer has the utility function U(x,y) =e^(ln(X)+Y)^1/3 where X is the good in concern and Y is the money that can be spent on all other goods. (So the price of Y is normalized to be 1). The income of this consumer is 100. (a. 10%) Derive the demand function of x for this consumer. (b. 10%) Calculate the price elasticity of the demand function in (a). Is it true that the absolute value of the elasticity of the demand decreases as the amount of x increases? (c. 10%) Suppose price of x decreases from 1/2 to 1/4. Calculate the change in consumer's surplus. (d. 10%) Suppose price of x decreases from 1/2 to 1/4. Calculate the compensating variation of this price change. (e. 10%) Suppose price of x decreases from 1/2 to 1/4. Calculate the equivalent variation of this price change . 2.Expected Utility: Suppose that a safety agency is thinking of establishing a criterion under which an area prone to flooding should be evacuated. The probability of flooding is 1%. There are four outcomes. (A)No flood and no evacuation is performed. (B)No flood but an evacuation is performed. (C)There is a flood and an evacuation is performed. (D)There is a flood but no evacuation is performed. Suppose that the agency is an expected utility maximizer. Suppose further that the agency is indifferent between the sure outcome B and the lottery of A with probability p and D with probability (1-p). Also assume that the agency is indifferent between the sure outcome C and the lottery of B with probability q and D with probability (1-q). Suppose it also prefers A to D and that 0<p<1 and 0<q<1 .Let us normalize by setting the utility of getting the sure outcome A to be 1 and the utility of getting the sure outcome D to be 0. (a. 10%) Determine the expected utility of sure outcome B and the expected utility of sure outcome C for the agency. (b. 20%) Consider two different policy criteria: Criterion 1: This criterion will result in an ecavuation in 90% of the cases in which flooding occurs and an unnecessary evacuation in 10% of the cases in which no flooding occurs. Criterion 2: This criterion is more conservative. It result in an evacuation in 95% of the cases in which flooding occurs and an unnecessary evacuation in 5% of the cases in which no flooding occurs. Recall that the probability of flooding is 1%. Derive the probability distribution over the four outcomes under these two criteria. Then, by using the utilities you calculate in (a), decide which criterion the agency will choose. 3.(20%) Explain what the winner's curse is. Briefly relate it to the swing voter's curse. --

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