課程名稱︰個體經濟學一 課程性質︰經濟系必修 課程教師︰陳添枝 開課學院：社會科學院 開課系所︰經濟學系 考試日期（年月日）︰2010.1.14 考試時限（分鐘）：180mins 是否需發放獎勵金：YES （如未明確表示，則不予發放） 試題 : Help: √2=1.414, √3=1.732, √5=2.236, √7=2.646, √10=3.162 1.(12 points) Larry Winters makes decisions under uncertainty based on the following expected utility function: U(c_1,c_2)=π_1v(c_1)+π_2v(c_2), where v(c_1)=√c_1, v(c_2)=√c_2; c_1, c_2 are consumptions at state 1 and state 2, and π_1, π_2 are probabilities of respective states. When Larry is about to graduate from the university, he is offered two jobs: Company A offers him a fixed annual salary of 360,000NT, company B offers him an annual salary of 300,000NT, plus a bonus of 150,000NT if the company's products are successful. No bonus will be given if the products fail. Suppose the probability for the products to succeed is 50%, will Larry take the offer from company A or B? At what probability of product success will the two offers be equally attractive? 2.(12 points) Larry Winters has a utility function as shown in question 1. He has a nice house worth $500,000. If typhoon hits the town, the house will be damaged by $50,000, with a value of $450,000 remaining. The probability of typhoon is 10%. Larry can purchase an insurance against typhoon for an amount he chooses, up to $500,000 of course. Suppose the insurance company charges a premium of 10% on the insurance policy. That is, if he purchases x amount of insurance, he has to pay 0.1x as the premium no matter what happens; the insurance company will pay him x in the event of typhoon. Will he purchase any insurance? If yes, how much? (Hint: treat two states of consumption as two commodities and maximize his utility by equating MRS to relative price of two commodities.) 3.(10 points) Taiwan government offers a lottery to its people. The price of lottery ticket is 100NT. The prize is 1,000,000NT; however, the probability of winning the prize is less than 1/10,000. Many people purchase the tickets despite the fact that the expected value of the lottery is less than its price. Could you use a risk-lover's utility function to explain this phenomenon? 4.(10 points) There are two assets on the market. Asset A offers a mean return of 5% and a standard deviation of 5%; asset B offers a mean return of 10% and a standard deviation of 10%. If you ask Larry Winters, who is risk averse, to choose between A and B, he would prefer A. However, he decides to divide his wealth between a risk-free asset (bank deposit) and asset B; no money is invested in asset A. Please explain why this is possible? (Hint: use the mean-devariance model to explain the portfolio choice.) 5.(15 points) The demand and supply function are given below: Demand: P=30-0.2Q Supply: P=10+0.2Q (1) Find the equilibrium price and quantity. (2) If the government imposes a tax of 2NT on each unit of good sold and the suppliers are obligated to pay the tax. What would be the equilibrium price and quantity? (Hint: as a result of tax, the price that suppliers are willing to accept at any quantity increases by 2.) (3) Calculate the effects of tax on consumer surplus and producer surplus. Also calculate the tax revenue. Are the losses in consumer surplus and producer surplus offset by tax revenue? 6.(14 points) The utility function is given by u(x,y)=xy, where x, y are the only two commodities to be consumed. Income of the consumer is 120. (1) Calculate the demand for x and y if the prices are Px=5, and Py=10, respectively. (2) If the price of x increases from 5 to 6, price of y remains the same at 10, what would be the demand for x and y? Please calculate the compensation variation (CV) and equivalent variation (EV) for the price change. 7.(12 points) The utility function is given by u(x,y)=xy, where x, y are two commodities to be consumed. Income of the consumer is m, and prices of x and y are Px and Py respectively. (1) Please calculate price elasticity for x and y when m=120, Px=5, Py=10. If Px changes from 5 to 10, while m and Py are unchanged, what will be the price elasticity for x and y? (2) Please calculate income elasticity for x and y when m=120, Px=5, Py=10. What will happen to income elasticity if income is 130 rather than 120? 8.(15 points) Consumer A's inverse demand function for a good is given by P=20-0.5Q (1) If there are five consumers and all have the above demand function, what is the aggregate demand? (2) What is the quantity demanded by the entire market when P=5? Calculate price elasticity and marginal revenue at this point. (3) At what price will the revenue be maxmized? --

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