e303practicefinal2005 - PART A: Answer 4 of 7 questions....

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PART A: Answer 4 of 7 questions .Eachquest ionisworth8marks . Be sure to explain your answer fully. Show any calculations required in order to arrive at your answer. Diagrams should be well-labeled. You may use point form in a written explanation as long as the meaning of the answer is clear. 1. Consider 2nd Degree Price Discrimination and the design of optimal contracts (spec- ifying a total expenditure by the consumer and a quantity recieved) that will achieve self-selection by 2 groups of consumers: a high demand group and a low demand group, where the (linear) low-demand curve lies entirely within the (linear) high-demand curve. The marginal costs of the monopolist are constant and equal to zero. What does it mean for a contract to be incentive compatible. What should the monopolist do if the maximium WTP L is only 1 4 the maximum WTP H ? 2. In a Cournot duopoly setting where identical (cost) ±rms choose level of output of a homogeneous good, explain why if ±rms set q 1 = q 2 = 1 2 q M (so that q 1 + q 2 = q M ) , a ±r m ( ±r m 1 say) has an incentive to increase output even though for a single ±rm with the same costs MR ( q M )= mc ( q M ) and q M is the pro±t-maximizing level of output. 3. A risk averse investor with mean-variance utility must decide how to allocate wealth between two risky assets A and B (there is no riskless asset). Short Sales are not permitted, if α is the fraction of wealth invested in asset A, 0 α 1 . The following information is known regarding the two assets: AB Expected Return r A r B r A >r B Standard Deviation σ A σ B σ A < σ B So asset A provides a higher expected return and lower standard deviation than asset B. Explain how the correlation between assets A and B will e f ect the set of e cient portfolios? Explain whether the utility-maximizing allocation can be the same for both the case ρ =1 and ρ = 1 ,where ρ is the correlation coe cient. s preferences for intertemporal consumption are such that her indi f erence curves are right angles along the 45 line (wealth levels in each period are perfect comple- ments). If the borrowing and lending rate are not the same, will a comparison of the Present Value of intertemporal bundles provide the same rankings as Future Value? Explain why or why not. If the lending (deposit) rate is r l =0% , for what borrowing rate, r b , is Jane indi f erent between the two allocations [noted by (wealth at t =0 , wealth at t =1) ]: A =( w, w 2 ) and B =( w 2 , 5 4 w )?
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5. A perpetual bond paying C every year has the same price as a T year annual coupon bond that pays C T each year for T -years with no repayment of the face value ( F =0) . Write an expression for the size of the perpetual coupon payment relative to the T year coupon payment ( i.e. C
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This note was uploaded on 10/21/2010 for the course STATISTICS Stat 200 taught by Professor Eee during the Spring '10 term at UBC.

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e303practicefinal2005 - PART A: Answer 4 of 7 questions....

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