practicefinal2002 - PART B Answer 3 of 4 questions Each...

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PART B: Answer 3 of 4 questions . Each question is worth 20 marks. Be sureto explain your answer fully. Show any calculations requiredinordertoarrive 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. (Oligopoly/Stackelberg) The demand in a market is Q =200 ¡ 1 2 P: (a) If …rm 1 is a monopolist with marginal costs c 1 =$100 ; …nd q M 1 and p M ; the pro…t maximizing quantity and price in the market. (3 marks) (b) Suppose instead that the industry is a duopoly. Firm 1 has marginal costs as above ( c 1 =$100) and …rm 2 has marginal costs, c 2 =$40 : Firms choose quantity (competition is quantity based). What is …rm 2’s best response function? (3 marks) 1
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(c) If …rm 1 can make its output decision before …rm 2 ; AND …rm 2 will know …rm 1’s choice of output before it sets its own quantity, what is …rm 1’s marginal revenue function as a Stackelberg leader? (2 marks) (d) Find the Stackelberg equilibrium. (4 marks) 2
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(e) Find the price in the market and the pro…ts to each …rm. (2 marks) (f) Show the Stackelberg equilibrium graphically. Include in your graph: the best response functions of both…rms, the iso-pro…t lines for …rm 1 ; andthe Stackelberg equilibrium. You should also label the Cournot equilibrium. (6 marks) 3
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2. (Uncertainty) Sarah has inherited a vineyard from a distant relative. In good years (when there is no rain or frost during harvest season), her income (in thousands of dollars) is w g =$100 from the sale of grapes from the vineyard. If the weather is poor, she earns only w b =$8 (again in thousands of dollars). Sarah estimates the probability of good weather is 60% : (a) Calculatethe expectedvalue of Sarah’s income(inthousands ofdollars). (3 marks) (b) What is the variance of Sarah’s income from the vineyard? (3 marks) (c) Sarah is risk averse. Marvin, a grape buyer, o¤ers Sarah a guaranteed payment of $70 thousand each year in exchange for her entire harvest. Will Sarah accept Marvin’s o¤er? Explain. (4 marks) 4
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