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

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Unformatted text preview: PART B: Answer 3 of 4 questions . Each question is worth 20 marks. 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. (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 (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 (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 ; and the Stackelberg equilibrium. You should also label the Cournot equilibrium. (6 marks) 3 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) Calculate the expected value of Sarah’s income (in thousands of dollars). (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 (d)...
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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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practicefinal2002 - PART B: Answer 3 of 4 questions . Each...

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