03 Jun Question Question 2. The inverse market demand for mineral wat
Question
Question 2. The inverse market demand for mineral water is P = 200 10Q, where Q is total market output and P is the market price. Two rms have complete control of the supply of mineral water and both have zero costs.
(a) Find the Cournot quantity, price, and each rms prot.
(c) Find the Bertrand price, quantity, and each rms prot.
(d) Denote the Bertrand price by pa , and denote the monopoly price by pb . Suppose that the two rms interact with each other for innite periods, and in each period they set prices simultaneously. Consider the following collusive strategy, the same as discussed in class: set price pb only if no one has cheated
so far, and to set price pa forever if some has cheated before. Assume each rm acts to maximize its sum of discounted prots where the interest rate is r. Find the values for r such that this collusive strategy is a Nash equilibrium, namely, for what values of r can the monopoly prots be sustained through collusion?
Compare your answer to (b) and explain.
Question 3. Two rms produce candies that are imperfect substitutes. This is reected in the demand curves of the two rms candies, D1 (p1 , p2 ) = 100
p1 + 0.5p2 and D2 (p1 , p2 ) = 100 p2 + 0.5p1 . Suppose each rm has constant marginal cost of 20.
(a) Interpret the demand curves, in particular, explain from the demand curves why the candies produced by the two rms are imperfect substitutes.
(b) Suppose the two rms compete by making simultaneous price decisions. Calculate the equilibrium price, quantity and prot for each rm.
(c) Suppose the two rms compete by making sequential price decisions, where rm 1 is the leader. Calculate the equilibrium price, quantity and prot for each rm. Compare the prots of the leader vs. the follower and explain.
Question 4. Suppose an industry has ten rms. The market shares of each rm are: 25%, 15%, 10%, 10%, 8%, 8%, 7%, 7%, 5% and 5%.
(a) What is the four-rm concentration ratio?
(b) What is the Herndahl-Hirschman Index?
(c) According to the merger guidelines, if the HHI is in the range of 1000-1800 after a merger, you will not allow the merger if it increased the HHI by 100 points or more. Would you allow a merger between the 2 rms that had 5% market share each? Would you allow a merger between the 2 rms that had 8% market share each?
(d) Suppose the ten rms compete in a Cournot oligopoly in this industry, and the current price elasticity of demand is -0.8. What are the prot margins for each of the four biggest rms? What is the average prot margin (weighted by each rms market share) of this industry?
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