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Unformatted text preview: Problems on Cournot and Bertrand competition 1. Suppose that an industry with 20 &rms has a Her&ndahl index of 500. What can you conclude about the four-&rm concentration ratio? Answer. If the Her&ndahl index is 500, it must be that all &rms have the same market share (H=10000/20=500). So the 4 &rm concentration ratio is 4/20 = 20%. 2. Median Her&ndahl index and median number of &rms for the US man- ufacturing sector are approximately 400 each. What can you conclude about the size distribution of &rms? Answer. With a median number of &rms of 400, if all &rms had same market share the Her&ndahl index would have to be 10,000/400=25. It is actually 8 times higher, re¡ecting a large assymetry in the share of &rms. 3. Consider game 1 played in class with the di/erence that there are three &rms in the market, each with probability 1¡2 of having one unit of capacity. What is the lowest price that you can expect a &rm to choose? (a) p = 0 : (b) p = 1 2 : (c) p = 1 4 (d) p = 3 4 : Answer. What is the probability that none of your competitors has capacity? Its 1/4 = 1/2 x 1/2. So by setting a price of one, you can guarantee an expected pro&t of 1/4. Hence you should never set the price below 1/4. The answer is (c). 4. As a consequence of a merger, the number of &rms in a market decreased from 3 to 2. All &rms have constant marginal cost. Her&ndahl index was initially 10000¡3. What will it be after the merger? Answer. If the Her&ndahl index was 10000/3 it follows that all &rms had the same market shares, so the same marginal cost. With two &rms left with the same marginal cost, H index will be 10000/2=5000. 1 5. Suppose market demand elasticity is equal to one and the market shares of Cournot competitors in this market are: 20%, 30% and 50%. If the market equilibrium price is 100, what are the marginal costs of each of the &rms? Answer. Using the results obtained in class: p & c i p = s i & = s i since the elasticity is one, so c i = p (1 & s i ) : Replacing the values, we get c 1 = 100(1 & : 2) = 80 ; c 2 = 70 and c 3 = 50 : 6. Consider two industries a and b: The &rst industry has twice the number of &rms of the second industry, but their Her&ndahl index is the same. Can you tell which industry is more competitive in the sense that their average price markups are lower? Answer. Not without knowing the demand elasticity in each of the two markets. 7. Suppose market demand elasticity is equal to two and the market shares of the 10 Cournot competitors are equal. If the market equilibrium price is 100, what can you conclude about the marginal costs of the &rms? Answer.Using the formula 100 & c 100 = s i & = 1 = 10 2 we get c = 95 : 8. A market with Cournot competitors has a Her&ndahl index of 2500....
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This note was uploaded on 10/15/2008 for the course ECON 171 taught by Professor Hopenhayn during the Spring '07 term at UCLA.
- Spring '07