ps5_sol2 - Solutions to Practice Problem Set 5 ECON 100C...

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1 Solutions to Practice Problem Set 5 ECON 100C Perloff Chapter 13 13.1 At each OPEC meeting, Saudi Arabia, the largest oil producer, argues that the cartel should cut production. The Saudis complain that most OPEC countries, including Saudi Arabia, produce more oil than they are allotted under their cartel agreement. Use a graph and words to explain why cartel members would produce more than the allotted amount given that they know that overproduction will drive down the price of their product. The profit maximizing agreement to collude would restrict output to the monopoly level (as if the OPEC cartel were a single firm), which would drive the price higher than it would be in the Cournot equilibrium. Each individual country has an incentive to overproduce relative to the collusive agreement to take advantage of the artificially high price, since they are not directly impacted by the lower revenue of other countries that results from their increase in production. Marginal revenue for the individual country exceeds the marginal cost of production, though marginal revenue for the cartel as a whole has been set equal to marginal cost. A graph of the firms’ reaction functions would show that under the collusive agreement each firm is under- reacting to the competitors’ output – the best (profit maximizing) response is to increase output. 13.5 Southwest Airlines’ cost to fly one seat 1 mile is 7.38 cents compared to 15.20 cents for USAir. Assuming that Southwest and USAir compete on a route, use a graph to show that their equilibrium quantities differ. As an example, consider a linear market demand curve PሺQሻൌaെbQ where Qൌq USA୧୰ q S୭୳୲୦୵ୣୱ୲ . The firms’ best response functions are: ݍ ௌ௢௨௧௛௪௘௦௧ ௔ି଻.ଷ଼ି௕·௤ ೆೄಲ೔ೝ ଶ௕ , ݍ ௎ௌ஺௜௥ ௔ିଵହ.ଶି௕·௤ ೄ೚ೠ೟೓ೢ೐ೞ೟ ଶ௕ These can be found by choosing the quantity that maximizing profits for each company, holding the quantity fixed for the other airline. These are plotted below:
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2 The lower cost firm, which is Southwest in this case, will produce a higher quantity. Though the slopes are the same, the intercept for Southwest is higher. For any given quantity that the rival produces, Southwest would choose to produce more than USAir would. 13.7 Plot the best-response curve of the second firm in Solved Problem 13.1 if its marginal cost curve is m and if it is m+x. Add the first firm’s best-response curve and show how the Nash- Cournot equilibrium changes as its marginal cost increases. The Nash-Cournot equilibrium at the higher marginal cost involves a decrease in output for firm 2 and an increase for firm 1. 13.19
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This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.

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ps5_sol2 - Solutions to Practice Problem Set 5 ECON 100C...

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