Entrepreneurial Skill and Market Conditions: We often treat all firms as if they must inherently face the same costs—but managerial, or entrepreneurial, skill in firms can sometimes lead to a decrease in the marginal cost of production. We investigated this in the competitive setting in exercise 14.5 of Chapter 14 and now investigate the extent to which effective managers can leverage their skill in oligopolies depending on the market conditions they face.
A: Suppose two firms in an oligopoly face a linear demand curve, constant marginal costs MC1 and MC2 and no recurring fixed costs.
(a) Suppose first that the market conditions are such that firms compete on price and can easily produce any quantity that is demanded at their posted prices. If the firms simultaneously choose price, what happens in equilibrium?
(b) Does your answer change if the firms post prices sequentially, with firm1 posting first?
(c) When firms face the same costs, we concluded that the Bertrand equilibrium is efficient. Does the same still hold when firms face different marginal costs?
(c) When firms face the same costs, we concluded that the Bertrand equilibrium is efficient. Does the same still hold when firms face different marginal costs?
(e) Could it be that firm 2 does not produce in the Cournot equilibrium? If so, how much does firm1 produce?
(f) If firms set quantity sequentially, do you think it matters whether firm1 or firm2moves first?
(g) In (b) you were asked to find the sub game perfect equilibrium in a sequential Bertrand pricing market where firm 1 moves first. How would your answer change if firm 2 moved first? Is there a sub game perfect equilibrium in which the efficient outcome is reached? What is the sub game perfect equilibrium that results in the least efficient outcome?
B: The two oligopoly firms operate in a market with demand x = A –αp neither firm faces any recurring fixed costs, and both face a constant marginal cost. But firm 1’s marginal cost c1 is lower than firm2’s—i.e. c1 < c2.
(a) In a simultaneous move Bertrand model, what price will emerge, and how much will each firm produce?
(b) Does your answer to (a) change if the Bertrand competition is sequential—with firm1 moving first? (Assume sub game perfection.)
(c) How does your answer change if the two firms are Cournot competitors (assuming that both produce in equilibrium)?
(d) What if the two firms are engaged in Stackelberg competition, with firm 1 as the first mover? What if firm2 is the first mover?
(e) How would each firm behave if it were a monopolist?
(f) Suppose A = 1000, α = 10, c1 = 20 and c2 = 40. Use your results from above to calculate the equilibrium outcome in each of the above cases. Illustrate your answer in a table with x1, x2, p and overall output X for each of the cases. Do the results make intuitive sense?
(g) Add a column to your table in which you calculate profit in each case. What market conditions are most favorable in this example for the good manager to leverage his skills?
(h) What would be the efficient outcome? Add a row to your table illustrating what would happen under the efficient outcome.
(i) Which of the oligopoly/monopoly scenarios in your table is most efficient? Which is best for consumers?
(j) Are there any scenarios in your table that would result in the same level of overall production if the marginal costs for each of the two firms were the same and equal to the average we have assumed for them(i.e. c1 = c2 = 30)?