Chapter 12: Problem 1
Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.
Chapter 12: Problem 1
Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.
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Get started for freeTwo firms compete in selling identical widgets. They choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the demand curve $$P=30-Q$$ where \(Q=Q_{1}+Q_{2}\). Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm \(2^{\prime}\) s marginal cost to \(\$ 15 .\) Firm \(1^{\prime}\) s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level Suppose that two identical firms produce widgets and
Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is \(Q=400-2 P .\) The dominant firm has a constant marginal cost of \(20 .\) The fringe firms each have a marginal \(\operatorname{cost}\) of \(\mathrm{MC}=20+5 q\) a. Verify that the total supply curve for the five fringe firms is \(Q_{f}=P-20\) b. Find the dominant firm's demand curve. c. Find the profit-maximizing quantity produced and price charged by the dominant firm, and the quantity produced and price charged by each of the fringe firms. d. Suppose there are 10 fringe firms instead of five. How does this change your results? e. Suppose there continue to be five fringe firms but that each manages to reduce its marginal \(\operatorname{cost}\) to \(\mathrm{MC}=20+2 q\). How does this change your results?
Two firms compete by choosing price. Their demand functions are $$Q_{1}=20-P_{1}+P_{2}$$ and $$Q_{2}=20+P_{1}-P_{2}$$ where \(P_{1}\) and \(P_{2}\) are the prices charged by each firm, respectively, and \(Q_{1}\) and \(Q_{2}\) are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price. b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.
A monopolist can produce at a constant average (and marginal) cost of \(\mathrm{AC}=\mathrm{MC}=\$ 5 .\) It faces a market demand curve given by \(Q=53-P\) a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. b. Suppose a second firm enters the market. Let \(Q_{1}\) be the output of the first firm and \(Q_{2}\) be the output of the second. Market demand is now given by $$Q_{1}+Q_{2}=53-P$$ Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of \(Q_{1}\) and \(Q_{2}\) c. Suppose (as in the Cournot model) that each firm chooses its profit- maximizing level of output on the assumption that its competitor's output is fixed. Find each firm's "reaction curve" (i.e., the rule that gives its desired output in terms of its competitor's output). d. Calculate the Cournot equilibrium (i.e., the values of \(Q_{1}\) and \(Q_{2}\) for which each firm is doing as well as it can given its competitor's output). What are the resulting market price and profits of each firm? *e. Suppose there are \(N\) firms in the industry, all with the same constant marginal cost, \(\mathrm{MC}=\$ 5 .\) Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as \(N\) becomes large, the market price approaches the price that would prevail under perfect competition.
Suppose that two competing firms, \(A\) and \(B\), produce a homogeneous good. Both firms have a marginal cost of \(\mathrm{MC}=\$ 50 .\) Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium. a. Because Firm \(A\) must increase wages, its \(\mathrm{MC}\) increases to \(\$ 80\). b. The marginal cost of both firms increases. c. The demand curve shifts to the right.
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