I need help with e-h
Two firms set prices in a market with demand curve Q = 6 â p, where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm 1 that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced firm. For example, if firms 1 and 2 post prices equal to 2 and 4 dollars, respectively, then firm 1âas the lower priced firmâmeets all of the market demand and, hence, sells 4 units. If the two firms set the same price p, then they each get half of the market, that is, they each get 6âp . Suppose that prices can only be quoted in dollar units, such as 2 0, 1, 2, 3, 4, 5, or 6 dollars. Suppose, furthermore, that costs of production are zero for both firms. Finally, suppose that firms want to maximize their own profits.
(a) Show that the strategy of posting a price of 5 dollars weakly dominates the strategy of posting a price of 6 dollars. Does it strictly dominate as well?
(b) Are there any other (weakly) dominated strategies for firm 1? Explain.
(c) Is there a dominant strategy for firm 1? Explain.
(d) Suppose for a moment that this market had only one firm. Show that the price at which this monopoly firm maximizes profits is 3 dollars.
(e) Can you give a reason whyâin any price competition modelâa duopoly firm would never want to price above the monopoly price? (Hint: When can a duopoly firm that prices above the monopoly price make positive profits? What would happen to those profits if the firm charged a monopoly price instead?)
(g) Show that when we restrict attention to the prices 1, 2, and 3 dollars, the (monopoly) price of 3 dollars is a strictly dominated strategy. (h) Find the outcome of iterated elimination of (weakly) dominated strategies.
(h) Find the outcome of iterated elimination of (weakly) dominated strategies.
I need help with e-h
Two firms set prices in a market with demand curve Q = 6 â p, where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm 1 that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced firm. For example, if firms 1 and 2 post prices equal to 2 and 4 dollars, respectively, then firm 1âas the lower priced firmâmeets all of the market demand and, hence, sells 4 units. If the two firms set the same price p, then they each get half of the market, that is, they each get 6âp . Suppose that prices can only be quoted in dollar units, such as 2 0, 1, 2, 3, 4, 5, or 6 dollars. Suppose, furthermore, that costs of production are zero for both firms. Finally, suppose that firms want to maximize their own profits.
(a) Show that the strategy of posting a price of 5 dollars weakly dominates the strategy of posting a price of 6 dollars. Does it strictly dominate as well?
(b) Are there any other (weakly) dominated strategies for firm 1? Explain.
(c) Is there a dominant strategy for firm 1? Explain.
(d) Suppose for a moment that this market had only one firm. Show that the price at which this monopoly firm maximizes profits is 3 dollars.
(e) Can you give a reason whyâin any price competition modelâa duopoly firm would never want to price above the monopoly price? (Hint: When can a duopoly firm that prices above the monopoly price make positive profits? What would happen to those profits if the firm charged a monopoly price instead?)
(g) Show that when we restrict attention to the prices 1, 2, and 3 dollars, the (monopoly) price of 3 dollars is a strictly dominated strategy. (h) Find the outcome of iterated elimination of (weakly) dominated strategies.
(h) Find the outcome of iterated elimination of (weakly) dominated strategies.
