Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
Please answer the following question fully and in detail!
Consider a Bertrand duopoly with two firms 1,2 who sell the same good. The demand curve of the good is given by Q = 15 − p if p < 15 and Q = 0 if p ≥ 15. Both firms have the same constant unit cost 2.
Firms 1,2 set prices p1, p2. If firms set different prices, then the firm which sets the minimum price of the two, receives the demand at that price while its rival receives zero demand. If both firms set the same price, they equally split the demand at that price.
(a) Determine the profit functions of firms 1,2.
(b) Find best response of firm 2 to p1 = 7
(c) Find best response of firm 1 to p2 = 3
(d) Show that (p1 = 3, p2 = 3) is a Nash Equilibrium (NE) of the Bertrand duopoly.
(e) Show that (p1 = 6, p2 = 6 is a not an NE of the Bertrand duopoly.
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Please answer the following question fully and in detail!
Consider a Bertrand duopoly with two firms...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms 1,2 who sell the same good. The demand curve of the good is given by Q = 30 − p if p < 30 and Q = 0 if p ≥ 20. Both firms have the same constant unit cost 5. Firms 1,2 set prices p1, p2. If firms set different prices, then the firm which sets the minimum price of the two, receives...
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consider the standard Bertrand model of price competition. There
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1 (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, Fi and Fa selling two varieties of a product. The demand curve for Fi's product is 91 (pi,P2) = 10-Pl + 0.5p2: and the demand for F's product is where p is the price charged by F). Both firms have a constant marginal cost of (a) Write down the profits of F1 and F2 as a function of prices P1 and P2. You have b) Derive...
consider the standard Bertrand model of price competition. There
are two firms that produce a homogenous good with the same constant
marginal cost of c.
a) Suppose that the rule for splitting up cunsumers when the
prices are equal assigns all consumers to firm1 when both firms
charge the same price. show that (p1,p2) =(c,c) is a Nash
equilibrium and that no other pair of prices is a Nash
equilibrium.
b) Now, we assume that the Bertrand game in part...
Consider a Bertrand duopoly in a market where demand is given by Q firm has constant marginal cost equal to 20 100 - P. Each (a) If the two firms formed a cartel, what would they do? How much profit would eaclh firm make? (6 marks) (b) Explain why the outcome in part (a) is not a Nash Equilibrium. Find the set of Nash Equilibria and explain why it/they constitute Nash equilibria. (6 marks) (c) Now suppose that instead of...
Consider the following variation of the Bertrand competition model (e.g., price competition) discussed in class. Two firms, 1 and 2, are producing the same identical product. Firms compete in prices: Firm 1 choses pı, and Firm 2 choses p2. Given pı and p2, the individual demands of fhrms are: 10-pi pi 〈 p2 Pi P2 0 P1〈P2 Both firms have constant marginal costs of c. To sum up, the payoffs are as follows: 2 C 92 (P1, P2 Unlike the...
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