Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. Suppose that the firms compete by simultaneously setting price, not simultaneously setting output. That is, suppose we consider the Bertrand model instead of the Cournot. Show that the two firms must earn lower profits. Hint: Create a two-by-two game using two different prices for each firm. One price should be the Cournot price (the Cournot is price of the good when firms produce the Cournot output you found above, which is 100 and 100, so the price is P = 400 − 100 − 100 = 200). The second price should be under 200 and over 150. Then show that the Nash equilibrium of this game is the lower of the two prices. When calculating profits, assume that each firm has equal sales (one half of demand) if they charge the same price and that consumers always buy from the lowest priced firm if prices are different
Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market
Hint: Create a two-by-two game using two different prices for each firm. One price should be the Cournot price (the Cournot is price of the good when firms produce the Cournot output you found above, which is 100 and 100, so the price is P = 400 − 100 − 100 = 200). The second price should be under 200 and over 150. Then show that the Nash equilibrium of this game is the lower of the two prices. When calculating profits, assume that each firm has equal sales (one half of demand) if they charge the same price and that consumers always buy from the lowest priced firm if prices are different
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