Bertrand price competition (homogeneous products): Suppose that we have two (duopoly) firms that set prices in...

 

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Bertrand price competition (homogeneous products): Suppose that we have two (duopoly) firms that set prices in a market whose demand curve is given by Q = 6 – p where is the lower of the two prices. If there is a lower priced firm, then it meets all of the demand. If the two firms post the same price p, then they each get half the market, that is, they each get (6 – p)/2. Suppose that prices can only be quoted in dollar units (0, 1, 2, 3, 4, 5, or 6 dollars) and that costs of production are zero. (a) Suppose for a moment that this market had only one firm. Show that the price at which this monopoly firm maximizes profits is $3. (b) Show that when we restrict attention to the prices 1, 2, and 3 dollars, the (monopoly) price of 3 dollars is a dominated strategy. (c) Argue that the unique outcome to IEDS in this model is for both firms to price at 1 dollar. Bertrand price competition (homogeneous products): Suppose that we have two (duopoly) firms that set prices in a market whose demand curve is given by Q = 6 – p where is the lower of the two prices. If there is a lower priced firm, then it meets all of the demand. If the two firms post the same price p, then they each get half the market, that is, they each get (6 – p)/2. Suppose that prices can only be quoted in dollar units (0, 1, 2, 3, 4, 5, or 6 dollars) and that costs of production are zero. (a) Suppose for a moment that this market had only one firm. Show that the price at which this monopoly firm maximizes profits is $3. (b) Show that when we restrict attention to the prices 1, 2, and 3 dollars, the (monopoly) price of 3 dollars is a dominated strategy. (c) Argue that the unique outcome to IEDS in this model is for both firms to price at 1 dollar.

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