Two software companies sell competing products. These products are substitutes, so that the number of units that
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(a) Write an expression for the total revenue of company 1, as a function of the its price p1 and the other company’s price p2.
b) Company 1’s best response function BR1(·) is defined so that BR1(p2) is the price for product 1 that maximizes company 1’s revenue given that the price of product 2 is p2. With the revenue functions we have specified, the best response function of company 1 is described by the formula BR1(p2) = __________
(c) Use a similar method to solve for company 2’s best response function __________
(d) Solve for the Nash equilibrium prices p1 = __________ and p2 = ___________
(e) Suppose that company 1 sets its price first. Company 2 knows the price p1 that company 1 has chosen and it knows that company 1 will not change this price. If company 2 sets its price so as to maximize its revenue given that company 1’s price is p1, then what price will company 2 choose? p2 = _____________ If company 1 is aware of how company 2 will react to its own choice of price, what price will company 1 choose? _________ Given this price for company 1, what price will company 2 choose? ___________
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