In Bertrand competition with differentiated products and zero marginal costs, Firm A faces the demand curve q_A = 80 - 2P_A + 0.50P_B_.If Firm A expects Firm B to charge a price of $20, what price should Firm A charge?

Question

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To find the optimal price for Firm A, we need to set its marginal revenue equal to zero. Let's first rewrite the demand curve in terms of Firm A's price (PA) and Firm B's expected price (PB), based on the information given in the question: q_A = 80 - 2PA + 0.50PBA To find Firm A's marginal revenue, we take the derivative of the demand curve with respect to PA: MR = 80 - 4PA + 0.50PB Setting MR equal to zero and solving for PA, we get: PA = (80 + 0.50PB) / 4 Plugging in PB = 20 (the expected price of Firm B), we get: PA = (80 + 0.50*20) / 4 = 22.50 Therefore, Firm A should charge a price of $22.50.

In Bertrand Competition with Differentiated Products and Zero Marginal Costs