Suppose a multi-product monopolist sells two complementary goods,A and B. Annual market demand for good A is Q^d_A = 600 - 25P_A - 12P_B. Each time a consumer buys A, his demand for B is Q^d_B = 4 - 0.4P_B. The marginal cost of good A is a constant $4, and the marginal cost of good B is a constant $0.50. Suppose the price of good B is $5. If the monopolist ignores the effect of additional sales of A on the sales of good B, how many units of good A will it produce? A) 665 B) 440 C) 332.5 D) 220

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Quizplus · Accepted Answer

To find the quantity of good A the monopolist will produce, we first substitute the price of good B ($5) into the demand equation for good A: QS = 600 - 25P - 12*5. Simplifying, we get QS = 600 - 25P - 60. To maximize profit, set marginal revenue (MR) equal to marginal cost (MC). Since MC of A is $4, we need to find the MR. However, without the complete demand function's derivative, we directly use the given information. Assuming linear demand, the monopolist sets price where MC = MR, but without the ability to calculate MR directly, we focus on the given MC and the need to balance production cost and demand. The question simplifies to understanding the impact of pricing on demand, but without explicit profit maximization steps, we acknowledge the monopolist's goal to produce where MC of producing A equals its MR, given as a constant $4 here. The correct answer involves recognizing the monopolist's decision-making process rather than a direct calculation from the provided information.

Suppose a Multi-Product Monopolist Sells Two Complementary Goods,A and B