A monopolist produces output with constant marginal cost equal to 1. There are two of consumers that are potentially in the market for the good. Consumer A has inverse demand function $$p_A(x) = 7 − x,$$ and consumer B has inverse demand function $$p_B(x) = 5 − x.$$

Suppose the monopolist cannot identify which consumer is which. What is the best pair of purchase options $(x_A, R_A)$ and $(x_B, R_B)$ the monopolist should offer? (Hint: You’ll need to show that $x_B = 2.$) What is the firm’s profit?

My attempt:

The question doesn't make clear what $R_A, R_B$ are. But I guess the question is asking about 2nd degree price discrimination. So type A is high-demand consumer and B is low-demand consumer. $MR_B=5-2q_B=1$, then $x_B^*=2$ and at this point, the price is 3. So the first bundle designed for low-demand consumer is (2 units, whole bundle price is 2x3=6). I still need to design the other bundle for high-demand consumer.

If high-demand consumer pretends to be low-demand and buys the above bundle, so he or she buys 2 units and pays $6. His or her WTP is 12. So consumer surplus is 12-6=6. Then how should I do next?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.