Question

A firm sells a good y to two consumers, A and B. A’s demand is p = 40 − y. B’s demand is p = 50 − y. The firm knows that both consumers exist, but can’t identify who is who. The firm has no costs (MC = AC = 0).

a. [8 marks] Suppose the firm wants to sell 40 units of y to A for a total price of TA and 50 units of y to B for a total price of TB. Find TA, TB and the firm’s profits. Show your work.

Answer 1

We have the following information

Demand of A: P = 40 – Y

Demand of B: P = 50 – Y

Total revenue (A) = P × Y = (40 – Y)Y = 40Y – Y²

Total revenue (B) = P × Y = (50 – Y)Y = 50Y – Y²

Marginal Revenue from A (MRA) = ∆TR/∆Y = 40 – 2Y

Marginal Revenue from B (MRB) = ∆TR/∆Y = 50 – 2Y

For equilibrium

MRA = MRB = Marginal Cost (MC)

MC = 0 (given)

40 – 2Y = 0

Y = 20

Price for A (TA): P = 40 – Y

TA = 40 – Y

TA = 40 – 20

TA = 20

Price for B (TB): P = 50 – Y

TB = 50 – Y

TB = 50 – 20

TB = 30