Question

A city has two newspapers. Demand for either paper depends on its own price and the price of its rival. Demand functions for papers A and B respectively, measured in tens of thousands of subscribers, are 21-2P_a+P_b and 21+P_a-2P_b The marginal cost of printing and distributing an extra paper just equals the extra advertising revenue from another reader, so each paper treats marginal costs as zero. Each paper maximizes its revenue assuming that the other’s price is independent of its own price. If the papers enter a joint operating agreement where they set prices to maximize their total revenue, by how much will newspaper prices rise?

Answer 1

When they compete for prices, they maximize their profits

Find the profit function that results in best response function

?a = QaPa = (21-2Pa+Pb)Pa and ?b = QbPb = (21-2Pb+Pa)Pb

Maximize profit

?a'(Pa) = 0

21 - 4Pa + Pb =0

Pa = 21/4 + Pb/4   

?b'(Pb) = 0

21 - 4Pb + Pa = 0

Pb = 21/4 + Pa/4

Solving them results in

Pa = 21/4 + (21/4 + Pa/4 )/4

Pa = (21/4 + 21/16)*16/15 = 7 and so Pb = 7

Joint profit maximization has same price so demand is Q = 21 - P. Revenue is (21Q - Q^2) and revenue is maximized when MR = 0

21 - 2Q = 0

Q = 10.5 , P = 21 - 10.5 = 10.5

If the papers enter a joint operating agreement where they set prices to maximize their total revenue, newspaper prices rises by 3.5 from 7 to 10.5