Question

Suppose Kiwi Inc. conducted a market survey and found that the New Zealand wholesale market for chicken can be divided into two segments with the demand functions given by P1 = 12-6Q1 and P2 = 3-3Q2. If Kiwi Inc. are able to discriminate the price between these two market segments and resale is impossible between the two segments, what price should Kiwi Inc. charge for each market segment?

Answer 1

Let the prices be P1 and P2.

First find the original demand functions as Q1 = 2 - (1/6)P1 and Q2 = 1 - (1/3)P2.

Profit is given by π = (P1 - LAC)Q1 + (P2 - LAC)Q2

π = (P1 - 2)(2 - (1/6)P1) + (P2 - 2)(1 - (1/3)P2)

π = 2P1 - 4 - (1/6)P1^2 + (1/3)P1 + P2 - 2 - (1/3)P2^2 + (2/3)P2

π = (7/3)P1 - (1/6)P1^2 + (5/3)P2 - (1/3)P2^2 - 6

Profit is maximum when π'(P1) = 0 and π'(P2) = 0

(7/3) - (1/3)P1 = 0 and (5/3) - (2/3)P2 = 0

P1 = 7 and P2 = 5/2 = 2.5

Thus, in market 1 price should be $7 per unit and in market 2 price should be $2.5 per unit.