Question

If price elasticity in region 1 is -2 and in region 2 is -3. In order to maximize profit in both region 1 and region 2, what relationship could be between optimal price P1 in region 1 and optimal price P2 in region 2?

		3P1 = 4P2
		4P1=3P2
		P1=3P2
		Can not be determined

Answer 1

The correct answer is (a) 3P₁ = 4P₂

Formula:

Profit = TR - TC = PQ - TC

First order condition:

d (Profit)/dQ = 0 => Q(dP/dQ) + P - MC = 0

=> P(1 + (Q/P)(dP/dQ)) = MC

=> P(1 + 1/e) = MC

where e = (P/Q)(dQ/dP) = elasticity of demand

In market 1 we have e = -2 and P = P₁

=> P₁(1 - 1/2) = MC

=> P₁(1/2) = MC----------------(1)

In market 2 we have e = -3 and P = P₂

=> P₂(1 - 1/3) = MC

=> P₂(2/3) = MC----------------(2)

Dividing (1) from (2) we get:

P₁(1/2)/(P₂(2/3)) = MC/MC = 1

=> P₁(1/2) = P₂(2/3) => 3P₁ = 4P₂

Hence, the correct answer is (a) 3P₁ = 4P₂