Question

Kashian Motors has determined that the price elasticity of demand for two customer segments (A Luxury Car’s price elasticity of demand is -1.25 while a Premium Car’s price elasticity of demand is -1.65. Based on their expectations of profitability, Kashian realizes the price of a Luxury Car should be $71,500. How much should Kashian charge for its Premium Car?

Answer 1

In order to maximize profit a firm produces that quantity at which MR = MC

where MR = d(P*Q)/dQ = P + Q(dP/dQ) = P[1 + (Q/P)(dP/dQ)] = P(1 + 1/e)

where MR = Marginal Revenue , MC = Marginal cost , P = Price , Q =quantity , Total revenue = P*Q and e = elasticity of demand.

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

For luxury cars we have P(1 + 1/e) = MC

=> 71,500[1 + 1/(-1.25)] = MC ------------------(1)

For Premium cars we have P(1 + 1/(-1.65)) = MC

=> P[1 + 1/(-1.65)] = MC ------------------(2)

Thus Equating (1) and (2) we get:

P[1 + 1/(-1.65)] = MC = 71,500[1 + 1/(-1.25)]

=> P = 71,500[1 + 1/(-1.25)]/[1 + 1/(-1.65)] = 36300

Hence, Kashian should charge $36300 for its Premium Car.