Question

Music Ventures sells a very popular MP3 player, the MP34u. The firm currently sells one million unites for a price of $100 each. Marginal cost is estimated to be constant at $40, where as average cost (at the output level of one million units) is $90. The firm estimates that its demand elasticity (at the current price level) is approximately -2. (a) Should the firm raise price, lower price, or leave price unchanged? Explain you answer

Answer 1

(a)

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

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

where MR = Marginal revenue, TR = Total revenue = P*Q , P = Price , Q = quantity and e = elasticity of demand = (dQ/dP)(P/Q)

Also MC = Marginal cost.

It is given that e = -2 and MC = 40(Constant)

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

=> P(1 + 1/(-2)) = 40

=> P = 2*40 = 80

Thus It should charge Price = 80 and hence in order to maximize profit, he should lower the price.

Hence This firm should lower the price.