Question

In 2018 Lamborghini was quite concerned with pricing the new Lambo, the Lambo Centenario. The manager is interested in maximizing revenue. The demand schedule for the Lambo Centenario is given by P=7 – (1/10) Q. The company plans to sell the Lambo Centenario for about $2M. (a) How many lambos is the company planning to sell? (b) What is the elasticity of demand at this given price? (c) Is this the price that maximizes revenue?

Answer 1

Demand is P = 7 - Q/10. This implies revenue is PQ or R = 7Q - Q^2/10 and marginal revenue, that has twice the slope of demand with same intercept, is MR = 7 - 2Q/10. When MR is 0, the firm is maximizing revenues. Hence revenue maximizing quantity is Q = 7*10/2 = 35 and revenue maximizing price is P = 7 - 35/10 = $3.5 M

a) Company sells Q = (7 - 2)*10 = 50 lambos at this price.

b) We know that MR = P(1 - 1/e). Here P = 2 and MR = 7 - 2*50/10 = -3. This gives -3 = 2(1 - 1/e) or 1/e = 1 + 1.5. Thus, elasticity of demand ed = 0.4.

c) No. Revenue maximizing price is $3.5 M. Also, when price is $2 M, marginal revenue is negative and not zero.