Question

The market demand for popcorn at the local theater is P = 48 - 0.4Q. The theater owner has been told that she should produce a quantity where the demand curve has unitary elasticity. a. How many should she sell and at what price? b. If she wants to get the highest revenue possible from the popcorn, what price should be charged? c. If she is a profit maximizer you can eliminate a portion of the demand curve as irrelevant to her      pricing. What price range would be eliminated and why?

Answer 1

The market demand is P = 48 - 0.4Q.

a. In order to produce a quantity where the demand curve has unitary elasticity (ed = -1), theater owner should find that elasticity is given by

ed = (1/slope) x P/Q

-1 = -(1/0.4) x 48 - 0.4Q/Q

-Q = -120 + Q

Q = 120/2 = 60 units and price P = 48 - 0.4*60 = $24 per unit.

Hence the price is $24 per unit and the quantity is 60 units that brings elasticity = -1.

b. Note that when revenue is highest, marginal revenue is 0. We know that MR = 0 when elasticity is -1. Hence revenue maximizing price is also $24 per unit.

c. If she is a profit maximizer, she would always charge a price in the elastic portion because when the price is charged in the inelastic portion, the revenue is increased as the price is increased so the firm continues to charge a price till the demand becomes unitary elastic. Now the price at this stage is $24 per unit and so the price range that can be eliminated is $0 to $24 because a price in this range can never be charged.