Question

7. Jeff, the manager of HiQ DVD and former president of the Guild of Graduates (UWI), seeks your expert advice. He has given you the following information: when he charged a price of $10, approximately 4,000 DVD were sold, however, when the price increased by 10% the demand decreased by 1,000 units (DVD). Jeff wants to know the following (based on operating cost of $7 per DVD):

a) What is the MR?

b) What price would maximize profit?

c) What impact would a price decrease have on revenue?

Answer 1

When price = $10, Qd or Qs = 4,000 units. When price is increased by 10% to reach 11, demand decreased by 1,000 units to become 3000 units. There is an operating cost or marginal cost = $7 per unit.

a) Total revenues under two conditions are 10*4000 = 40000 and 11*3000 = 33000. Marginal revenue = (40000 – 33000)/(4000 – 3000) = $7.

b) The profit maximize price is the one that equates MR = MC. Here when price is increased from 10 to 11, the marginal revenue is $7 and the marginal cost is also 7. Hence profit maximizing price is $11.

To measure the profit maximizing price accurately, we need to find demand function. This generally takes the form of P = A – BQ. We have two coordinates of price and quantity so that we have 10 = A – 4000B and 11 = A – 3000B. Solving them gives demand function P = 14 – 0.001Q, MR = 14 – 0.002Q and profit is maximized when MR = MC. 14 – 0.002Q = 7 or Q = 7/0.002 = 3500. At this quantity, price is P = 14 – 3500*0.001 = 10.50. This is the accurate profit maximizing price.

c) We see that price increase is decreasing revenue. Hence price decrease will increase revenue.