Question

A typical customer who buys from a firm has a demand given by P = 90 - 3 Q. The firm has a constant marginal cost MC = $18 and no fixed cost. It currently uses a uniform pricing strategy (i.e., it charges a single price for all the units it sells), but it is contemplating to switch to the following block pricing strategy: “Buy the first 5 units at a price of $75 per unit, and any subsequent unit at a price of $54 per unit.” If the firm uses this pricing strategy, then compared with uniform pricing, profits per customer under the above block pricing are

a) The same as in uniform pricing.

b) $450 greater under block pricing.

c) $105 greater under block pricing.

d) lower under block pricing than under uniform pricing.

Answer 1

P = 90 -3Q

TR = P*Q

= (90 - 3Q)*Q

= 90Q - 3Q^2

MR = 90 - 6Q

Equilibrium MR=MC

90 -6Q = 18

90 -18 = 6Q

72 = 6Q

Q = 72/6

= 12

P = 90 - 3(12)

= 90 - 36

= $54

Profit = TR - TC

= 12*54 - 18*12

=648 - 216

= $ 432

Hence profit per customers in single pricing is $ 432

Profit when block pricing is followed:

TR = 5*75 +7*54

= 753

TR = 18*12

= 216

Profit = 753 - 216

= 537

Difference = 537 - 432

= 105

Profit per customers in bock pricing is $ 105 greater.

Hence, right answer is (c)