A typical customer who buys from a firm has a demand given b

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

A)Each customer will buy 5 units

Each customer will buy 7 units

C)Each customer will buy 12 units

D)Each customer will buy 17 units

Solution

As monopoly charges $75 units for the first 5 units

so we put this in the demand curve and get the amount that each consumer will buy at this price

P = 90 - 3Q

75 = 90 - 3Q

Q = 5 so each consumer will buy 5 unit at price $75.

afterward the price is $54 the consumers will consumes

P = 90 - 3Q

54 = 90 - 3Q

Q = 12 so at price $54 the consumers will buy 12 units.

it means the first 5 units the buyers will buy at $75 and rest 7 units from 12 units they will buy at $54 price.

Also the firm will only produce 12 units as the MR = MC

MR = d(TR) / dQ = 90- 6Q

MR = MC

90 - 6Q = 18

Q = 12.

so total quantity the firm sell is 12 units.

it means each consumer will buy 12 units.

so option C) is correct.

others options are incorrect-

- option A) is incorrect as each consumer will buy 5 units at price $75 it means when uniform price.

- option B) is incorrect as the consumers will buy 12 units not 7 units.

- option D) is incorrect as if they buy 17 units it means the price must be equal to p = 90 - 3*17, i.e., P = $39 but the firms charges last price is $54.