If the firm facing the demand curve P = 10

Question

If the firm facing the demand curve P = 10 - Q still has zero marginal costs and is now a perfect price discriminator instead of a single price monopolist, what will profits be if fixed costs are 12? 
A)10 
B)12 
C)13 
D)38

Quizplus · Accepted Answer

As a perfect price discriminator, the firm charges each customer their reservation price, which is equal to the maximum price they are willing to pay. In this case, the demand curve is P=10-Q, so the reservation price for each unit is different. To find the reservation price for any quantity Q, we need to rearrange the demand equation as Q=10-P.

For the first unit, the reservation price is $10, because this is the maximum that anyone is willing to pay. The second unit has a reservation price of $9, because if the firm charged $10, the second customer would go elsewhere. The reservation price for the third unit is $8, and so on until the reservation price for the tenth unit is $1.

So the firm can sell all ten units at different prices, but the total revenue will be the same as if they charged a single price of $5 (the midpoint of the demand curve). Total revenue is therefore 10*$5 = $50.

Since the firm has zero marginal costs, all of this revenue is profit, except for the fixed cost of $12. Therefore, profits are $50-$12=$38, which is answer choice (D).