Answer:

22. To determine the profit maximizing quantity and price if this firm charges a single price for its product we need to equate MR to MC and then use the determined quantity in the monopolist’s demand curve to find the price the monopoly will charge. We are given the MC curve for the firm; we need to find the MR curve for the firm. We can use the demand curve to find the MR curve for the firm: P = 250 – 5Q and thus, MR = 250 – 10Q since the MR curve shares the y-intercept of the demand curve and has twice the slope of the demand curve provided the demand curve is linear. Thus, 30 = 250 – 10Q or Q = 22. The single price monopolist will produce 22 units. Use this quantity and the demand curve to find the price the monopolist will charge: P = 250 – 5(22) = $140 per unit.

To find the single price monopolist’s profit remember that profit = TR – TC. TR is easy to calculate: TR = P * Q = ($140 per unit)(22 units) = $3080. TC is a bit more of a challenge: we do not have the TC curve or the ATC curve, but we do have the MC curve and the assumption that FC are equal to zero. Since MC is constant, that implies that the ATC of producing a unit of output is equal to the MC of producing an additional unit of output (if the average height of the basketball team is six feet and all the additional players we add to the team are six feet tall, then the average will not deviate from six feet). So, ($30 per unit)(22 units) = TC = $660. Profit = $3080 – $660 = $2420.

The completed table will be provided at the end of the problem.

3880. If the monopolist charges two different prices-$140 for the first 22 units and $100 for the next 8 units, it will earn TR = ($140 per unit)(22 units) + ($100 per unit)(8 units) = $3880. Its TC will be equal to ($30 per unit)(30 units) = $900. Its profits will therefore be equal to $3880 – $900, or $2980.
3881. If the monopolist is a perfect price discriminator then the monopolist will produce that amount of the good where P = MC for the last unit produced. This will be the socially optimal amount of the good. To find this quantity use the demand curve and the MC curve: 30 = 250 – 5Q or Q = 44 units. The firm will price each of these units at a different price: basically the firm will price along its demand curve with the first unit being sold at P = 250 – 5(1) = $245 per unit; the second unit being sold at P = 250 – 5(2) = $240 per unit; and on and on. Notice however that this provides a step by step oriented to this TR calculation (review this in your text if you find this hard to understand) and we would prefer to use a smooth orientation to this TR calculation. So, let’s imagine that we can price this good at really small q’s so that we basically take the TR as the sum of the area of the triangle above the MC curve and the rectangle below the MC curve. Thus, TR = (1/2)($250 per unit – $30 per unit)(44 units) + ($30 per unit)(44 units) = $4840 + $1320 = $6160. TC = ($30 per unit)(44 units) = $1320. (Notice, we could have save some steps by recognizing that the rectangle ($30 per unit)(44 units) is part of TR and also equivalent to TC: this area therefore is “netted out” and does not need to be even calculated in order to find the firm’s profits.) Profit for the perfect price discriminating monopolist is equal to $4840.

1. If we examine the table we see the more price discrimination there is the greater the profit for the firm. Note, also that the more price discrimination there is the closer we get to producing the socially optimal amount of the good: it’s just with perfect price discrimination the monopolist is able to “capture” all of the consumer surplus and the consumer gets none of this surplus.

Here’s the completed table: