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answerstohomework4summer2014.docEconomics 101 Sum...
answerstohomework4summer2014.docEconomics 101 Summer 2014 Answers to
answerstohomework4summer2014.docEc...
answerstohomework4summer2014.docEconomics 101 Summer 2014 Answers to
Page 9
The completed table will be provided at the end of the problem.
b. 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.
c. 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.
d. 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:
Pricing Scheme
Price Charged
Quantity Produced
Profit
a) Single Price Monopolist
$140 per unit
22 units
$2420
b) Monopolist charges two
prices
$140 per unit for the first 22 units and
$100 per unit for the next 8 units
30 units
$2980
c) Monopolist practices
perfect price discrimination
A different price for every unit
produced
44 units
$4840
6. Consider a monopolist who sells her product to two different classes of customers. Suppose this
monopolist knows the following information:
Demand for product from class one: P = 10 – Q
Demand for product from class two: P = 5 – (1/2)Q
MC = $2 per unit; and assume there are no fixed costs for this monopolist
a. Find the market demand curve for the monopolist’s product if there are only these two classes of
buyers. Make sure you identify any ranges (or domains) where appropriate.
b. If the monopolist charges a single price to all the buyers of its product, what price will she charge and
how many units will the monopolist produce? Show how you found this price and quantity. Then,
calculate the amount of profits the monopolist will earn with this combination of price and quantity.
c. Suppose this monopolist decides to engage in third degree price discrimination. What price and
quantity will she provide to class one buyers? What price and quantity will she provide to class two
buyers? What will profits from class one be for this price discriminating monopolist? What will profits
from class two be for this price discriminating monopolist? What will total profits be for this price
9
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