Homework Question 1
Which of the following statements is/are correct? Choose all that apply.
First degree price discrimination means that a monopolist sells different units of a
product for different prices. As different units of the good may be purchased by
different individuals, these prices may differ from consumer to consumer.
Second degree price discrimination means that a monopolist sells different units
of the product for different prices, but every consumer who buys the same
quantity of output pays the same price.
Third degree price discrimination means that a monopolist sells different units of
the product for different prices, but every consumer who buys the same quantity
of output pays the same price.
First degree price discrimination means that a monopolist sells output to different
consumers for different prices, but each unit sold to any one consumer group
carries the same price.
First degree and second degree price discrimination are as defined in the first two
statements. The 4th statement is only correct if each consumer group consists of a
single consumer. Otherwise, this is the definition of third degree price
discrimination. Similarly, the 3rd is the definition of second degree price
discrimination, not third degree price discrimination. It is, then, incorrect.
Homework Question 2
The consumer's reservation price for a good is:
The price the monopolist would charge for a good.
Different for each different consumer.
The consumer's maximum willingness to pay for the good.
The consumer's reservation price for a good is defined as the consumer's maximum
willingness to pay for the good. The monopolist might not charge the consumer's
reservation price for a good if, for example, price discrimination is not possible. For
example suppose that arbitrage is easy. In this case, the monopolist would have to
follow a uniform pricing strategy. Hence, it would optimally charge the price at which
marginal revenue equaled marginal cost. This could very well not be the reservation
price of any single customer. Hence, the 1st choice is incorrect. Further, the 2nd is
incorrect, as the reservation price across customers may or may not be the same. For
example, I might have the same maximum willingness to pay as another person for an
apple. I might also like apples much more than other people and have a high
maximum willingness to pay compared to others. Either is possible.
Homework Question 3
A strategy of mixed bundling is:
a case when customers may buy one product only if they agree to buy another
product as well.
a case when many units of the same good are sold in a package.
a case where different products are available either as a package or as separate
products.
The third answer is the definition of mixed bundling. The first is the definition of a
strategy of tying. The second one is the definition of a strategy of pure bundling.
Mixed bundling allows the product to be sold separately as well as in a bundle.
Homework Question 4
In order to follow a policy of price discrimination:
A firm must have market power only.
A firm must be able to prevent arbitrage only.
A firm must have some idea of the different amounts people will pay for its
product, have some market power, and be able to prevent arbitrage.
A firm must both have market power and be able to prevent arbitrage only.
All three degrees of price discrimination can only work when certain underlying
conditions are fulfilled. First, the firm that conducts the price discrimination must
have market power: it must face a downward-sloping demand. If it is a price taker,
then consumers will flock to the lowest priced supplier and it is impossible for any
firm to raise price above this level. Second, it must not be possible for consumers to
resell the product. In other words, it must not be possible for a customer who buys the
product for a low price to resell the product to another customer with a higher
willingness to pay. If such resale were possible, the surplus would be captured by the
customers who bought the product for the low price and not by the monopolist. Third,
the firm must have some idea of the amounts people will pay for the product in order
to have an idea of how to conduct discrimination.
Homework Question 5
Which of the following refer(s) to a "screening mechanism"? Choose all that apply.
A case where prices vary across consumers.
Any form of price discrimination.
A case where a firm uses observable characteristics to sort consumers into
groups.
Asking a customer to show a student identification card.
Screening mechanisms can be defined as in the 3rd answer. Hence, screening
mechanisms are a narrower class than all price discrimination or all price differences
across customers. For example, consider a pricing schedule including a fixed hook-up
fee and a usage charge. Consumers can choose a large hook-up charge with a low
usage charge or a small hook-up charge with a high usage charge. We might expect
consumers who anticipate high usage to select the first option (large hook-up and low
usage charge) while consumers who anticipate low usage to select the second option
(small hook-up and high usage charge), even if the firm has no way of telling by
observing each customer which is a high usage and which is a low usage consumer.
This is a case where self-selection and not screening allows price differences to occur.
Hence, the first two answers are incorrect.
Homework Question 6
With first degree price discrimination by a monopolist (choose all that apply):
Consumer surplus is small, but greater than zero and deadweight loss is small, but
greater than zero.
Consumer surplus is zero and deadweight loss is large.
Consumer surplus is zero and deadweight loss is zero.
Producers' surplus is the same as total surplus.
With first degree discrimination, the marginal revenue generated by each unit sold is
exactly the price of that unit. Because the monopolist is now able to charge a different
price for each unit of the good, an additional unit of the good can be sold without
having to decrease the price of the other (inframarginal) units. The sale of the
additional unit can be secured by setting the price for this unit equal to the consumer's
willingness to pay. As a result, the monopolist continues to sell units as long as the
price of that unit exceeds the marginal cost of producing the unit. This occurs at the
point where demand exactly equals marginal cost since, at this point, the maximum
willingness to pay for the last unit placed on the market is exactly equal to marginal
cost. Hence, the price discriminating monopolist maximizes profits by selling Q*
units such that demand equals marginal cost. As usual, we calculate producer's
surplus as the difference between the market price and the marginal cost for every unit
sold. When the monopolist price discriminates, however, market price is traced out by
the demand curve for every unit sold. Hence, at output level Q*, producer's surplus is
the entire area below the demand curve and above marginal cost for all units up to Q*.
Consumer's surplus is zero, since each consumer pays a price equal to his maximum
willingness to pay. Moreover, the deadweight loss is zero because output is sold up to
the point where the willingness to pay is just equal to the opportunity cost of
resources. In other words, at Q* every consumer who is willing to pay at least the
opportunity cost of the resources needed to produce the extra output is able to buy.
Further, every consumer who is not willing to pay the opportunity cost of the extra
output does not buy. In fact, Q* is exactly the same output level as the perfectly
competitive equilibrium output level: total surplus is maximized and deadweight loss
is zero at this point. Comparing the figure with the standard uniform pricing
monopolist's diagram, however, it is clear that the surplus is distributed very
differently. In the competitive equilibrium consumer's surplus is positive. With
perfect price discrimination, consumer's surplus is zero and producer's surplus exactly
equals the total surplus. In other words, the perfectly discriminating monopolist
manages to capture the whole consumer surplus.
Homework Question 7
Suppose that a monopolist faced demand P = 120 - 4Q and has constant marginal cost
MC = 30. If this monopolist engages in first degree price discrimination, total output
will equal:
11.25
22.5
30
The monopolist will sell units up to the point where marginal cost equals price, or
where 120 - 4Q = 30. Solving this equation, the optimal output will be Q* = 22.5.
11.25 is obtained by setting marginal revenue equal to marginal cost for a uniform
pricing monopolist. For such a firm, marginal revenue is less than price, so that output
is lower. For a price discriminating monopolist, marginal revenue equals price.
Hence, the correct response is obtained by setting price equal to marginal cost. If we
do this, we obtain 22.5.
Homework Question 8
Suppose a monopolist faces demand P = 60 - 3Q and constant marginal cost MC = 30.
If this monopolist engages in first degree price discrimination, producer surplus will
be:
300
150
100
The price discriminating monopolist produces up to the point where price equals
marginal cost or 60 - 3Q = 30. Solving this, we see that Q* = 10 (and P* = 30).
Hence, the welfare triangle above marginal cost and below demand is the area of
producer's surplus. The vertical height of the triangle is 60 - 30 and the horizontal
width of the triangle is 10. We must divide this by 2 and multiply to obtain the
area of the triangle so that PS = (60-30)(10)/2 = 150. The 1st answer fails to divide
by 2.
Homework Question 9
A block tariff is a form of
second degree price discrimination
first degree price discrimination
third degree price discrimination
A common example of second-degree discrimination is a block tariff, which is a
particular type of quantity discount. To illustrate, a block tariff with two 'blocks'
means that a consumer pays a price for the first x units consumed and a different price
for any additional units consumed. For example, suppose that all consumers have
demand as shown in the figure in Question 10. Interpret this figure as meaning that
consumers demand multiple units of output, but have decreasing marginal utility of
the good as their consumption increases. Let marginal cost be zero for simplicity. A
block tariff with two blocks might charge a price of 8 for the first 3 units and a price
of 6 for the next 2. This allows the firm to capture a surplus of (8x3 + 6x2 = 36) units,
whereas a single price of 6 for all units would only capture a surplus of (6x5 = 30).
This is second degree price discrimination because different quantities of output are
priced differently, but all consumers face the same price schedule.
Homework Question 10
Let there be two types of customers in the market for a good, type 1 has a low demand
for the good and type 2 has a high demand, as shown in the figure in Question 10.
Compare two pricing schemes. In the first scheme, suppose that all customers are
charged price P1 for the good. Call this the uniform pricing scheme. In the second, all
customers are charged P1 for the first Q1 units consumed and P2 for any additional
units. Call this the block pricing scheme. Which of the following statements is true?
Type 1 will consume Q1* under uniform pricing. Type 2 will consume Q2* under
the uniform pricing scheme.
Type 1 will consume Q1* under the block pricing scheme. Type 2 will consume
Q2* under the block pricing scheme.
Type 1 will consume Q1** under the block pricing scheme. Type 2 will consume
Q2* under the block pricing scheme.
Type 1 prefers the block pricing scheme.
All customers prefer the uniform pricing scheme.
The statements other than in the second answer are not fully correct. Under uniform
pricing at a price of P1, each type of consumer simply purchases at the point where P1
touches the demand curve. In the case of type 1, this is at point Q1* and in the case of
type 2 this is the point Q1. Hence, the 1st statement is incorrect. Under the block
pricing scheme, the price schedule is traced out by the thick line at level P1 until
quantity Q1 and falling to P2 thereafter. The two types will consume at the points
where this line touches their demand curve. In the case of type 1, this is still at point
Q1*. In the case of type 2, the price schedule touches at two points: Q1 and Q2*. The
type 2 consumer captures an additional triangle of consumer's surplus (the vertically
shaded area) if she consumes at point Q2*, however, so Q2* is the optimal point for
any type 2. Hence, the 2nd statement is correct and the 3rd one is incorrect. Type 1
consumers purchase the same amount and capture the same amount of consumer's
surplus under both schemes, so type 1 consumers are indifferent between the two
schemes. Hence, the 4th statement is incorrect. Finally, type 2 captures additional
consumer's surplus (the vertically shaded area) under block pricing so that the 5th
statement is incorrect. Note that the monopolist also captures additional surplus when
block pricing is used so that, in fact, block pricing represents a Pareto improvement
for all agents in this market.
Homework Question 11
Suppose that a monopolist supplies a good to its home market at a marginal cost of
10. It also supplies the good to a foreign market, but since all its production facilities
are in the home market, it must add a transportation cost of 5 per unit to the
production cost in order to sell the units in the foreign country. Inverse demand at
home is PH = 60 - 5Q. Inverse demand in the foreign country is PF = 30 - .25Q. What
is the profit maximizing price for the monopolist in each country?
PH = 25; PF = 25
PH = 35; PF = 25
PH = 35; PF = 22.5
Since each consumer can be identified as a member of a particular group, the profit
maximizing price will be chosen to equate marginal revenue to marginal cost for that
group's demand curve. If the marginal cost differs across the two markets, the profit
maximizing price will be chosen to equate each market's marginal revenue equal to
each market's marginal cost (MR1 = MC1 and MR2 = MC2, where MRi and MCi are
the marginal revenue and marginal cost in market I). Hence, the monopolist sets
marginal revenue at home equal to marginal cost at home so that MRH = 60 – 10Q =
10 = MCH so that Q*H = 5. Substituting into home demand, PH = 35. The monopolist
sets marginal revenue abroad equal to marginal cost abroad so that MRF = 30 - .5Q =
15 = MCF so that Q*F = 30. Substituting into foreign demand, P*F = 22.5.
Homework Question 12
Consider the following willingnesses to pay (reservation prices) for one unit of each
of two goods in a market with four customers. The market is supplied by a monopolist
with zero marginal cost of production of both goods.
What is the monopolist's profit-maximizing (uniform) price for good 1 separately, P1,
good 2 separately, P2 under a strategy of selling the goods separately? What is the
price of a bundle consisting of one unit of each good, PB if only the pure bundle will
be offered?
P1 = 600; P2 = 600; PB = 1000
P1 = 900; P2 = 900; PB = 1000
P1 = 600; P2 = 600; PB = 1200
The demand when the price of either good 1 or 2 is 100 is 4 so that the monopolist
earns 400 + 400 = 800 from setting this price and selling the goods separately. If the
price is 600, only three units of each good will be sold, resulting in profits of 1800 +
1800 = 3600. If the price rises further to 800, profits will be 1600 + 800 = 2400.
Finally, if price rises to 900, profits are 900 + 900 = 1800 since only a single unit of
each good will be demanded. Hence, the profit-maximizing price for the goods when
they are only sold separately is P1 = 600 and P2 = 600 for a profit of 3600. The profitmaximizing price for the bundle is 1000. Here, demand is 4 so that profits are 4000. If
the price of the bundle rises to 1200, only two units will be bought, resulting in profits
of 2400. If price rises further to 1400, only a single unit is bought and profits are
1400. Hence, the profit-maximizing price for the bundle when pure bundling is
conducted is 1000 for a profit of 4000.
Homework Question 13
Consider the following willingnesses to pay (reservation prices) for one unit of each
of two goods in a market with four customers. The market is supplied by a monopolist
with zero marginal cost of production of both goods.
What is the optimal price to set for each good and the bundle if a strategy of mixed
bundling is followed ?
P1 = 900; P2 = 900; PB = 1200
P1 = 100; P2 = 100; PB = 1000
P1 = 600; P2 = 600; PB = 1200
The profit-maximizing price for goods 1 and 2 sold separately under a strategy of
mixed bundling is 900 for each good. The profit-maximizing price for the bundle
when mixed bundling is used is 1200. At these prices, customers 1 and 4 consume
their high valuation good only and customers 2 and 3 consume only the bundle.
Profits are 900 + 900 + 1200 + 1200 = 4200.
Homework Question 14
The profit maximization condition for the advertising monopolist is (choose all that
apply):
Output is chosen optimally by setting marginal revenue equal to marginal cost,
holding constant the level of advertising, as we have seen before. Advertising is
chosen optimally by setting the marginal revenue due to an increase in
advertising, holding output constant equal to the marginal cost of increasing
advertising, also holding output constant.
A/(PQ) = -EQ,A/EQ,P, where A is the advertising expenditure, P is the price of
output, Q is the quantity of output, EQ,A is the elasticity of output with respect to
advertising, and EQ,P is the price elasticity of demand.
The ratio of advertising expenditure to sales revenue must vary according to the
relative responsiveness of demand to advertising expenditure.
If there were no advertising, the monopolist would choose
output as we have seen in our treatment of monopoly
maximization problems in Chapter 11. If we add advertising,
we can think of this as causing a parallel shift out in demand.
This shift increases profit, but it is also costly to achieve. As
usual, the profit maximizing amount of advertising must
balance this cost against the potential benefits that can be
earned. Hence, all three responses are correct and are
alternative statements of the monopolist's profit maximization
conditions when it can choose both advertising and output
levels. The first is, perhaps, the easiest to see since it says that
for a given level of advertising the monopolist's output
maximization problem is the same as before. For a given level
of output, it says that the monopolist must balance the gains
from advertising against the cost of advertising, using marginal
reasoning. The second answer is obtained by manipulating the
conditions in the first answer. The third states the second
condition in words.
Homework Question 15
Let a monopolist face inverse demand curve P = 10Q -2A1,
ERROR! P = 100Q -2A1
where P is price, Q is output, and A is advertising expenditure. Define advertising
intensity as the share of revenues that is spent on advertising. If the monopolist
chooses P and A to maximize profits then its advertising intensity is:
1
0.5
-0.5
From the inverse demand, we get Q = 10A1/2P-1/2 so that EQ,A = ½ and EQ,P = -1/2.
Hence, the advertising intensity is A/(PQ) = - EQ,A/EQ,P = -(1/2)/(-1/2) = 1.