PROBLEM 1
In Albrecht v. Herald Co., the Supreme Court in 1986 decided a case involving the publisher of a St.
Louise newspaper and one of the carriers that delivered the newspaper to individual households. The publisher
had established a system in which each carrier was granted an exclusive territory that was subject to
termination if the carrier charged a retail price for the newspaper exceeding the maximum price suggested by the
publisher. In 1961, the carrier for route 99 raised the price for its customers to a level that exceeded the
suggested retail price. The publisher took retaliatory actions that eventually caused the carrier to lose the route,
and the carrier sued for treble damages under section 1 of the Sherman Act. The Supreme Court decided that
enforcing resale price restrictions in this manner constituted per se illegal price-fixing.
To model this situation, let the inverse demand function for newspapers on Route 99 be P =
a – Q, where a > 0, and Q denotes the number of newspapers sold in the route. Suppose that
the publisher’s marginal cost of producing newspapers is a constant denoted by c while the
carrier incurs a constant marginal delivery cost denoted by d. The carrier pays the wholesale
price w and sells papers at a retail price P. Both the carrier and the publisher are profit
maximizers.
(A) Suppose that resale price restrictions could be enforced legally, so the publisher
chooses the prices w and P. Show graphically, how optimal w* and P* are chosen.
Would the carrier prefer a retail price that is greater or less than P*? Again justify your
reasoning graphically.
(B) Suppose now that the resale price restrictions cannot be legally enforced, so the
carrier is free to choose P. Let w** and P** denote the equilibrium prices without the
resale price restrictions. Find w** and P** and show them on the graph together with
w* and P*.
(C) Compare now the consumer surplus in both cases. Do the same with the total
surplus. Comment.
(D) Suppose now that the demand for newspapers depends on carriers’ selling efforts, e,
such that P = a + e – Q. The marginal cost of applying efforts for the carrier is αe (can
set α = 1 if it simplifies the analysis). Suppose that the carrier’s effort level is not
contractible. In this case, will RPM be sufficient to implement the fully integrated
monopoly outcome? Redo points (A), (B) and (C).
(E) The purpose of this point is to show that even if resale price restrictions cannot be
legally enforced, still firms may implement the fully integrated monopoly outcome.
For the sake of concreteness, assume that the publisher can use non-binding resale
price recommendations. Furthermore, assume that the publisher and the carrier can
sign only a short-term contract valid for a single period and at the beginning of each
period the parties have to renew it. As before, let the contract specify the wholesale
price w only. The twist is that the publisher can recommend the retail price P, i.e., the
carrier buys the newspapers for w and is formally free to sell them at whatever price
(and apply whatever the level of efforts). At the end of each period both the publisher
and the carrier obtain their profits. Assuming that the parties have a common
discount factor δ, show that even if the resale price is non-binding, still under some
circumstances (i.e., for some δ) there exist subgame perfect equilibria that support the
fully integrated monopoly outcome (you can restrict attention to grim-trigger
strategies). Would the result hold if the publisher observed only imperfectly the
demand for the newspapers?
PROBLEM 2
The purpose of this exercise is to show that the problem of double marginalization still
remains even if there is imperfect competition downstream. Suppose that there is a single
manufacturer seeking to distribute its product through N imperfectly competitive retailers.
The retailers are assumed to compete a la Cournot and the contracts are restricted to linear
wholesale prices. Formally, the game unfolds as follows: in stage 1 the manufacturer makes a
public offer to each retailer i with each offer specifying the wholesale price wi at which it is
willing to sell the product to retailer i. In stage 2 each retailer i observes the offers made to its
rivals and decides the quantity qi to purchase from the manufacturer. Assume that for any
given profile of quantities (q1 ,..., q N ) supplied on the market, retailer i will face the consumer
price pi at its store which is given by:
1
1
pi  1  qi    q j ,
j i
where   0 (introduced for the sake of generalization) while   [0,1] measures the degree
of substitutability of the retailer’s services: when   0 , then the retailer’s services are
perceived to be independent while when   1 they become closer substitutes. Furthermore,
assume for simplicity that the manufacturer incurs the unit cost of production c > 0 while the
retailers incur no distribution costs.
(A) Suppose first that the manufacturer is able to control the sales in each retail outlet.
Characterize the market outcome in that case.
(B) Characterize the market outcome in case of decentralized decision making. How does it
depend on the number of retailers and the degree of substitutability of the retailer’s services?
Comment.
PROBLEM 3
The purpose of this exercise is to show that vertical integration might reduce welfare.
Consider the situation where there is a single supplier and two identical distributors. There are
two types of consumers on the market: consumers of the first type have a high willingness to
buy the good and do not care about the retailer’s services. They derive the utility uh   h  p
from consuming the good. In contrast, consumers of the second type have a lower
willingness to buy the good and do care about the retailer’s services. They derive the utility
ul   l  e  p where e  e1  e2 is the combined level of services provided by two retailers.
The idea is that each retailer cannot fully appropriate the benefits of its provision of services
which can be regarded as a public good (a consumer may go to a more expensive store to get
to know the product, say, for free but then buy it at a less expensive one). Denote by  k the
proportion of consumers of type k  {h, l} with h  l  1 . Assume that each retailer i =

1,2 incurs the cost Ci (q, ei ; wi )  wi q  ei2 where wi is the wholesale price at which it
2
purchases the good from the supplier and ei is the level of services it chooses to provide.
1
Assume that  
and  h   l . Furthermore, assume that the supplier is restricted to
h  l
set the same wholesale price to both retailers (i.e., price discrimination is not allowed).
(A) Social Optimum. Find the socially optimal level of services. In particular, calculate the
consumer surplus and total welfare.
(B) Vertical separation. In that case the game is as follows. First, the supplier announces
the wholesale price w( w1  w2 ) to both retailers. Second, the retailers choose the levels of
their services and set their retail prices. Third, consumers decide at which store (if any) to buy
the goods, then all the payments are made and the payoffs are realized. Solve for the
equilibrium of this game. Calculate the consumer surplus and total welfare in equilibrium.
(You may also try to solve the task by relaxing the assumption of price discrimination).
(C) Vertical Integration with two retailers. Calculate the consumer surplus and total
welfare in that case. Identify the range of parameter values for which the level of welfare is
lower than that obtained in point (B or A?). Comment.
(D)* Would the result be different if you instead assumed that the supplier merged with only
one retailer? (you can skip this point if you wish)
PROBLEM 4
A monopolist produces a good with constant returns-to-scale technology. Denote by c < 1
the unit cost of production. The size of the market consists is normalized to 1. Assume for
now that all consumers have the identical demand Q(p) = 1 − p.
(A) Suppose that the monopolist is restricted to apply a simple uniform pricing rule.
Find the profit maximizing price and the value of the profit.
(B) Suppose now that the monopolist is allowed to charge a two-part tariff (f, p) where
f is the fixed fee and p is the price per unit sold to the consumer. Find the optimal two-part
tariff and the profit of the monopolist. Compare the result with the one obtained in (A).
Comment.
(C) Compare uniform pricing with the two-part tariff in terms of the total welfare and
consumer surplus. Comment.
Assume now that there are two types of consumers. The consumers of type 1 have the
demand function Q1(p) = 1 − p while the consumers of type 2 have the demand function
Q2(p) = 1 − p/2. The proportion of consumers of type 1 is given by λ Є (0, 1).
(D) Suppose that it is prohibited to practice price discrimination, i.e., the monopolist is
obliged to set either a single uniform price or a single two-part tariff. In both cases, find
the optimal pricing policies and the corresponding profits. Is there a scope for
improvement?
(E)* Suppose that the monopolist is allowed to engage in second degree price
discrimination (this is the situation where it cannot distinguish among the consumers but
can design the payment schemes so as to extract the relevant information; at the optimum
it typically offers a menu of offers letting the consumers to self-select). Find the optimal
menu for the cases of linear pricing and two-part tariffs, respectively. Compare the
corresponding profits. What is the most efficient tool to discriminate?