1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y 2 1 + y 2 2 , where α is some constant. a) What restriction on α is required to guarantee that this cost function exhibits economies of scope? b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 and y2.
1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y
2
1 + y
2
2
, where α is some constant.
a) What restriction on α is required to guarantee that this cost function exhibits economies of
scope?
b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 and
y2.
2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:
• The market is a
cost of 12 in this perfectly competitive market.
• The market is dominated by one monopolist with a marginal cost of 12. This monopolist is
able to achieve 1st degree pricing.
• The market is dominated by one monopolist with a marginal cost of 12, but the monopolist
is able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:
(Q∗
1 = 30, p∗
1 = 35), and (Q∗
2 = 60, p∗
2 = 20).
• The market is dominated by one monopolist with a marginal cost of 12, but the monopolist
now uses 3rd degree pricing. Assume the firm can distinguish between low-demand consumers
on the weekday and high-demand consumers on the weekend such that Qh = 55 −
1
2
ph and
Q` = 45 −
3
2
p`. The monopolist charges a difference price, p` and ph, in each distinct market.
• The market is dominated by one monopolist that is not able to price discriminate.
Calculate the following values and fill in the table according to the 5 scenarios above
1st Deg. 2nd Deg. 3rd Deg. No Price Discrim.
Profits π
CS
PS
DWL
Quantity Sold
in Market
In this setting, if the monopolist has the opportunity to go from no
degree pricing for a fee of 800, should it make the switch? Why or why not?
3. Given the information requirement for price discrimination, what are your thoughts about the
connection between information and firm profits? Do we see evidence of a connection between
information and firm profits in reality? How do data brokers (i.e. information brokers) fit into
this?
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