Timothy Van Zandt - Insead

208 Nonlinear Pricing Chapter 12
Figure 12.3
€
P
9
8
7
6
5
4
3
2
1
Variable
consumer
surplus
Consumer faces two-part tariff t(Q) = T + PQ:
consumes Q ∗ if he trades at all;
trades if variable consumer surplus ≥ T .
d(P )
Standard demand curve
(marginal valuation curve)
10 20 30 40 50 60 70 80 90 100
Q Q
∗
Using two-part tariffs in perfect price discrimination
In perfect price discrimination, the firm makes a take-it-or-leave-it offer of a single quantity
at a single tariff to each customer. You can think of such an offer as an extreme form of
nonlinear pricing.
There is a two-part tariff that leads to the same outcome while appearing to give the
customer more choice. Since the firm gets all the gains from trade and hence wants the
customer to purchase the socially efficient amount of the good, the usage fee P should
be set to the firm’s marginal cost. The customer then purchases up to the point where his
marginal valuation equals the firm’s marginal cost. Then the firm sets the entry fee in order
to extract all the gains from trade, so that the customer is indifferent between entering the
market and staying out. Thus, the firm sets T equal to the consumer surplus the customer
would receive if he faced the linear price P .
That perfect price discrimination can be achieved with a two-part tariff helps us understand
both perfect price discrimination and two-part tariffs. However, it is not an explanation
of why two-part tariffs are used. First, recall that perfect price discrimination is only a
hypothetical benchmark. Second, a two-part tariff is a more complicated scheme than the
“single quantity at a single tariff”.
Exercise 12.3. Suppose the demand curve in Exercise 7.3 is that of a single customer, and
let your marginal cost be 25. Suppose you implement perfect price discrimination with a
two-part tariff. What is your usage fee? What is the entry fee?