Example: 2 parttariff with 2 consumer groups.
Suppose there are 1000 consumers (Type 1) with a demand curve given by:
Q1 = 10
–
P
Another 100 consumers (Type 2) have the demand curve given by:
Q2 = 32
–
2P
Marginal cost is constant at $1
Find the optimal two parttariff for a monopolist to charge in this case.
We need to maximize profits by choosing a price per unit (P*) and an entry fee (T*).
First, note that the
entry fee will be equal to the smaller of the consumer surpluses from the two groups.
The entry fee can be expressed (see graph above) as
T* = (1/2)*(10P)Q[P1].
Where Q1[P] represents
the quantity demanded by group 1 at a price of P.
We can now write the profit function entirely in terms of P. First , write the profit function in terms of P
& Q.
Recall that profits will consist of the entry fee (charged to 2000 customers) plus units sold to 1000
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 Winter '09
 PARMAN
 Microeconomics, Supply And Demand, Inverse demand function, Graph of a function, entry fee

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