Consider a monopoly art museum that has two representative consumers with the demands P=16-2Q (for Consumer A) and P=10-2Q (for Consumer B). The museum's marginal cost is $2 per visit.
a. If the museum practices first degree two-part pricing, what will be the prices charged to each consumer type?
Two-part tariff is a pricing strategy that could be employed by a monopolist to extract more profit from consumer than an ordinary monopolist. The pricing strategy involves a one-time fee for access to the product and a constant unit price.
Answer and Explanation:
a. The museum will charge a fee of $49 to consumer A and a fee of $16 to consumer B.
The optimal two-part pricing is to set (1) the entry fee equal to consumer surplus in a competitive equilibrium; and (2) the unit price to the marginal cost.
We first compute the entry fee. In a competitive market, the museum would set price equal to marginal cost, thus the equilibrium quantity for consumer A is:
- 16 - 2Q = 2
- Q = 7
So the consumer surplus for consumer A = (16 - 2)*7/2 = 49
For consumer B, the quantity in a competitive equilibrium is:
- 10 - 2Q = 2
- Q = 4
So the consumer surplus for consumer B = (10 - 2)*4 / 2 = 16
Hence, the museum should charge a fee of $49 to consumer A and $16 to consumer B, and set a price per visit to $2.
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