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Homework answers / question archive / Natch
Natch.com is an internet dating site that helps people meet partners by showing them profiles of potential matches. When a person signs up, she or he fills out a profile, then pays money to view profiles of others. The company has hundreds of profiles in the computer system and it costs nothing to email profiles to customers (so MC = 0). Suppose that there are two types of customers: desperate customers have an inverse demand for profiles given by pd = 40 − 2qd 1 and not-desperate customers have inverse demand pn = 20 − 2qn. The company has exactly one of each type of customer.
Now suppose that the information that the customers provide in their profile does provide the company with some information. Specifically, it is not enough to allow the company to perfectly price discriminate, but it does allow the company to observe whether or not the customer is desperate. What will its profits be if it sells profiles individually, but charges different prices to the desperate and non-desperate customers (that is, it engages in multi-market price discrimination)?
Desperate Customers inverse demand function:- Pd = 40 - 2qd
Non- desperate Customers inverse Demand function:- Pn = 20 - 2qn
If the company sells profiles individually and charges different prices to the desperate and non-desperate customers then :-
Desperate Customers:-
The company will maximise it's profits-
The Optimal condition is MR = MC
40 - 4qd = 0
qd* = 10 and Hence, Pd = 20
Company's profits = TR - TC = 200
Non - desperate Customers:-
The company will maximise it's profits:-
The Optimal condition:- MR = MC
20 - 4qn = 0
qn* = 5 and hence, Pn = 10
Company's profits= TR - TC = 50
So The company's total profits be (200 + 50) = 250
