isi

[parul jain]

(b) Consider the market for a particular good. There are two types of customers: those
of type 1 are the low demand customers, each with a demand function of the form
 p = 10 - q1 , and those of type 2, who are the high demand customers, each with a
demand function of the form p =2(10 - q2) . The firm producing the product is a
monopolist in this market and has a cost function C(q) = 4q2( its q square) where  q = q1 + q2 .

(i) Suppose the firm is unable to prevent the customers from selling the good to one
another, so that the monopolist cannot charge different customers different prices.
What prices per unit will the monopolist charge to maximize its total profit and
what will be the equilibrium quantities to be supplied to the two groups in
equilibrium?
(ii) Suppose the firm realizes that by asking for IDs it can identify the types of the
customers (for instance, type 1’s are students who can be identified using their
student IDs). It can thus charge different per unit prices to the two groups, if it is
optimal to do so. Find the profit maximizing prices to be charged to the two
groups.

[Anakin Skywalker]

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The author has deleted this message.

[Rajat]

skywalker, can you please show your working

[L]

Part (i) Since P is same in both markets, so,
Profit = (40/3 -2Q/3) - 4Q2
Which gives Q=40/28 and P= 260/21. But, at this P, Q1<0. So, Q1=0.
q2=3.81, but, Profits are -ve.
Since, at this price, no one  from low demand market will buy, better will be if monopolist produces for the high demand market as it gives higher profit instead of zero.
Now, setting MR=MC
20-2Q= 8Q
=> Q=2 and P = 16 and profit = 32-16=16.

For part (ii), as low demand market is not profitable, better for monopolist to produce the same amount as in (i), though, one can easily show that even price discrimination will not be profitable to produce for low demand market.