Question

Suppose you are a pricing analyst for DataXX Corporation, a firm that recently developed a new
software program for data analysis. You have two types of clients who use your product. Type A’s
inverse demand for your software is P = 120 – 10Q, where Q represents users and P is in dollars per
user. Type B’s inverse demand is P = 60 – 2Q. Assume that your firm faces a constant marginal cost of
$10 per user to install and set up this software for a Type A user and $20 per user to set up for a Type B
user.
(a) Suppose you can tell which type of buyer is buying the product before a purchase is made. What
kind of price discrimination will you practice in this case. Using marginal analysis, determine the
prices you will charge each type. What will be DataXX’s profit?
(b) However, suppose you were wrong in your assumption that you could correctly identify the
buyer type. Instead it is possible that a Type A buyer can come in and pose as a Type B buyer and
vice-versa and get a price you intended for the other type. What will be DataXX’s profit in this
case?

(c) In the situation described in (b), describe the type of price discrimination that can still work.
Explain how you could use a menu of two-part tariff to implement this price discrimination. In
words, explain how you can ensure that the two types will end up paying different prices.
(d) Assuming that you pick the per-unit price for one of the two-part tariffs as the same as that you
obtained in (a) to be charged to the Type B buyers and that you pick the per-unit price for the
other two-part tariff equal to $10, determine the fixed charges you would want to pick for the
two-part tariffs. In your answer, describe which Type of consumer will you be targeting each of
these two-part tariffs. What will be DataXX’s profit in this case?

Answer 1

a) Inverse demand for Type A users is

P = 120-10Q , Therefore, total Revenue of DataXX corporation from Type A users is PQ = 120Q-10Q²

or, Marginal Revenue of DataXX corporation from Type A users is d(PQ)/dQ=120-20Q

Also constant marginal cost for type A users is $10/user

Under equiibrium condition, Marginal Revenue = Marginal Cost

i.e., 120-20Q =10 or 12-2Q=1 or Q=11/2 = 5.5

and P= 120-10Q= 120-10*5.5= 120-55= 65

Again inverse demand function for Type B users is P= 60-2Q , total revenue is PQ= 60-2Q²

Therefore, marginal revenue is d(PQ)/dQ=60-4Q

Also constant marginal cost for Type B users is $20/user

Therefore, 60-4Q=20 or 4Q=40 or Q=10

Also P= 60-2Q=60-2.10=40

From prices for Type A and Type B users, it is clear that the firm DataXX corporation is practising third degree of price discrimination. It is charging very high price of a product to Type A users than the price of the same product to Type B users.

Total profits from Type A users = Total Revenue-Total Cost= PQ- Average Cost *Q

We know constant marginal cost is equal to average cost of the product i.e., AC= $10/user

Therefore, total profits(π ) = 65*5.5-10*5.5 = $302.5

b) Total number of type A users(Q) = 5.5

Also price for Type B users = $40

Therefore total profit of DataXX in this case or π= PQ-total cost = 40*5.5- 10*5.5= $165

c) In case b) there is second degree of price discrimination where a firm charges same price for diifferent quantities of a product.   We can show the price discrimination in this case in following table:

Users	Price or Average Revenue(P)	No. of users(Q)
Type A	$40	5.5
Type B	$40	10

Please note that here DataXX corporation is charging same price to both Type A and Type B users for diifferent values of Q i.e., 5.5 and 10.

d) Price or P for type A users as computed in a) is P=$65 which is to be charged for Type B users

Also Price for type A users in this case is P = $10

Therefore, the fixed charges to be used for the two-part tariffs is $10 which is least price among two-part tariffs. With fixed charges, Type A users are targeted here.

Firm total profit (π) from Type A users = PQ - Total Cost = 5.5*10-10*5.5 = 0   (From (a) Q =5.5)

Total profit (π) from type B users = PQ-Total Cost = 65*10-10*20 = $450 (From (a) Q=10)