Question

Suppose there are only five customers (A, B, C, D, and E) interested in buying widgets. Customer A is willing to pay $11, customer B is willing to pay $9, customer C is willing to pay $7, customer D is willing to pay $5, and customer E is willing to pay $4. Lastly, suppose that all costs of production are zero.

1. (18 points) If the market is served by a monopolist that chooses a single price, then what is the monopoly price? Who purchases a widget and what is each customer’s consumer surplus? What is monopoly profit?
2. (18 points) Suppose that the 5 customers can be divided into two groups: Adults are customers A, B, and D and children are customers C and E. If the monopolist can use third-degree price discrimination, then what price does it charge adults and children? Who purchases a widget and what is each customer’s consumer surplus? What is monopoly profit?
3. (18 points) Instead if the monopolist can use first-degree (perfect) price discrimination, then what price does the monopolist charge each customer? Who purchases a widget and what is each customer’s consumer surplus? What is monopoly profit?
4. (6 points) Which pricing regime (standard pricing, third-decree, or first-degree price discrimination) is best for customer A and which is best for customer D.

Answer 1

1. Standard pricing:

Monopoly price = $7; A, B and C will buy widgets;
A' s CS = 4 (11 - 7 = 4); B's CS = 2 (9 - 7 = 2); and C's CS = 0 (7-7 = 0);
Monopoly profit = 21
We see in the table that total revenue is maximum when he charges a price of $7 and sells 3 widgets.
So, he will sell at $7 tot eh first three customers - A, B and C.
As MC = 0, revenue = profit. that is, 7*3 = 21 is the profit of the monopolist.

2. Third degree price discrimination:

Price for adults = $9; price for children = $4
A, B, C and E will purchase widgets;
A's CS = 2 (11 - 9 = 2); B's CS = 0 (9-9=0); C's CS = 3 (7-4=3); and E's CS = 0 (4-4=0)
monopoly profit = revenue =( 2*9)+(2*4) = 18+8 = 26

3. Perfect price discrimination:
Monopoly price is different for each customer.
He will charge A price = $11; for B, price = $9; for C, price = $7; for D, price = $5; and for E, price = $4.
All 5 customers will buy widgets as MC = 0, the monopolist sell widgets to all 5 customers as per their willingness to pay.
Each customer's CS = 0 as price = WTP for each of them.
Monopoly profit = 36 (11+9+7+5+4 = 36)

4. Pricing regime best for customer A = standard pricing.
  best for customer D = First degree (perfect price discrimination)
From Standard pricing, A's CS = 4, from third degree pricing, his CS = 2; and from first degree pricing, his CS = 0. He gets the highest CS from standard pricing.
D does not get to buy in the standard or third degree pricing. He can buy only under perfect price discrimination where his CS = 0.