Question

A company sells a service with demand for service Q = 500 - P.

The cost of each service is $3000 + $100 per user of the service

1) What is the profit maximizing price the business will charge? How many people can use the service? What is the companys profit for each service?

2) The company decides to open up an upper market version of the service. Regular demand is shown as Q1 = 260 - 0.4P, and the upper market being Q2 = 240-0.6P.

The uppermarket version having a higher price, What price does the company charge the upper market service? What price does the company charge the regular service? Will the change reduce number of total custoemrs?

3) WIll the new price system provide profit for the company

4) What is the total change in consumer surplus with the price discrimination?

5) Will DWL be changed due to the price change?

Answer 1

1) Initially, demand curve is given by Q=500-P or, P=500-Q

Then, total revenue TR = P*Q = 500Q-Q²

and marginal revenue MR = dTR/dQ = 500-2Q

Again, C=3000+100Q

Then, marginal cost MC = dC/dQ = 100

For profit maximization, MR=MC

or, 500-2Q=100

or, 2Q=400

or, Q=200 is the equilibrium quantity

and P=500-200=$300 is the equilibrium price

Profit = Total revenue - Total cost = (300*200)-{3000+(100*200)} = 60,000-(3,000+20,000) = $37,000

2) In the regular market, Q₁ = 260-0.4P₁ or, P₁ = 650-2.5Q₁

Then, MR₁ = 650-5Q₁

Now, for maximizing profit in the regular market,

MR₁=MC

or, 650-5Q₁ = 100

or, 5Q₁ = 550

or, Q₁ = 110 units is the equilibrium quantity in the regular market

and P₁ = 650-(2.5*110) = $375 is the equilibrium price in the regular market.

Again, in the upper market, Q₂ =  240-0.6P₂ or, P₂ = 400-1.67Q₂

Then, MR₂ = 400-3.33Q₂

Now, for maximizing profit in the upper market,

MR₂=MC

or, 400-3.33Q₂ = 100

or, 3.33Q₂ = 300

or, Q₂ = 90 units is the equilibrium quantity in the upper market

and P₂ = 400-(1.67*90) = $250 is the equilibrium price in the upper market.

Thus, total number of customers in these two markets (110+90 = 200) is equal as in (a).

3) New profit = total revenue - total cost

or, New profit = (P₁*Q₁)+(P₂*Q₂)-C

or, New profit = (375*110)+(250*90)-{3000+(100*200)}

or, New profit = 63,750-23,000

or, New profit = $40,750

Thus, the new system provided more profit.

4) Consumer surplus under single market is = 1/2*200*(500-300) = $20,000

But consumer surplus with two markets = {1/2*110*(650-375)}+{1/2*90*(400-250)} = 15,125 + 6,750 = $21,875

Thus, consumer surplus increases with price discrimination.

5) Dead-weight loss gets decreased with price discrimination as dead-weight loss gets transferred to higher consumer surplus and higher profit for the monopolist.