Answer to Question #272876 in Microeconomics for Imasha

Question

Following information shows that a firm offering a good at different prices to groups of consumers with different levels of willingness to pay.

Inverse Demand for movies: P1 = 20 – 4Q1

Inverse Demand for students: P2 = 10 – Q2

MC = 4Q LKR /ticket

(a) What price and quantity and maximizes profits if the firm charges each market?

(b) Demonstrate that charging different prices for the two groups results in higher profits than charging the same price for everyone.

Answer 1

(a)

Movies:

$P=20-4Q$

$TR=PQ$

$TR=20Q-4Q^2$

$MR=20-8Q$

$MC=4Q$

At maximum profit, MR=MC

$\implies20-8Q=4Q$

$Q=1.67$

Price:

$20-4(1.67)=13.32$

$P_1=13.32$

Students:

$P=10-Q$

$TR=10Q-Q^2$

$MR=10-2Q$

$MC=4Q$

At maximum profit, MR=MC

$\implies10-2Q=4Q$

$Q=1.67$

Price:

$10-1.67=8.33$

$P_2=8.33$

(b)

As seen from the calculation of profit maximizing quantity and price, profit is maximized when the two groups are charged different prices.

This is a demonstration of third degree discrimination which reflects different prices for different consumer groups. This is practised based on the seller's belief that customers in certain groups can be asked to pay more or less based on certain demographics or on how they value the product in question.

Price discrimination is valuable since the profit that is earned as a result of separating the markets is greater than the profit earned as a result of keeping the markets combined.