Answer to Question #274859 in Microeconomics for AMA

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 = 4 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.

(c) Graph the demand curves, the marginal revenue curves, the marginal cost curve and highlight the equilibrium. 

Answer 1

(a) The price and quantity that maximizes profits if the firm charges each market are:

MR = MC,

$MR_{1} = TR'(Q_{1}) = 20 - 8Q_{1},$

20 - 8Q1 = 4,

Q1 = 2 units,

P1 = 20 - 4×2 = 12.

$MR_{2} = TR'(Q_{2}) = 10 - 2Q_{2},$

10 - 2Q2 = 4,

Q2 = 3 units,

P2 = 10 - 3 = 7.

(b) Charging different prices for the two groups results in higher profits than charging the same price for everyone, because more consumer surplus is used.

(c) The demand curves are above the marginal revenue curves, all of them are downward-sloping, and the marginal cost curve is a horizontal line.