Question

A monopolist sells in two states. The demand function in state 1 and 2 respectively is Q1(p1)=50 – p1 and Q2(p2)=90-1.5p2. The monopolist produces at a constant marginal cost of 10. If a government regulation prevents the monopolist from charging different prices in the two states, then the profit maximizing price will be p*= _____. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p* is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

Answer 1

$33

Step-by-step explanation:

Given that,

Demand function in state 1: Q1 (p1) = 50 - p1

Demand function in state 2: Q2 (p2) = 90 - 1.5p2

Constant Marginal cost (MC) = 10

Inverse demand:

State 1: p1 = 50 - Q1

State 2: p2 = 60 - (2 ÷ 3) × Q2

Market demand (Q) :

= Q1 + Q2

= (50 - p1) + (90 - 1.5p2)

= 140 - 2.5p

This implies p = 56 – 0.4Q

Now, Monopolist equate Marginal revenue = Marginal cost

Total revenue (TR) = p × Q

= (56 -0.4Q)Q

Marginal revenue (MR) = 56 – 0.8Q

Hence, at equilibrium conditions

56 - 0.8Q = 10

Q = 46 ÷ 0.8

= 57.5

P* = 33

Therefore, the profit maximizing price will be $33.