Question

The cost curve for a monopoly in the coffee market is given by the following: MC=AC = 60

The market demand curve for coffee is given by the following: P = 200 – 2Q

a) Calculate the monopoly equilibrium price and quantity in the tea market.

b) Calculate consumer surplus, producer surplus, and deadweight loss under monopoly. Illustrate your answer with a graph. Label all the relevant curves, points and areas carefully.

Answer 1

A) Profit is maximized where marginal revenue and marginal cost both are equal

Demand Function

P = 200 - 2Q

Marginal revenue can be calculated from demand function by doubling the coefficient of Q

Marginal Revenue Function

MR = 200 - 4Q

Equating MR and MC

200 - 4Q = 60

140 = 4Q

Q = 35

Hence the profit-maximizing quantity is 35 units.

To find the profit-maximizing price we will use this quantity in demand function.

P = 200 - 2Q

P = 200 - 2(35)

P = 130

Hence the profit-maximizing price is $130

So in a nutshell

Equilibrium Price = $130

Equilibrium Quantity = 35 units

B)

So the graph of monopoly will look like this

The blue triangle represents the consumer surplus hence the area of this triangle will be equal to consumer surplus.

Consumer Surplus = Area of Triangle

Consumer Surplus = 1/2 x base x height

Consumer Surplus = 1/2 x 70 x 35

Consumer Surplus = 1225

The orange rectangle represents the producer surplus hence the area of this rectangle will be equal to producer surplus.

Producer Surplus = Area of Rectangle

Producer Surplus = Length x Breadth

Producer Surplus = 70 x 35

Producer Surplus = 2450

The yellow triangle represents the deadweight loss hence the area of this triangle will be equal to deadweight loss.

Deadweight Loss = Area of Triangle

Deadweight Loss = 1/2 x base x height

Deadweight Loss = 1/2 x 70 x 35

Deadweight Loss = 1225