Question

[Monopoly Pricing] A monopolist operates with the following data on cost and de- mand. It has a total fixed cost of $1,500 and a total variable cost of Q2, where Q is the number of units of output it produces. The market demand function is Qd = 60 − 0.5P . The firm expects the conditions of demand and cost to continue in the foreseeable future.

1. (a) What is the profit maximizing monopoly price and quantity?

2. (b) What is the dead weight loss from the monopoly pricing?

3. (c) Should the firm continue to operate in the short run, or should it shut down? Explain briefly.

Answer 1

Fixed Cost = 1500

Variable Cost = Q²

Total Cost = Fixed Cost + Variable Cost

Total Cost = 1500 + Q²

Marginal cost can be calculated from the total cost function by differentiation

Marginal cost = dTC / dQ

Marginal cost = 2Q

Demand Function

Q = 60 − 0.5P

Inverse Demand Function (In terms of price)

P = 60 - Q / 0.5

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

Marginal Revenue

MR = 60 - 2Q / 0.5

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

Equating both MR and MC

60 - 2Q / 0.5 = 2Q

60 - 2Q = Q

60 = 3Q

Q = 20

Hence the profit-maximizing quantity is 20 units

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

P = 60 - Q / 0.5

P = 60 - (20) / 0.5

P = $80

Hence the profit-maximizing price is $80

B) The graph of monopoly looks like this

The blue 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 40 x 10

Deadweight Loss = 200

C) A firm should shut down if the firm is not able to cover its variable cost from the total revenue or we can if the firm price is less than average variable cost.

So the firm is producing 20 units at a price of $80

Total Revenue = Price x Quantity

Total Revenue = 80 x 20

Total Revenue = 1600

Variable Cost = Q²

Variable Cost = (20)²

Variable Cost = 400

As total revenue is greater than variable cost hence the firm will not shut down and continue to produce