Suppose a monopolist has a constant marginal cost of $20 per unit, and a fixed c

Question

Suppose a monopolist has a constant marginal cost of $20 per unit, and a fixed cost of $100. The demand curve for the product of the monopolist is given by P=100-Q, and its corresponding marginal revenue is given by MR=100-2Q, where Q is the amount of sales.

What are the profit maximizing price, quantity

What is the maximum profit?

Suppose that the above monopoly market was once a perfectly competitive one before it suddenly become a monopoly. So the current monopolist demand, P=100-Q, was the industry demand under perfect competition, and the (constant) marginal cost of each firm was $20 under perfect competition.

What was the industry equilibrium price and output under perfect competition?

Calculate the deadweight-loss from monopoly and use graphs to demonstrate it.

Explanation / Answer

MR=MC the profit maximizing condition

100-2Q =20

2Q = 80

Q = 40

P = 100-Q

=100-40

=60

MR at Q =40, 100 – 2*40 = 20

TC = MCdQ

=20Q + FC

= 20Q + 100

Profit =TR-TC

=100Q – Q2 - (20Q + 100)

=100*40-40*40-(20*40+100)

=4000 – 1600 – 900

= 1500

Under Perfect Competition

The profit maximizing condition

P = MC

100 – Q = 20

Q = 80

P = 100 – 80

= 20

Deadweight Loss = 0.5*(60-20)*(80-40)

=0.5*40*40

=800

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