Question

1. A monopolist faces demand of Q = 20 - P. Its costs are TC = 2Q + 10.

f) If we had a perfectly competitive market with demand of Q = 20 – P and a supply of P = 2, what market price and quantity would have been the equilibrium? Is Q lower and P higher with a monopoly?

g) Now, go back to the original monopolist. The firm has unveiled a successful new ad campaign. Its costs are the same as above, but it now faces a demand of Q = 30 - P. (Satisfy yourself that this is an increase in demand.) Find, using either a table or a graph, the new price, quantity, and profits of this firm.

Answer 1

1 - f) Perfectly competitive market:-

Demand: Q = 20 - P, or, P = 20 - Q

Supply: P = 2

Market equilibrium price and quantity is where the Demand = Supply.

20 - Q = 2

Q = 20 - 2

Q = 18 and P = 2.

In perfect competition, Equilibrium price = 2, Equilibrium Quantity = 18

With a monopoly:-

Demand: Q = 20 - P, or, P = 20 - Q

Total Revenue = Price * Quantity = (20 - Q) * Q = 20Q - Q2

Marginal Revenue = ∆TR/∆Q = 20 - 2Q

Total Cost = 2Q + 10

Marginal Cost = ∆TC/∆Q = 2

Equilibrium occurs in a monopoly where the Marginal Revenue = Marginal Cost

20 - 2Q = 2

2Q = 18

Q = 9.

P = 20 - Q

P = 20 - 9

P = 11.

In Monopoly, Equilibrium Price = 11, Equilibrium Quantity = 9.

So, yes, P is higher and Q is lower in a monopoly.

g) Going back to the original monopolist,

Demand: Q = 30 - P, or, P = 39 - Q

Total Revenue = Price * Quantity = (30 - Q) * Q = 30Q - Q2

Marginal Revenue = ∆TR/∆Q = 30 - 2Q

Total Cost = 2Q + 10

Marginal Cost = ∆TC/∆Q = 2

Equilibrium occurs in a monopoly where the Marginal Revenue = Marginal Cost

30 - 2Q = 2

2Q = 28

Q = 14.

P = 30 - Q

P = 30 - 14

P = 16.

The new price = 16, new quantity = 14,

Profit = Total Revenue - Total Cost

Profit = 30Q - Q2 - (2Q + 10)

Profit = 30Q - Q2 - 2Q - 10

Profit = 28Q - Q2 - 10

Profit = 28(14) - (14)2 - 10

Profit = 392 - 196 - 10

Profit = 186.