Question

1. Consider the following demand, TC, MC and MR equations:

P=56-Q

TC=3Q²+20

MC=6Q

MR=56-2Q

1. What is the quantity set by a monopolist?

2. What is the price set by the monopolist?

3. What is the quantity set in perfect competition?

4. What is the price set in perfect competition?

5. Draw the demand and supply graph. Include and label appropriately the marginal revenue curve, and indicate the equilibrium in perfect completion and in monopoly.

6. On the graph shade in the area denoting DWL if there is monopoly.

Answer 1

(a)

Under monopolistic market profit is maximised when,

Marginal revenue(MR) = Marginal cost(MC)

So we get answer to the first part by solving MR and MC equation where

MR = MC

56 - 2Q = 6Q

8Q = 56

Q = 7

Therefore the quantity set by the monopolist is 7 units.

(b)

For the second part we can get by substituting the value of Q in the first equation -

P = 56 - Q

P = 56 - 7

P = 49

Therefore price set by the monopolist is $49.

(c)

Under perfect competition profit is maximised when,

Price(P) = Marginal cost(MC)

So solving the equations

P = MC

56 - Q = 6Q

7Q = 56

Q = 8

So the quantity set in perfect competition market is 8 units.

(d)

To get the price in perfect market we can substitute the value of Q we got in (c) in equation 1 -

P = 56 - Q

P = 56 - 8

P = 48

Therefore price set in perfect competition is $48.

(e)

In the above graph, PM is the price charged in monopolistic marketmark PC is the price charged in perfect competition.

(f)

The dead weight loss (DWL) is denoted by the shaded area in the above graph.