Question

Question 3: Consider a monopoly which faces the demand curve P= 55-2Q and having a marginal cost function MC= 2Q-5. a) (2pts) Calculate the marginal revenue (MR) function. b) (2 pts) State the profit maximizing output rule for the monopoly in the short-run. c) (4 pts) What is the profit maximing output level? Next, calculate the price and the profit of the monopoly?

Answer 1

A.

Marginal revenue can be find by taking derivative of total revenue.

TR =p*Q

=(55-2Q)*Q

=55Q-2Q^2

MR =dTR/dQ

=55-4Q.

B.

In monopoly, firm maximizes its profit where MR equals MC.

C.

Output level

MR=MC

55-4Q=2Q-5

55+5=2Q+4Q

60=6Q

10=Q.

Price of the monopoly.

P=55-2Q

=55-2(10)

=55-20

=35.

Profit =TR-TC

=350-50

=300.

MC is the derivative of TC.

So TC=Q^2-5Q

TC =10^2-5(10)

=100-50

=50.

TR=55Q-2Q^2

=55(10)-2*(10)^2

=550-200

=350.

Note : fixed cost can not be determined for the above information. So, from Mc we will find the variable cost and so we will find profit accordingly.