Question 1 Suppose a monopolist has costs represented by the

Question 1. Suppose a monopolist has costs represented by the cost function c()40+4q and faces demand q(P) 22 -1p (a) What is the monopolist\'s profit function? b) What is the first order condition corresponding to the monopoly profit maximization problem? c What are the monopolist\'s profits and what is consumer surplus?

Solution

For Monopolist Profit Maximising conditin is MR=MC

Reveue=Price*Quantity

We have q=22-p then p=22-q

Revenue=q(22-q)=22q-q^2

Marginal Revenue=dR/dq=22-2q

Cost=40+4q

MC=4

22-2q=4

18=2q

q=9

Now Profit Function of Monopolist

Profit=Revenue-Cost=q(22-q)-(40+4q)=9(22-9)-(40+4(9))=$41

Ans b)

Profit=q(22-q)-40-4q

=22q-q^2-40-4q=18q-q^2-40

Differentiating above profit function to get FOC

d(Profit)/dq=18-2q=0

q=9 and Price=13

ANs c)

Consumer Surplus=1/2(22-13)(9)=40.5 and Profit =$41