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Q6. The monopolist produces and distributes the Cartoon Magazine. Demand is given by P = 1200-10Q....

Q6. The monopolist produces and distributes the Cartoon Magazine. Demand is given by P = 1200-10Q. The cost function is TC = 200Q+15Q2
Your work:

a. What output maximizes its profit?

b. What is the profit-maximizing price?

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Homework Answers

Answer #1

a. What output maximizes its profit?

Monopolist maximises it's profit where MR equals MC.

MR can be find by taking derivative of total revenue.

Total revenue =Price *quantity

=1200-10Q*(Q)

=1200Q-10Q^2.

MR =dTR /dQ

=1200-20Q.

MC can be find by taking derivative of total cost.

MC =dTC /dQ

=200+30Q.

Now, profit maximising quantity is where,

MR =MC

1200-20Q=200+30Q

1200-200=30Q+20Q

1000=50Q

1000/50=Q

20=Q.

So profit maximising quantity is 20 units.

b. What is the profit-maximizing price?

Put Q=20 in inverse demand function to get price.

P=1200-10Q

=1200-10(20)

=1200-200

=1000.

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