Question

Your firm A is a monopoly in a particular market. You can produce at constant marginal cost of $50 for every additional unit you produce. You have avoidable fixed costs of $6,000 per year. You face a market demand curve given by Q = 540 – 2P, where Q is the number of units sold per year, and P is the price per unit.

a. What is the equation of your marginal revenue curve?

b. What is your firm’s profit-maximizing price and quantity? What will be your annual profit contribution at this quantity?

c. Suppose that you face a capacity constraint that allows you to sell at most 200 units per year. As long as you produce less than 200 units per year, your marginal cost of an additional unit continues to be $50. What is your profit-maximizing quantity and price? (Hint: a picture may help here.)

Answer 1

a)

Given

Q=540-2P

or

2P=540-Q

P=270-0.5Q

Total Revenue=TR=P*Q=(270-0.5Q)*Q=270Q-0.5Q^2

Marginal Revenue=MR=dTR/dQ=270-Q

b)

Set MR=MC for profit maximization

270-Q=50

Q=220

P=270-0.5Q=270-0.5*220=$160

Total Revenue=TR=P*Q=160*220=$35200

Total Cost=F+MC*Q=6000+50Q

Total Cost=6000+50*220=$17000

(Fixed cost can be avoided if there is no production. we have considered this cost as fixed cost as firm is working)

Profit=TR-TC=35200-17000=$18200

c)

Profit=TR-TC=270Q-0.5Q²-(6000+50Q)=-6000+220Q-0.5Q²

Following schedule can be made with the help of given information

Q	Price	Profit
	P=270-0.5Q	-6000+220Q-0.5Q2
0	270	0
10	265	-3850
40	250	2000
80	230	8400
120	210	13200
160	190	16400
200	170	18000
220	160	18200
240	150	18000
280	130	16400
320	110	13200
360	90	8400
400	70	2000

We have taken fixed cost as zero at zero activity as fixed costs are avoidable.

We can see that profit is increasing at Q=200. So, this will be profit maximizing output at this level.

So, output is 200 units

Price=270-0.5*200=$170

Maximum profit at this stage =$18000 (Refer above table)