Question

What if a price ceiling of $100 is imposed on the demand curve above? (Q = 1000 - 4P; TC = 50Q). How much does the monopolist earn?

		$20,000
		$30,000
		$40,000
		$50,000
		$60,000

Answer 1

Q = 1000 - 4P

4P = 1000-Q

P = 250 - 0.25 Q

So, MR = 250 - 0.5Q { MR has double slope of demand}

Monoplist will produce where MR = MC

Here, MC = d(TC)/dQ = 50

MR = MC

250 - 0.5Q = 50

250 - 50 = 0.5Q

200 = 0.5Q

Q = 400

P = 250 - 0.25*400 = 150 { which is above the price ceiling}

So, at price $100

Q = 1000 - 4*100= 600

TC = 50*600 = 30000

TR = Q*P = 60000

Monopolist will earn = 60000 - 30000

= 30000  

Ans is $30,000