Question

Suppose the monopolist’s demand curve is P=306-6Q and its cost function is TC=15+6Q. Determine the profit maximizing price and quantity and the maximum profits Price and Output: Profits: Suppose the government gets involved and mandates that the monopoly compete like a perfectly competitive firm. Now, what are the new profit maximizing price and quantity?

Answer 1

Answer : For monopoly firm :

P = 306 - 6Q

TR (Total Revenue) = P * Q = (306 - 6Q) * Q

=> TR = 306Q - 6Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 306 - 12Q

TC = 15 + 6Q

MC (Marginal Cost) = TC / Q

=> MC = 6

At monopoly equilibrium, MR = MC.

=> 306 - 12Q = 6

=> 306 - 6 = 12Q

=> 300 = 12Q

=> Q = 300 / 12

=> Q = 25

Now, P = 306 - (6 * 25)

=> P = 156

Therefore, the monopoly profit maximizing price is $156 and quantity is 25 units.

TR = P*Q = 156 * 25

=> TR = 3,900

TC = 15 + (6 * 25)

=> TC = 165

Profit = TR - TC = 3900 - 165

=> Profit = 3,735

Therefore, monopoly profit is $3,735.

For competitive firm :

At equilibrium condition, P = MC.

=> 306 - 6Q = 6

=> 306 - 6 = 6Q

=> 300 = 6Q

=> Q = 300 / 6

=> Q = 50

Now, P = 306 - (6 * 50)

=> P = 6

Therefore, the profit maximizing price is $6 and quantity is 50 units for perfectly competitive firm.