Question

P = 20 - .25Q

MR = 20 – 0.5Q

MC = 8 = Average Cost

If the cost increases, what happens to the monopoly P, Q, and Profit?

Answer 1

A monopolist produces at that level of output where his MR=MC.

So the profit maximizing level of Q is given by

20 - 0.5Q = 8

-0.5Q = -12

Q' = 24

The price at this level of Q' is P' = 20 - .25*24 = 20-6 = 14

So monopolist maximizes profit at P' and Q'

Total revenue of monopolist (TR') = P'*Q' = 14*24 = 336

Total cost of monopolist (TC') = AC*Q' = 8*24 = 192

So profits (PR') = TR'-TC'= 336-192 = 144

Now when cost rises then it would raise marginal costs and average costs. For the sake of explanation lets say MC rises to 10 (which equals AC). Demand is unchanged and so is MR.

New profit maximization level =

MR = MC' = 10

20-0.5Q = 10

Q'' = 20

P'' = 20- .25*20 = 15

So TR'' = 20*15 = 300

TC '' = 10*15 = 150

Profit (PR'') = 300-150 = 150.

This demonstrates that when costs rise for the monopolist, its MC and AC rises. This leads to rise in price levels while quantity levels fall (because monopolist faces a downward sloping demand). While profits rise here. The reason profits rise because observe that at a higher price, total revenue and total cost both decreases due to fall in quantity. So due to fall in Q, total costs falls more than the fall in total revenue and so profits rises. (accurately TR falls by about 10.7% while TC falls by about 21.9% due to fall in quantity at higher prices).