Question

Assume that a monopolist sells a product with inverse demand given by  p = 12 – 0.5q, where  p is the price of the product and  q is its quantity, and the monopolist’s marginal and average cost is equal to 6.

(a) Find the profit maximising level of q and p, and the firm’s profit. Find the profit maximising level of output and profit if the maximum price that can be charged per unit is (i) p = 7, (ii)  p = 10.

(b) What effect on price and output would a tax of 2 per unit have on the firm’s output and price? What if the tax were 6 per unit?

Answer 1

a) Profit maximizing quantity = 6; price = 9

Calculation:

demand: 12 - 0.5Q; so MR = 12 - Q ( double slope).
MC =6

Monopolost' profit maximizing quantity is where MC = MR

12 - Q = 6; so Q = 6; plugging in Q to find the  P:

P = 12 - 0.5*6 So P = 9

profit = TR - TC or (P- MC)*Q = (9 - 6)*6 =18

When price= 7,

P= 12 - 0.5 Q or 7= 12-0.5Q

So, Q = 10

Profit = (7-6)*10 = 10

when price = 10,

10= 12 - 0.5Q. So, Q = 4

Profit = (10-6)*4 = 16

b) when tax = 2, MC increases by 2. (MR= MC+2)
So MC = 6+2=8
12- Q= 8 so Q = 4; P = 12 - 0.5*4 So P= 10

when tax = 6 , MC = 6+6 12

12- Q = 12. So Q = 0. (monopolist will not produce any output.