Question

The Company X has a monopoly on the beer market. Market demand is given by ?? = 200 - 4? and the company's short-term cost as a function of ? is given by ? (?) = ?2 + 40

What is the monopolist's total revenue (?) as a function of ? and what is the monopolist's total profit (?) as a function of ??

Answer 1

The market demand is given by PD = 200 - 4Q

Company's short term cost function is given by

C(q) = Q2 + 40

Total revenue (R) is given by:

R = PD*Q

Substituting PD from the demand function in the above equation, we get:

R = (200 - 4Q)Q

or,

R= 2000 - 404

Hence monopolist's total revenue (R) as a function of Q is:

R= 2000 - 404

Total profit is given by:

T = R-CIQ

or,

T = 2000 – 402 – 02 – 40

or,

T = 2000 - 502 – 40

Thus, total profit as a function of Q is given by:

T = 2000 - 502 – 40