You are the manager of a monopoly, and your demand and cost functions are given by P = 300 – 2.5Q and C(Q)=1000 + 2.5Q2.

Question

a.At what price and quantity are firm’s profits maximized?

Answer 1

revenue = price * quantity
profit = revenue - cost
so, the profit is

Q(300-2.5Q) - (1000 + 2.5Q^2)
= 300Q - 2.5Q^2 - 1000 - 2.5Q^2
= -5Q^2 + 300Q - 1000
= -5(Q^2 - 60Q + 200)
max profit at Q=30, P(30)=225