Posted by **Turner** on Tuesday, October 23, 2012 at 2:37pm.

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.

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

- Managerial Econ -
**Steve**, Tuesday, October 23, 2012 at 2:54pm
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

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