Question

2. For the following total revenue and total cost functions of a firm:

TR = 800Q – 10Q2

TC = (2/3)Q3 -30Q2 + 672Q +4000

(a) Determine the level of output at which the firm maximizes total profit

(b) Calculate the profit

(need step by step, please)

Answer 1

a)	For a firm's supply under perfect competition, a firm will maximize profits when it produces at that level
	where Marginal cost = price
	MC = P
	For perfect competitors , P = MR (marginal revenue)
	TR = 800Q - 10Q^2
	Marginal revenue (MR) is the first derivative of the Total revenue(TR)
	MR = 800 - 20Q
	TC (Total cost) = (2/3)Q^3 - 30Q^2 +672Q + 4000
	MC (marginal cost) = 2Q^2 - 60Q + 672
	We find Q when MR = MC
	800 - 20Q = 2Q^2 - 60Q + 672
	2Q^2 - 40Q -128 = 0
	Q^2 - 20Q -64 = 0
	Solving the quadratic equation
	(20 +/- (20^2 +4*64)^(1/2))/2
	(20 +/- 25.6)/2
	45.6/2
	22.8
	Q = 22.8
b)	Profit = TR - TC when Q = 22.8
	TR - TC =
	(-(2/3)Q^3 +20Q^2 +128Q - 4000
	Profit = $1413.63