Given that a firm's inverse demand function is P = 100 - 5Q and total cost is given by C = 550 + 10Q, what is the firm's profit-maximizing level of output?
A) 10 units
B) 15 units
C) 9 units
D) 8 units
E) 5 units

Question

Quizplus · Accepted Answer

To maximize profit, we need to find the level of output where marginal revenue (MR) equals marginal cost (MC).

First, we need to find the firm's marginal revenue. The inverse demand function can be rewritten as Q = 20 - 0.2P, which means that the firm's total revenue (TR) is TR = P * Q = (100 - 5Q) * Q = 100Q - 5Q^2. Taking the derivative of this with respect to Q, we get the marginal revenue function: MR = 100 - 10Q.

Next, we need to find the firm's marginal cost. Taking the derivative of the total cost function with respect to Q, we get the marginal cost function: MC = 10.

Setting MR equal to MC, we get: 
100 - 10Q = 10 
Solving for Q, we get Q = 9.

Therefore, the firm's profit-maximizing level of output is 9 units.

Given That a Firm's Inverse Demand Function Is P =