Question

A company has $10,000 in variable cost per unit and $500,000 in fixed cost. The company faces demand: P = 30,000 - Q. What is the profit function in terms of Q?

Answer 1

If a company has $10,000 in variable cost per unit and $500,000 in fixed cost, then total cost is:

$TC = 10,000Q + 500,000.$

If the company faces demand: P = 30,000 - Q, then total revenue is:

$TR = P*Q = 30,000Q - Q^2.$

The profit function in terms of Q is:

$TP = TR - TC = (30,000Q - Q^2) - (10,000Q + 500,000) = -Q^2 + 20,000Q - 500,000.$