Question

Problems 1-6 are based on the following information: A company sells PC software whose price is determined by p = 200 - 5Q, where Q is the quantity purchased per day. It has fixed costs of $100 per day and variable costs of $10 per unit sold.

Price = __________ at the profit-maximizing quantity.

	A.	$2025
	B.	$1705
	C.	$290
	D.	$105
	E.	$2995

Answer 1

Profit is maximized where marginal revenue and marginal cost both are equal.

Marginal cost = Change in variable cost / change in quantity

Variable cost is $10 per unit that means change in variable cost will be constant at $10

Hence marginal cost will be equal to $10

Marginal revenue can be calculated from the demand curve by doubling the coefficient of Q

Demand Function

p = 200 - 5Q

Marginal Revenue

p = 200 - 10Q

Equating MR and MC

200 - 10Q = 10

10Q = 200 - 10

Q = 190 / 10

Q = 19

Hence the profit-maximizing quantity is 19 units

To find the profit-maximizing price we will use this quantity in demand function

p = 200 - 5(19)

p = 200 - 95

p = 105

Hence the profit-maximizing price is $105

Option D is correct