The market demand for MP3 players is p = 50

Question

The market demand for MP3 players is p = 50 - 0.5Q,and the marginal cost for Nick to obtain and sell a MP3 player is $10.If he signed a fixed-fee rental contract with the store owner and pays $400 as the rent,
A)Nick will sell 20 MP3 players.
B)Nick will sell 30 MP3 players.
C)Nick will sell 40 MP3 players.
D)Nick will sell 50 MP3 players.

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we need to set marginal revenue (MR) equal to marginal cost (MC). MR is the change in revenue from selling one more unit, so it is the derivative of the demand function: MR = d(pq)/dq = p + q(dp/dq) = 50 - Q. MC is given as $10.
Setting MR = MC, we get:
50 - Q = 10
Q = 40
Thus, Nick should sell 40 MP3 players to maximize his profit. We can confirm this by calculating his profit at this quantity:
Total revenue = pQ = (50 - 0.5Q)Q = 50Q - 0.5Q^2 = 50(40) - 0.5(40)^2 = $1400
Total cost = rent + variable cost = $400 + $10(40) = $800
Profit = total revenue - total cost = $600
Selling any other quantity will result in a lower profit.