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 an MP3 player is $10.If Nick receives 60% of the total profit,then
A)Nick will produce 50 MP3 players.
B)Nick receives $500 as profit.
C)total profit is $800.
D)the efficiency in production is not achieved.

Quizplus · Accepted Answer

To find the optimal quantity to produce, we need to set marginal cost equal to marginal revenue, which is the derivative of the demand equation: 
MC = MR = d(pQ)/dQ = p + Q(dp/dQ) 
10 = (50 - 0.5Q) + Q(-0.5) -> Q = 80 
So producing 80 MP3 players will give us the maximum profit. 
Total revenue = pQ = (50 - 0.5Q)Q = 2000 - 0.5Q^2 
Total cost = MC(Q) * Q = 10Q = 800 
Total profit = TR - TC = 1200 - 800 = 400 
Nick receives 60% of the total profit, so he gets $240. 
Therefore, the correct answer is C.