Question

VisualEyes Inc. operates in a highly competitive market for eye glasses. Price is set at $30 and total cost is as follows:

TC = 722,500 + 10Q + 0.0004Q²

a) Calculate the output level (Q) that will maximize profit

b) Calculate the maximum profits

Answer 1

Answer :

Price = $30

TC = 722500 + 10Q + 0.0004Q^2

So marginal cost (MC) is calculated by differentiating TC with respect to Q :

MC = 10 + 2*(0.0004Q) = 10 + 0.0008Q

a) Profit maximized at the point where P = MC

Thus : 30 = 10 + 0.0008Q

20 = 0.0008Q

Q = 25000 is the profit maximizing quantity

b) When Q = 25000

Total Revenue = P * Q = $30 * 25000 = $750000

Total Cost = 722500 + 10*25000 + 0.0004*(25000)^2

Total Cost = $1222500

Profit = Total Revenue - Total Cost = $750000 - $1222500 = - $472500 at this level.

answered by: anonymous