Answer to Question #180633 in Microeconomics for Eva

Question

Suppose that an industry is dominated BT a single producer, the demand for it's product is Q=300-6p.suppose further that TC=5Q+1/480Q×2 is the cost function of the firm

Answer 1

The profit-maximizing quantity is produced at MR = MC, so:

Q = 300 - 6p or p = 50 - 1/6Q,

$MR = TR'(Q) = 50 - 1/3Q,$

$MC = TC'(Q) = 5 + 1/240Q,$

50 - 1/3Q = 5 + 1/240Q,

81/240Q = 45,

Q = 45×240/81 = 133.33 units.

p = 50 - 1/6×133.33 = 27.78.