Answer to Question #103585 in Microeconomics for Sunday afo

Question

A firm producing a particular products is faced with a demand cost function, given as qd=150-0.25p. And the total cost function of the firm is given as tc=2q^2+50q+100. Determine the profit maximizing output of the firm. Calculate the profit of the firm

Answer 1

qd = 150 - 0.25p, so p = 600 - 4qd.

The profit maximizing output of the firm is:

MR = MC,

MR = TR' = (p×q)' = 600 - 8q,

MC = TC' = 4q + 50,

600 - 8q = 4q + 50,

12q = 550,

q = 45.83 units,

p = 600 - 4×45.83 = $416.67.

Total profit is: TP = p×q - TC = 416.67×45.83 - (2×45.83^2 + 50×45.83 + 100) = $12,503.71.