Question

Profit maximization: Suppose you have a firm that, because it has some market power, faces a market demand curve of $LaTeX: P\left(Q\right)=25-1.1Q$ P ( Q ) = 25 − 1.1 Q. Your Total Cost function is the same as before: $LaTeX: TC\left(Q\right)=34+1.2Q+0.8Q^2$ T C ( Q ) = 34 + 1.2 Q + 0.8 Q 2 , where Q is your production quantity. What is your profit-maximizing output Q*, to the nearest 0.1 unit?

Answer 1

Demand function: P = 25 - 1.1*Q --------------------- (1)

Cost Function: TC = 34 + 1.2*Q + .8*Q^2 ------------------- (2)

Multiplying eq. 1 with Q and differentiation with respect to Q gives MR.

MR = 25 - 2.2*Q

Differentiation of eq. 2 with respect to Q, will give MC.

MC = 1.2 + 1.6*Q

For profit maximizing output,

MR = MC

25 - 2.2*Q = 1.2 + 1.6*Q

Q = (25 - 1.2)/(2.2+1.6)

Q = 6.26 units or 6.3 units

so,

Profit maximizing output is 6.26 units or 6.3 units.