Question

A firm has the following revenue and cost functions.

TR = 120 Q – Q²

TC = 12 Q² +30 Q + 10

Determine the quantity level at which the firm maximizes its total profit. 

Answer 1

Marginal revenue:

MR  $=\frac {d}{dQ}$ $(TR)$ $=$ $\frac{d}{dQ}$ $($ 120Q$-$ Q$^2$ $)$

$=$ 120$-$ 2Q

Marginal Cost:

$MC$ $=$ $\frac{d}{dQ}$ ($TC$ $)$ $=$ $\frac{d}{dQ}$ $($ 12Q$^2$ $+$ 30Q$+$ 30$)$ $=$ 24Q$+$ 30

Firm maximizes total profit when:

MR $=$ MC

120$-$ 2Q$=$ 24Q$+$ 30

26Q$=$ 90

Q$=$ 3.46