Question

A firm’s total revenue and total cost function are given as follows
TR = 160Q – 5Q2
TC = 100 + 30Q
(a) Determine the Marginal Revenue (MR)
(b) Determine the Marginal Cost (MC)
(c) Find the best level of output
(d) Find the total profit of the firm at its best level of output

Answer 1

a) $MR = \frac{d TR}{d Q}=160 - 10Q$

(b) $MC = \frac{d TC}{d Q}= 30$

(c) best level of output

$MR=MC$

$160-10Q=30$

$10Q = 130$

$Q = 13$ (best level of output)

(d) $profit =TR -TC$

$=(160Q-5Q^{2})-(100+30Q)$

$=160Q - 5Q^{2}-100-30Q$

= $130Q-5Q^{2}-100$

$=130\times13 - 5\times13^{2}-100=745$