Answer to Question #236199 in Macroeconomics for Medico

Question

A firm operates in a perfectly competitive market. The market price of its product is 4 birr and the total cost function is given by TC= Q3-15Q2+60Q +150, where TC is the total cost and Q is the level of output.

a) What level of output should the firm produce to maximize its profit?

b) Determine the level of profit at equilibrium.

c) What minimum price is required by the firm to stay in the market?

Answer 1

a)

At the output level where the profit maximized,

$MC=\prod$

$MC=\frac{dTC} {dQ}$

$\prod=4$

$$MC=3Q^{2}-30Q-60$$

$3Q 2 −30Q+60=4$

$3Q2−30Q+56=0$

$Q=\frac{-b+/-\sqrt {b^{2}-4ac}}{2a}$

Where;

a=3, b= -30 and c=56

$Q=\frac{30+/−\sqrt{ {-30}^ 2 −4\times3\times56} }{ 2\times 3}$

$Q=\frac {30+/-\sqrt {900-672}} {6} ​$

$=\frac{30+/-\sqrt {228}} { 6}$

$=\frac{30+/-15.10}{ 6}$

$Q=7.52\space OR\space 2.48$

The level of output that will maximize profit;

$Q=7.52$

b)

$\prod=7.52\times4$

$=30.08\space Birr$

c)

$=\frac{30−15.10} {6}$

$2.46$