Answer to Question #145325 in Microeconomics for Maksim Murray

Question

A firm has a total cost function equal to:


TC(q)=20+4q+0.1q^2



And faces a demand curve given by


P(q)= 15-0.3Q


What is the profit maximising production quantity, q, for this firm?

Answer 1

To determine the profit maximizing production quantity the steps below should be followed;

i) Determine the Marginal Cost from the the Total Cost function.

$TC_{(q)}=20+4q+0.1q^2$

Differentiate the Total cost in respect to quantity to obtain the marginal cost.

$Therefore\\ \frac{\Delta\ TC}{\Delta\ q}=4+0.2q\\ MC=4+0.2q$

ii) Determine the Total revenue from the price function.

$Total\ Revue(TR)=Price(p)\times\ quantity(q)\\ TR=q(15-0.3q)\\ =15q-0.3q^2$

Differentiate the function to obtain the Marginal Revenue.

$MR=\frac{\Delta\ TR}{\Delta\ q}=15-0.6q$

iii) To determine the maximum production quantity then, the Marginal Revenue$(MR)$ =Marginal Cost$(MC)$

$Therefore\ 15-0.6q=4+0.2q\\ q=13.5$