Question

If TC= 3+Q^2 and demand Is P=3-1÷2Q. Calculate total profit

Answer 1

Using the cost function, marginal cost would be:

$\frac {dTC} {dQ} =MC=2Q$

Using the value of MC, market quantity will be the one at which MC equates to price such that:

$MC=P$

$2Q=3-(\frac {1} {2} )Q$

$2Q+(\frac {1} {2} )Q=3$

$(\frac {5} {2} )Q=3$

$Q=\frac {6} {5}$

At the quantity of 6/5 units, market price would be:

$P=3-(\frac {1} {2} )(\frac {6} {5} )$

$P=3-(\frac {3} {5} )$

$P=\frac {12} {5}$

Therefore, at the price of $\frac {12} {5}$ and quantity of $\frac {6} {5}$ firms profit would be=

$=TR-TC$

$=Q[3-(\frac {1} {2} )Q]-(3+Q^2)$

$=(\frac {6} {5} )[3-(\frac {1} {2} )2]-[3+(6)5)^2)]$

$=[(\frac {6} {5} )×2]-[3+1.44]$

$=-2$

Therefore, firm will incur loss.