Answer to Question #295640 in Microeconomics for Taffe Belay

Question

Suppose that the average revenue of a short run perfectly competitive firm is 2 and its marginal and fixed costs are given as MC=3Q²-8Q+6 and TFC=10 then

A. Determine the level of profit at equilibrium and identify whether the firm makes positive profit ,normal profit or incure profit

B. What is the price level required for the firm to stay in the market ?

Answer 1

At equilibrium price:

$AR=MR=P=2$

Profits is maximum when $MR=MC$$Therefore$

$3Q^{2}-8Q+6=2$

$3Q^{2}-8Q+4$

Using quadratic formula we can solve for Q

$\frac{-b+-√(b^{2}-4ac)}{2a}=Q=$

$\frac{8+-√(8^{2}-4×3×4)}{2×3}=2$

Total Revenue$=P×Q=2×2=4$

To get TVC we integrate MC which gives us$TVC= 6Q^3-8Q^{2}+6$

$TC=TVC+TFC=$

$6Q^{3}-8Q^2+6+10= 6Q^{3}-8Q^{2}+16$

$TC=6(2^{2})-8(2^{2})+16=96$

Total Revenue$=TR-TC$

$=4-96=-92$

The firm is incurring a Loss.

- The firm should sell its products at $P=96$ which is equal to the total cost so that it can break even.