2 Using the following total cost equation for a firm in a co

2) Using the following total cost equation for a firm in a competitive market: TC 15+302 a. Write the AC funtion for this cost equation (answer should have Q in it). b. For the shown TC function, MC-6Q. Then, if P* 18, calculate: i. The quantity the firm produces (Q) ii. AC iii. Profit. Write answers for all three of these as numbers (you may leave y profit in the form of \"A B\" if you don\'t have a calculator). No nee draw a graph.

Solution

We have the following information

Total cost (TC) function: 15 + 3Q²

Average cost (AC) function: TC/Q where Q is the quantity

AC = (15 + 3Q²)/Q

AC = (15/Q) + 3Q

It is given that the marginal cost (MC) is 6Q and the price (P) is 18.

In competitive market the equilibrium is at the point where the MC is equal to the P.

MC = P

6Q = 18

Q = 3, so equilibrium quantity is 3

AC = (15/Q) + 3Q

AC = (15/3) + 3(3)

AC = 5 + 9

AC = 14

Profit = Total Revenue – Total Cost

Total Revenue = P × Q

Total Revenue = 18 × 3

Total Revenue = 54

Total Cost = 15 + 3(3)²

Total Cost = 15 + 3(9)

Total Cost = 15 + 27

Total Cost = 42

Profit = 54 – 42

Profit = 12