A firms revenue and cost functions are TR 4Q MR 4 TC 004Q

A firm’s revenue and cost functions are

TR = 4Q

MR = 4

TC = 0.04Q³ - 0.9Q² + 10Q + 5

MC = 0.12Q² - 1.8Q + 10

A. Determine the best level of output.

B. Determine the total profit of the firm at its best level of output.

( From the TC function we see that the total fixed cost of the firm is 5. Should the firm produce or shut down?)

The firm would be in equilibrium when MR=MC

0.12Q2- 1.8Q+10= 4

10-4=1.8Q-0.12Q2

6=1.8Q-0.12Q2 ------------------------------ 1

Moreover,

4Q/Q=4

4Q=4Q Hence Q=1 Therefore,

TR=TC

4Q=0.12-O.9+15

4Q=14.3

Q=3.6

Profit = TR-TC

= 4Q- 0.12-1.8+15

= 3.6

Therefore,

Profit= 3.6.

The firm should shut down as its fixed cost is greater than profit

By,

Nishant Bhatt