Question

Consider the following TR and TC function for a firm operating in a perfect competition

market:

TR = 21Q

TC = 1/3Q3 – 5Q2 + 42Q + 81

A. Determine the profit maximizing or loss minimizing equilibrium level of output?

B. Compute the level of profit or loss at the above equilibrium quantity and comment on

the decision of the firm?

Answer 1

Solution:

A.). Profit maximizing or loss minimizing equilibrium level of output is where MR = MC:

TR = 21Q

Derive MR from TR:

MR = $\frac{\partial TR} {\partial Q}$ = 21

 

TC = $\frac{1}{3}$Q³ – 5Q² + 42Q + 81

Derive MC from TC:

MC = $\frac{\partial TC} {\partial Q}$ = Q² – 10Q + 42

 

Set MR = MC

21 = Q² – 10Q + 42

Q² – 10Q + 42 – 21 = 0

Q² – 10Q + 21 = 0

Q = 7

The profit-maximizing or loss minimizing equilibrium level of output = 7 units

 

B.). Profit/Loss = TR – TC

TR = 21Q = 21 x 7 = 147

TC = $\frac{1}{3}$Q³ – 5Q² + 42Q + 81 = $\frac{1}{3}$(7)³ – 5(7)² + 42(7) + 81 = 114.3 – 245 + 294 + 81 = 244.3

Profit/Loss = 147 – 244.3 = (97.3)

Loss = (97.3)