Answer to Question #275546 in Microeconomics for ARRR

Question

XTC Ltd has total costs of $45,000 and it is currently producing 5,000 units. It has examined its cost structure and has found that its variable costs share a linear relationship with output. Fixed costs are $10,000. The market price is $10.

(a) Determine the MC, AVC and ATC functions (write down the equation) for the firm.

(b) Determine the current profit of the company.

c. Determine the degree of operating leverage at current output

Answer 1

Solution

Total Cost = TC = $45,000

Quantity = q = 5000 units

Variable Cost = VC = bq=5000b

Fixed Cost = FC = $10,000

Price = p = $10

(a)

The MC, AVC, and ATC functions for the firm will be determined as follow.

$TC=FC+VC$

$45000=10,000+5000b$

$35000=5000b$

$b=7$

So, $VC=7q=7*5000$ = $35,000

Also,

Variable Cost function:

$VC=7q$

Total Cost function:

$TC=10,000+7q$

$MC=dTC/dq=7$

$AVC= VC/q=7q/q=7$

$AFC =FC/q=10,000/q$

$ATC=AFC+AVC=10,000/q+7$

Thus, the MC, AVC, and ATC functions for the firm are:

$MC=7$

$AVC=7$

$ATC=10,000/q+7$

(b)

The current profit of the company is given by Sales Revenue(S) minus Total Cost.

Sales revenue(S):

$S = q*p=5000*10=$ $50,000

Profit:

$Profit=S-TC=50,000-45,000=$ $5,000

So, the current profit of the company is $5,000

c)

The degree of operating leverage(DOL) at the current output is given by

$DOL=(S-VC)/(S-VC-FC)$

$=(50,000-35,000)/(50,000-35,000-10,000)$

$=15,000/5,000$

$=3$

Thus, the degree of operating leverage(DOL) at the current output is 3