Question

Following is Ahmed’s competitively firm data:

Output (Q) Total Cost Total Revenue
0 62 0
30 90 40
60 110 80
90 126 120
120 138 160
150 150 200
180 165 240
210 190 280
240 230 320
270 296 360

a. Find the profit maximizing output. 1 mark
b. Find: 1 marks
a. FC
b. VC
c. ATC
d. AFC
e. AVC
f. MC
c. Find the efficient scale of output. 1 mark
d. Draw all the curves for the variables in part b using two-dimensional space. 2 marks

Answer 1

Solution:

a.). Profit maximizing output is where: MR = MC

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

$MC = \frac{\partial TC} {\partial Q}$

As per the table derived, the quantity at which MR is equal to MC is 240.

Therefore, 240 is the profit-maximizing quantity.

This has been depicted from the below table:

b.). Find the following:

a. FC = 62

b. VC = $TC - FC$

c. ATC = $\frac{TC}{Q}$

d. AFC =$\frac{FC}{Q}$

e. AVC = $\frac{VC}{Q}$

f. MC = $\frac{\partial TC} {\partial Q}$

The following costs have been calculated as per the below table:

c.). The efficient scale of output is the quantity of output that minimizes the average total cost. Productive efficiency occurs when a firm is combining resources in such a way as to produce a given output at the lowest possible average total cost (ATC). Costs will be minimized at the lowest point on a firm’s short-run average total cost curve.

This also means that ATC = MC, because MC always cuts ATC at the lowest point on the ATC curve.

Therefore, the efficient scale of output will be 210, a point where the ATC is at its lowest figure of 0.90.

 

d.). The graph of all variables is as below: