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Exercise: Cost in the short run

We have so far talked about the short run cost for firms. It is now time to do some problems to make sure that the reader gets conformable with these types of problems. Exercise 1 requires the use of a cost data table, and exercise 2 requires knowledge in Calculus.

 1). A firm has the following cost data:
Ouput (Q) Total Cost (TC)  Variable Cost (VC)
 523
$6500
$2500
 524
$6725
$2725
 525
$7025
$3025

Find the ATC, AFC, AVC, and MC at these output levels.

Remember the total cost formula:



Then, in order to find FC just do the following:


Finally all you need to do is to divide each of these terms by each output level to find the ATC, AFC, and AVC. 

Regarding the MC, remember the formula:



Then,

Solution to problem 1:
ATC  AFC  AVC  MC
$(6500/523)
$(4000/523)
$(2500/523)
n.a
$(6725/524)
$(4000/524)
$(2725/524)
$225
$(7025/525)
$(4000/525)
$(3025/525)
$300


2). A firm's short run total cost function is as follows:


Find the ATC, AVC and MC functions, then graph the curves with respect to output (assume TC=525 when Q=0).

FC is just a constant and VC must be equal to 0 when no output is being produced:


Then, just divide VC, FC, and TC by Q:

Another way to find the MC which was mentioned in the previous lecture is by taking the derivative of TC or VC with respect to Q:


Let's graph the curves:



Source: the problems were inspired by the exercises on page 129 in Study Guide For Microeconomics, 8th edition (2013) by J.Hamilton, and V.Suslow.

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