Skip to main content

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.

Labels:

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever   any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP).  Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...
Post a Comment
Read more

Exercise: maximizing profit

Assume that you are the owner of a small business that produces T-shirts. Your the total revenue for your business can be modeled by the following equation: and your total cost corresponds to this function: Find the point at which your firm maximizes its profit. Then, find how much profit the firm if able to earn at that point. Using the total cost and total revenue functions we can set up the profit function: Then, realize that if you want to find the maximum profit, take the derivative of the function and set it up equal to zero, and solve for Q. This is equivalent of taking the derivative of the total cost and total revenue functions and setting them equal to each other. In this problem, I chose the latter option as it was explained in the previous lessons. Notice that profit is often denoted by a capital pi.  We are assuming that the TR>TC for some positive value, you can check for yourself. However, if we did not know that, we would first take the first ...
Post a Comment
Read more

A short interlude...

Hello all, it's been quite some time since I have made any major announcements since the creation of this blog about a year and a half ago. I am currently in graduate school and will soon take a portion of my comprehensive examination (i.e exams in Micro, Macro, and Metrics that will allow me to continue my studies in my graduate program), wish me luck! Thus, I will not be able to post consistently until at least mid-June. The roadmap is as such, if I pass, I will start introductory lessons in Econometrics and Statistics (if not, then I'll have to study until I can retake the comps in August). I hope that once I am done, I will be able to add more advance materials to the blog, such as general equilibrium, indirect utility functions, and game theory/mechanism design for Micro. The Solow, Ramsey, RBC, New Keynesian models, permanent income hypothesis (PIH) and more for Macro. By the way I think I still need to add notes on the IS-LM curves, so I will do that before jumping to t...
Post a Comment
Read more