Cost functions based off of birthday

This assignment is designed to set you up for success on Quiz 5 and the Final Exam. It is worth 200 points. There are 50 points worth of extra credit at the end!

 

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Please follow all directions step-by-step; read carefully and you should have no issues with this assignment. This assignment uses concepts both covered in lecture and available on Tophat in Module 11 and the Addendum included on Cost and Industry Structure.

 

You can work with others on this assignment but all work you turn in for credit must be your own. For example, do not use someone else’s numbers or copy someone else’s graph.

 

Use one sheet of graph paper. All graphs need to be hand drawn. Here are some reminders about presenting graphical work.

  • Think about the scale of your graph or do a rough, preliminary sketch and make the units you have chosen on each axis is appropriate to show a readable graph of your work. (That is, the interesting parts of your graph should be bigger than a few tiny squares.)
  • Label each axis.
  • Units on each axis must be of uniform size.
  • Be sure to label areas of interest, especially ones asked for in the assignment.

 

If you want to use software to get an idea about what the final graph looks like, that is fine. But all work you turn in should be hand drawn. There is a piece of graph paper associated with this assignment. Please use this graph paper or something similar. If you do not use graph paper, please make sure you draw a careful graph that is well-labelled.

 

Once you finish the assignment upload your graph and the following two pages with your work to Crowdmark. This will be three pages total. Please do me a favor and change your font color to something like red or blue or purple, just not black. It is going to be very hard to grade 200 of these if everyone answers in black. This does not apply if you choose to print this word doc out and submit that way, since your handwriting will obviously stand out against the computer text.

 

You may delete and reupload your work as many times as you like before the deadline. Again, you may fill out the word doc on your computer or print it out and write on it. You MUST hand draw the graph, though. All work should be submitted through crowdmark.

 

 

 

 

 

You will create a cost function for this exercise using your birthday. Make note of your birthday using the number of the month (1-12) and the number for the day of the month (1-31) below.

Month (m):     10                                                    Day (d):     18

Use the two numbers above, m and d, to complete the cost function for a perfectly competitive firm: My birthday is August 28th, so my cost function looks like Cost(q)  = 8 q+ 28

Cost (q) = m q2 + d =  Cost(q)=10q^2+18

To be clear, the thing you see above is just a mathematical expression for Total Cost. It represents Cost as a “function of” quantity. Think back to f(x) in high school algebra.

For a cost function like yours, Marginal Cost (MC) = 2 m q

(60) Specifically, what are the following values/formulas for your cost function? (Hint: one of these will just be a number, the rest will be functions of q.)

Fixed Cost = Average Total Cost =
Variable Cost = Average Fixed Cost =
Marginal Cost = 2 m q = 20q Average Variable Cost =

(30) Fill in the table with your values from your cost function now that you’re being given quantities to contend with.

q Total Cost AVC AFC ATC MC
0        
1          
2          
3          
4          

(50) Create a graph with ATC on it. Properly label the minimum of your ATC function (both it’s value ($) and its quantity). For a cost function like yours, minimum ATC is where q = (d/m)1/2 . ß (1/2 exponent means square root)

(30) Add AVC and MC to your graph.

(30) Here MC is always increasing. As q increases, what happens to ATC when it is less than MC and what happens to ATC with is more than MC? (before and after MC=ATC?)

 

 

 

(20) Extra Credit: At what price will your competitive firm break even? Show your work.

 

 

 

 

(20) Extra Credit: At what level of production is AVC at its minimum? (the table you made is enough information for you to find this value.) For any price, will your firm always be able to cover its variable cost?

 

 

 

 

(10) Extra Credit: Indicate the supply curve of your firm in the short run.  You may do this on the graph or you can describe it here.

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