Wednesday, November 21, 2012

MR, MC, ATC, and Profit Max

Today, Muscatine was so foggy that school was delayed for an hour.  This combined with the Mr. Muscatine Pageant and an early release for the holidays, left me with four students to teach.  I gave this problem and welcome you to work through it.

Suppose you produce fingernail clippers in a perfectly competitive market.  The price of your product is $4 and you have fixed costs of $2.  Suppose that your variable costs take the form of a function and the function is: .05Q^2 where Q is the quantity produced.  Using a spreadsheet, calculate the profit maximizing quantity and the profit earned at the profit maximizing level. Using the spreadsheet software, draw the graph, shade the area of profit then answer the following questions:  What happens if fixed costs increase from $2 to $3?  Does the profit maximizing output change?  Explain the shape of the ATC curve.
Here are my answers.

You should find that the profit maximizing output is 40 where MR = MC.  MR = P since this is a perfectly competitive market.  I used calculus and took the derviative of the total cost function and found that MC .1Q describes the cost.  I found that ATC = 2/Q = .05Q.  The graph follows.  You should find that the profit max quantity does not change as fixed costs increase.  The ATC curve takes the shape that does because fixed costs are spread out over a larger portion of output then diminishing marginal returns set it.

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