RELATIONSHIP BETWEEN PRODUCT CURVES AND COST CURVES
Consider this table, which shows the production function per hour for nine inch nails in a particular (heavy) metal factory.
Fixed Variable
Input Input Output Wage
(K) (Labor) (TP) MP Rate TVC AVC TFC TC MC ATC
6 0 0 $10 $ $ $20 $__ $_____
} } $ ___
6 1 6 10 20 $30 _
_ _____
6 2 15 10 20 2.67
12 _____
6 3 27 10 20 ____
__
6 4 37 10 $40 20 __
___
6 5 45 10 1.11 20 __
_____
6 6 50 10 20 __
5.00
6 7 52 10 20 __
_____
6 8 53 10 20 ___
I. THE PRODUCTION FUNCTION
1) Are these data for the short run or the long run? How can you tell? (What is the definition of each of those periods, in economics?)
2) Graph total product and notice its shape. (What goes on each axis?) On a separate graph directly below the first, graph marginal product. (Remember to graph MP at the midpoints.) Why does MP have the type of slope that it does? Must it have this type of slope?
3) How is MP in the second graph related to TP in the top graph? Explain briefly and show the connection on the graph.
4) In what units is MP measured? Between 2 and 3 units of labor, MP is 12. 12 what?
5) Where does diminishing marginal returns (DMR) set in on each of these two graphs? Circle the relevant points. How can you spot the point of DMR on the graphs themselves, without a table?
6) Why does DMR occur? Explain it in plain English.
7) How is DMR different from diminishing marginal utility? How are they similar?
8) Is DMR a short-run concept or a long-run concept? (Hint: If you're not sure, look at the formal definition of the Law of DMR. There's a key phrase in it that will answer this question.)
II. THE COST CURVES
9) Calculate the TVC column in the table above. (Note: assume that labor is the only variable input in this case. In such a case, TVC could also be called "Total Labor Cost", couldn't it?) If you're not sure of how to calculate TVC, review the explanation of it in the book and/or your notes, and look at the first five columns above, especially the second and fifth.
10) Fill in the AVC, TC and ATC columns in the table. In calculating the averages (AVC and ATC), look carefully at the denominator in the formulae. What does this "Q" stand for? ...quantity of what?
11) Calculate the MC column above. (Note: if you got a column of 10's, you did something wrong! Look again at the formula for MC--especially the denominator.)
12) Interpret the MC numbers. Take the first number in the column, for example, and explain what it really means. What does it tell you?
13) Graph the TFC, TVC, and TC curves on one graph. (What goes on the axes?) How are these three curves related? (Are they related?)
14) Directly below that graph, graph AVC, ATC and MC. (Remember: MC is graphed at the midpoints of the quantities. The first MC value is graphed midway between 0 and 6--i.e., at 3--or as a step covering that whole range.)
15) How are AVC, ATC and MC related on the graph? Are they tied together in any way?
16) How is MC related to TC? ...to TVC? ...to TFC? (Is MC related to all of them?)
17) How do you get down from an elephant?
18) Carefully consider the graphs of MP and MC. Notice what is measured on each axis. Now for the $64 question: How are these two related?? (Perhaps looking at the table will also help.) If you wished to line these two graphs up, one under the other, would you have any problems?
19) Conclusion: Why does MC have the kind of slope that it does? (Why does MP have the kind of slope that it does?) Explain.
20) What would happen to the cost curves if the price of labor rose to $15? (You can rework the whole problem (i.e., all the numbers) if you'd like, or just consider the effect. What will this change in input price do to the cost curves?)
21) Similarly, what would be the effect of a change in technology? How is it similar to the previous question? How is it different?