Exercise: Below are data on quantity produced at a group of shirt manufacturing plants. Each plant also reports its total cost. This exercise tests your knowledge of empirically verifying economic theory of short-run production cost. From the Principles of Microeconomics, we discussed that the short-run cost equals (1) TC = TFC + TVC. This equation can be further reduced to as: (2) TC = TFC + mc*Q, where mc is the marginal cost which is the slope of the TC equation. Now, let us convert equation 2 into a simple linear equation learned in college algebra: (3) TC = a + b*Q, where a=TFC and b=mc (marginal cost).
a. Using equation 3, a theoretical regression equation of the short-run total cost, estimate the short-run total cost using the data below. Then write the estimated cost equation. Indicate the value of the total fixed cost and of the marginal cost from the estimated cost equation.
b. Forecast total cost for a plant producing 28 (000s) units.
Quantity (000s) Total Cost ($000s)
21.80 $ 171.11
20.81 $158.40
20.96 $165.24
19.73 $161.18
16.65 $137.53
20.54 $165.39
22.24 $171.58
19.44 $153.54
17.24 $142.82
18.67 $153.43
19.78 $143.63
18.86 $148.53
17.58 $147.89
26.64 $203.29
22.16 $176.69
17.41 $149.36
22.02 $176.38
26.39 $194.31
26.71 $196.37
23.77 $177.11
17.42 $136.14
21.76 $166.04
23.97 $180.82
21.01 $159.99
26.34 $187.62