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8.1 Production Costs in the Short Run
In the short run, not all input factors are variable. We therefore distinguish between fixed cost, FC, and variable cost, VC. Total cost, TC, is the sum of the two:
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We also need to define a few other central concepts. Regarding average cost, we will have use for the averages of all three of the above. If we divide each of them with q, we get average total cost, ATC, average variable cost, AVC, and average fixed cost, AFC:
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Note that the following must hold:
AFC AVC ATC= +
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The marginal cost, MC, in turn, measures the cost of producing one more unit of the good:
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Note that we can use either the change in total cost or the change in variable cost. Both must give the same answer, since the fixed cost does not change (∆FC = 0). As before, the expression for marginal change is only an approximation.
Now, we will construct a graph to illustrate these different measures of costs (see Figure 8.1).
The fixed cost, FC, is constant, independent of how many units we produce, so the curve illustrating FC must be a horizontal line. Total cost, TC, must always increase with production;
else, the production is not efficient. Furthermore, since if we produce nothing TC must equal FC, the curve for TC must start in the same point as FC on the Y-axis. Since TC = VC + FC, the curve for variable cost, VC, must have the same shape as TC. Obviously, VC of producing nothing is zero, so the curve for VC must start at the origin.
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I joined MITAS because
Maersk.com/Mitas�e Graduate Programme for Engineers and Geoscientists
Month 16 I was a construction supervisor in the North Sea
advising and helping foremen solve problems I was a
he s
Real work International opportunities
�ree work placements al
Internationa or
�ree wo
I wanted real responsibili�
I joined MITAS because
Maersk.com/Mitas
�e Graduate Programme for Engineers and Geoscientists
Month 16 I was a construction supervisor in the North Sea
advising and helping foremen solve problems I was a
he s
Real work International opportunities
�ree work placements al
Internationa or
�ree wo
I wanted real responsibili�
I joined MITAS because
Maersk.com/Mitas
�e Graduate Programme for Engineers and Geoscientists
Month 16 I was a construction supervisor in the North Sea
advising and helping foremen solve problems I was a
he s
Real work International opportunities
�ree work placements al
Internationa or
�ree wo
I wanted real responsibili�
I joined MITAS because
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69
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Figure 8.1: The Cost Function with Average and Marginal Costs
Using the curves we have drawn in the upper part of the figure, we will now construct the ones in the lower part, i.e. ATC, AVC, AFC, and MC. First, we use the same technique as we did in Section 7.3.1. Lay a ruler in the upper part of the figure such that it has one point at the origin and another point on the TC curve. Find the point on TC where the ruler has the smallest slope. In the figure, this corresponds to line L1 and point A. You have now found the smallest possible average cost, ATC. Proceed in the same way to find the point on VC where the ruler has the smallest slope: the line L2 and point B. That point corresponds to the lowest possible average variable cost, AVC.
Draw the two curves for ATC and AVC in the lower part of the figure. Of course, ATC must lie above AVC. ATC should have its lowest point at a, and AVC at b. If you wish to find the numerical value for, for instance, point a, then read off the location of point A in the upper part of the figure: (53,75). Then calculate 75/53 = 1.4. Point a should then be at (53,1.4).
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You can now also draw MC in the lower part of the figure. It must run through both point a and point b (for the same reasons as in Section 7.3.1) and it should correspond to the slope of TC (or VC, since it has exactly the same slope) in the upper part of the figure. Note that, since the slope of TC becomes higher and higher, MC should increase as we move to the right.
Lastly, AFC must become smaller and smaller the more products we produce, since FC is a constant and we divide with an increasingly higher quantity, q.