Minimum Average Cost
Do not confuse average cost with marginal cost-it’san easy mistake to make. Indeed, average cost can be much higher or lower than marginal cost, as Figure 7-2(b) shows. ‘
But Figure 7-2(b) also shows that there is an important link between MC and .4C: When the ,\fC of an added unit of output is below its AC, its AC is dedining: And when MC is above AC, AC is increasing. At the point where M~ equals AC, the AC curve is flat. For the typical U-shaped AC curve, the point where MC eqcals AC is also the point where AC hits its minimum level, Check this for yourself on the graph.
Focus a microscope on the total cost curve to examine the cost of going from an output of 3999 to 4000. The figure clarifies the distinction between (I) MC as the increments cost for a finite-step change in output and (2) MCas the cost for an infinitesimal change in output measured by the tangent, TIle distance from a to b represents I extra unit of output. The b to d distance represents the resulting increase in total cost. Hence MC = (d:- b)/(b – a). which is first and simplest definition of marginal cost.
The second definition of marginal cost i~ as the slope total cost curve. The slope of the curve at point a by the slope of the tangent at point n, which is the distance from b to c divided by the distance b. In the limit for a smooth curve, as the size of increment becomes smaller and smalIer and we ~cz.caI;ne the ratios in the new, smaller triangle, the ennoble the two definitions becomes negligible.
Remember these important rules:
• A’hen margin a below average cost it pulling average cost down.
• When MC is above AC, it is pulling Cup.
• When MC just equals AC, AC is neither rising nor falling and is at its minimum. Hence. at the bottom of a L-shaped AC. Me = AC = minimum AC.
This, is a critical relationship. It means that a firm searching for the lowest average cost of production should look for the level of output at which marginal costs equal average costs.
Why is this so? If MC is below AC, the last unit produced costs less than the average cost of all the previous units produced. If the last unit costs Ie than the previous ones, the new AC (i.e., the AC including the last unit) must be less than the old AC. so AC must be falling. By contrast, if MCis above AC. the last unit costs more than the average cost of the previous units. Hence the new average cost (the AC including the last unit) must be higher than the old AC. Finally, when MC is just equal to AC, the last unit
costs exactly the same as the average cost of all previous units. Hence the new ,4C, the one including the last unit, is equal to the old AC; the AC curve i flat when AC equals Me To better understand the relationship between MC and AC, study the curves in Figure 7-2(b) and the numbers in Table 7-3. Note that for the first 3 units, MC is below AC, and AC is therefore declining.
At exactly 4 units, AC equals MC over 4 units. MC is above AC and pulling AC up steadily. Graphically that means the rising MC curve will intersect the AC curve precisely at the point where it turns uI’ ward: the AC curve is always pierced at its minimum point by the rising MC curve. In terms of our cost curves, if the MC curve is below the AC curve, the AC curve must be falling.
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