In this article we will discuss about the relation between the short-run and long-run cost curves.
In the long run all factors are variable. Therefore, the producer can operate without facing the constraints of the fixed factors. The long-run cost (LAC) is not more than the short-run cost (SAC) because the unconstrained minimum average cost at any output cannot be more than the constrained minimum.
Another point that we should note is that at any output other than that at the minimum point of the LAC curve, the firm operates at a point on the downward-sloping or the upward-sloping portion of its plant curve (i.e., SAC curve), not at the minimum point of the latter.
For example, if the firm wants to produce q = q, along the downward-sloping portion of its LAC curve, it would find that it is better to operate on the downward-sloping portion of plant curve 2 than to operate at the minimum point of plant curve 1, for average cost in the former case is smaller than that in the latter case.
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Let us note at this point that the output at the minimum point of the plant curve is considered to be the capacity of the plant. So the capacity is not the maximum possible output that the plant can produce.
If a producer produces an output which is smaller than the capacity output, he is said to be operating with excess capacity, and if he produces an output which is larger than the capacity output, then he operates above capacity.
In Fig. 9.17, we see that the firm would produce any output q = q1 along the downward sloping portion of its LAC curve at point F on plant 2 where it would have excess capacity instead of producing the output at point E on plant 1 where it would be operating on capacity because the average cost in the former case is smaller than that in the latter case.
Now how can we explain this? Why would the firm operate with excess capacity? Apparently, here is a paradox.
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The paradox centres round the fact that production on capacity entails a higher cost than production with excess capacity. But the paradox can be resolved immediately if we take note of the fact that as the size of the plant increases along the downward-sloping portion of the LAC curve, the firm’s SAC diminishes up to larger quantities of output and towards a lower minimum owing to the economies of scale.
Similarly, if the firm wants to produce q = q3 along the upward-sloping portion of its LAC curve, it would find that it is better to operate on the upward-sloping portion of plant curve 3 at excess capacity than to operate at the minimum point of plant curve 4 on capacity, because the average cost in the former case is smaller than that in the latter case. Here we find that production on capacity entails a higher cost than production with excess capacity.
Here also the paradox will be resolved if we remember that as the size of the plant increases along the upward-sloping portion of the LAC curve, the firm’s SAC along the larger plant 4 diminishes up to a larger quantity of output because of economies of scale but towards a higher minimum because of the diseconomies of scale.
In the context of above analysis, we have to remember that operating a given plant at the minimum point on the average cost (SAC) curve and producing a given output at minimum average cost arc two different things. A profit-maximising producer is interested in the latter. The two objectives would be the same at only one point on the LAC curve, which is its minimum point.
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In Fig. 9.17, at the minimum point of the LAC curve, the firm’s output is q2. At this output, the firm is at the minimum point of its SAC curve 3 and at the same time it is producing the output at the minimum average cost. Only at this output, i.e., q2, the firm is operating on capacity and yet producing at the minimum average cost.