Long run costs are called as planning costs or ex-ante costs, as the firm has to plan its future course of action from a wide range of options. An economic agent operates in the short run, while it plans in the long run. It may expand the existing plant, install a new plant, change the management style, etc.
Long run total cost (LTC) curves showing the relationship between output and total cost are derived from the long-run production functions in which all inputs are variable. Such a production function can be represented by an isoquant map.
As we know that, for any given output level, short-run total cost is greater than or equal to the long-run total cost. For only one level of output, the costs under the two periods are equal. This is also clear from Fig. 11.10, which shows the derivation of long-run total cost curve from short-run total cost curves.
Image Source: ltc.com.sg
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We have, here, a family of short-run cost curves, one for each capacity, depending on the output it wants to produce in the long-run. The long-run envelops on the short-run cost curves, for the long-run cost cannot exceed the short run cost for any level of output.
The long-run cost curve would be smooth, if there is short-run cost curve for every size of the plant. In Fig 11.10, the long-run and short-run costs are equal only at output levels Q1 Q2, Q3 and Q4, which correspond to the points of tangency between LTC and STC curves.
It is also clear from the figure that when output is small, the total cost is less for a small plant than for a large plant. Likewise, for larger outputs, larger plants are more suitable. Such plants remain underutilised for small output, while a small plant is inadequate for large outputs.
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That is why, short-run total cost curves cut each other and extend to the output axis up to different lengths. For output OQ1, the smallest plant is most appropriate, as total cost OC1 under this plant is less than that for any other plant size (OC2, OC3 and OC4).
It is not viable to produce OQ1, or more output with such a small plant. For output levels of OQ2 OQ3, and OQ4 plants with short-run cost curves STC2, STC3 and STC4 respectively are most suitable.
Like short run variable cost curve, the LTC curve first increases at a decreasing rate, then at an increasing rate (Fig. 11.10). This inverse S-shaped curve starts from the origin implying thereby that in the long-run, if nothing is produced, no resources will be used.
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While the shape of short run variable cost curve is due to the law of variable proportions in the short-run, the shape of LTC curve is due to the existence of returns to scale. Similar to short run variable cost curve, the long run total cost curve is initially concave from below and thereafter it is convex from below.
Further, if LTC curve is concave, the output elasticity of total cost is less than one. Likewise, when this curve is convex, the output elasticity of total cost is greater than 1. The LAC curve falls and rises in these two cases respectively, as explained here.