■ Definition: A locus of the tangency points between various isoquants and various isocosts is called the expansion path , since it shows the least-cost combinations of labor and capital a firm would choose as it expanded its output level, if it were free to vary both labor and capital and if it were given constant factor prices and a constant state of technology. This expansion path is shown as the line EP in Figure 6A-2. Note that this must be the long-run expansion path, since all factors must be variable to allow the adjustment in both capital and labor involved in the movement along the line EP.
Suppose the firm wishes to produce 40 units of output and thus selects the combination of factors represented by point B on the long-run expansion path. The firm’s capital input will now be fixed at K* units, and the firm is in a short-run situation. If the firm wishes to vary its output level in the short run, it must simply add or subtract labor to or from the fixed capital input K*. The short-run expansion path is therefore a horizontal line at the capital input level K *, and we have shown it as the line TP in Figure 6A-2. This short-run expansion path is in fact the total product curve, viewed from a different perspective.
Notice that for every output level except the one where TP crosses EP, it costs more to produce the output in the short run than it does in the long run. Any isocost
250 Production and Cost Analysis
line that intersects an isoquant curve on the TP line must lie farther to the right when compared with the isocost line that is tangent to each isoquant curve. This statement is demonstrated in Figure 6A-2 for the output level of 20 units. In the long-run situation the optimal input combination is at point A, and the lowest attainable isocost line is shown as MTV. In the short-run situation with capital input of K*, 20 units must be produced by the input combination represented by point A ', since the firm is constrained to the “short-run expansion path,” TP. The minimum cost of producing 20 units with combination A', is shown by the isocost line M'N', which lies to the right of the line MTV. The short-run situation costs more than the long-run situation for all except one output level, because the firm is unable in the short run to change the input of capital and is thus forced to have an inappropriate factor combination for all except one output level. In the case shown, only at the output of 40 units does the level of capital ( K *) allow the tangency situation of economic efficiency to be attained. 2