Question

A firm uses capital and labor in its production process. Capital is fixed in the short run while labor is variable. Assume that the firm has acquired the optimal quantity of capital for the production of 100 units of output. Using typically shaped isoquants and isocost lines, demonstrate that the cost to the firm of increasing output to 200 units will be greater in the short run than in the long run. Identify the short-run expansion path and the long-run expansion path.

Answer 1

The given firm uses capital and labor in its production process. Capital is fixed in the short run at quantity K1 while labor is variable. Currently, firm has acquired the optimal quantity of capital at K1 and labor at L1 for the production of 100 units of output. This is shown by point E where isoquant I(qo) = 100 is tangent to the isocost line CC'.

Now the firm has decided to raise production to 200 units which is represented by the isoquant I(q0) = 200. Since the firm cannot increase capital unit in short run, it uses same capital units at K1 and uses more labor at L2 to produce 200 units in the short run. This incurs a cost which is shown by the isocost line AA'. The optimum production point has no tangency at G.

Capital units А В С K* K1 I(qo) = 200 (qo) = 100 В А' C' L2 L1 L Labor units LL -H

In the long run however, firm can raise capital units to K* and reduce labor units to L* to reach the same isoquant I(q0) = 200 but at a lower cost shown by the isocost line BB'. The long run equilibrium is shown at F. Hence, the cost to the firm of increasing output to 200 units will be greater in the short run than in the long run.

Combinations at E and G when joined, represent the expansion path in the short run that displays capital rigidity. Combinations at E and F when joined, represent the expansion path in the long run that displays capital flexibility.

Capital units А В Long run expansion path С K* Short run G expansion path 7(qo) K1 = 200 (qo) = 100 В А' C' L2 L1 L Labor units