Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.

An expansion path is the locus of all the equilibrium points between an isoquant and isocost curve. It shows different points where the MRTS is equal to the ratio of factor prices.

The expansion path connects the optimal combinations of input factors when the production scale (producer’s budget) expands with constant factor prices. If the factor prices change, the production scale remains unchanged; the isocost will not shift parallelly. The isocost will either become steeper or flatter, and the expansion path will move accordingly.

The fall in labor costs by 50% (half) will double the labor demand, other things being constant. Suppose the firms initially hired K amount of capital and N amount of labor. A fall in labor cost by 50% will increase the labor to 2N, provided the cost of capital and firms’ budget remains constant. Also, the labor demand will change only if the wage cut seems permanent in the long run.

The following graph shows the change in the isocost curves due to a cut in labor cost.

Due to the wage cut, the isocost curve will pivot to the right from KN to K2N. The isocost curve has become flatter at K2N. Thus, the expansion path after the wage cut has shifted and become more balanced or flatter.