Question

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.

Short answer

The decrease in labor costs shifts the isocost line outwards reflecting more affordability of labor for the same amount of capital. This in turn shifts the firm's equilibrium point along the isoquant. Consequently, the firm's expansion path, represented by the line joining these equilibrium points, changes.

Step-by-step solution

Understanding the Context

Initially, the firm is in equilibrium at some point on its expansion path. The expansion path of a firm is the path traced out by the tangency points of isoquants and isocost lines as the firm expands its output level. Here, we use the labor market as an example, where capital is maintained constant and labor and the output vary.

Analyzing the Shift

A decrease in labor costs implies that for the same amount of capital, a firm can now afford more labor. This shifts the isocost line outwards. The isocost line will now intersect the isoquant at a different point.

Graphically Representing the Shift

On graph, draw the original isocost line and the isoquant curve with their tangency representing the firm's equilibrium. Then, show the reduction in labor cost by drawing a new isocost line to the right of the original one, indicating more labor can be afforded. Mark the new tangency point with the isoquant.

Indicating the New Expansion Path

The expansion path changes because the new equilibrium point is different from its previous one. The new expansion path will now be the line joining all such new equilibrium points for different levels of output. On the graph, draw this new expansion path.