6.11 : Taxa Marginal de Substituição Técnica (TMST)

The slope of an isoquant measures the marginal rate of technical substitution or MRTS, which plays an important role in production decisions.

MRTS measures how many units of one input, such as labor, can be replaced by one unit of another input, like capital, while maintaining the same level of output. It reflects the trade-off between inputs in production.

When moving down along an isoquant, there is a trade-off between labor and capital. An increase in labor contributes to output by the amount of Marginal Product of Labor multiplied by the change in labor.

However, there is a decrease in the output from capital since it's being replaced by labor. This can be represented as the marginal product of capital multiplied by the change in capital.

Since this movement is along the isoquant, the change in total output will be zero.

Now, rearranging for the slope of the isoquant, which is a negative ratio of delta K by delta L, gives the MRTS of Labor for Capital. It is the ratio of the marginal product of labor to the marginal product of capital.

 The MRTS typically diminishes as we move along an isoquant, reflecting the principle of diminishing marginal returns. This explains the convex shape of isoquants.