# Marginal Rate of Technical Substitution

February 26, 2014

The rate at which one factor has to be decreased in order to retain the same level of productivity if another factor is increased. The marginal rate of technical substitution shows the tradeoffs between factors, such as capital and labor, that a firm must make in order to keep output constant. The marginal rate of technical substitution is different than the marginal rate of substitution (MRS). MRTS focuses on producer equilibrium, while MRS focuses on consumer equilibrium.

The marginal rate of technical substitution is the slope of a graph that has one factor represented on each access. The slope is an isoquant, which is a curve that connects the points of the two inputs when the output is kept the same. For example, the MRTS of a graph that has capital (K) on its X-axis and labor (L) on its Y-axis is calculated as dL/dK. The shape of the isoquant depends on whether the inputs are perfect substitutes (straight line), complements (L-shaped) or if inputs are not perfect substitutes (curve).

A decline in the MRTS along an isoquant is called a diminishing marginal rate of technical substitution. For example, a firm plots out a graph of capital and labor. Moving from point A to point B means reducing labor by 1 to increase capital by 4. To move from point B to point C means reducing labor by 1 to increase capital by 2. If MRTS = dK/dL, point A to point B has a MRTS of 4, and from point B to point C has a MRTS of 2.