# Marginal Rate of Technical Substitution

## What is the 'Marginal Rate of Technical Substitution'

The marginal rate of technical substitution (MRTS) is the rate at which one aspect must be decreased so that the same level of productivity can be maintained when another factor is increased. The MRTS reveals the give-and-take between factors, such as capital and labor, that firms make out of the necessity to maintain a constant output. MRTS differs from the marginal rate of substitution (MRS), because MRTS is focused on producer equilibrium and MRS is focused on consumer equilibrium.

## BREAKING DOWN 'Marginal Rate of Technical Substitution'

The MRTS is the slope of a graph, having one factor that is represented on each axis. The MRTS slope is an isoquant, meaning itās a curve that connects the two input points as long as the output remains the same.

## Examples

For example, a MRTS graph that has capital (represented with K) on its X-axis and labor (represented with L) on its Y-axis is calculated as: dL / dK. The isoquant shape is dependent upon whether input values are exact substitutes, which result in a straight line, or complements, which create an āLā shape. When input values are not exact substitutes, the line is curved.

If there is a decline within the MRTS, along the isoquant, it is referred to as a diminishing marginal rate of technical substitution. Consider that a company plots a graph for capital and labor. In order to move from point A to point B on the graph, labor must be decreased by two in order to increase capital by six. In order to move from point B to point C, labor must be decreased by two so that capital increases by four. So, if MRTS = dK / dL, then point A to point B has an MRTS of three and point B to point C has an MRTS of two.

## Producer Equilibrium

All producers strive hard to generate the maximum amount of profit for the minimum amount of cost. The producer obtains equilibrium by putting together factors of production in a combination that requires the least amount of money. Thus, the producer is responsible for determining the combination of production factors that best achieve this result.

The decision the producer makes involves the MRTS and the principle of substitution. Consider the producer has only two production factors, factor A and factor B. Factor A is able to produce a greater amount of output than factor B, with an equal amount of capital being spent on both. This leads to the producer substituting factor A for factor B.