Marginal rate of technical substitution

In microeconomic theory, the marginal rate of technical substitution (MRTS)—or technical rate of substitution (TRS)—is the amount by which the quantity of one input has to be reduced ( − Δ x 2 {\displaystyle -\Delta x_{2}} ) when one extra unit of another input is used ( Δ x 1 = 1 {\displaystyle \Delta x_{1}=1} ), so that output remains constant ( y = y ¯ {\displaystyle y={\bar {y}}} ). M R T S ( x 1 , x 2 ) = − Δ x 2 Δ x 1 {\displaystyle MRTS(x_{1},x_{2})={\frac {-\Delta x_{2}}{\Delta x_{1}}}} It can be shown that M R T S ( x 1 , x 2 ) = M P 1 M P 2 {\displaystyle MRTS(x_{1},x_{2})={\frac {MP_{1}}{MP_{2}}}} , where M P 1 {\displaystyle MP_{1}} and M P 2 {\displaystyle MP_{2}} are the marginal products of input 1 and input 2, respectively.

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