In microeconomics the marginal rate of technical substitution measures how much one input is reduced in order to increase another input by a unit of one while keeping output constant. Often abbreviated to MRTS, the marginal rate of technical substitution is a fundamental concept of production theory. It is derived by first calculating the marginal rate of substitution for each input.
Calculate the marginal product for the first input. The marginal product is equal to the change in output divided by the change in input. So, if an increase in five units of input results in an increase in four units of output, then the marginal product for the first input would be 0.8.
Calculate the marginal product of the second input, using the same method as the first method. Assume that in this example increasing five units of the input results in an increase of seven units of the output. Dividing seven by five yields 1.4.
Divide the marginal product of the second input by the marginal product of the first input in order to obtain the marginal rate of technical substitution for the first input with respect to the second. Using the same example, if the marginal product of the first input was 0.8 and the marginal product for the second input was 1.4, then dividing 1.4 by 0.8 results in a marginal rate of technical substitution of 1.75. Thus, a firm would have to reduce 1.75 of the second input in order to use one extra unit of the first input while keeping production constant.
Calculate the marginal product for the first input. The marginal product is equal to the change in output divided by the change in input. So, if an increase in five units of input results in an increase in four units of output, then the marginal product for the first input would be 0.8.
Calculate the marginal product of the second input, using the same method as the first method. Assume that in this example increasing five units of the input results in an increase of seven units of the output. Dividing seven by five yields 1.4.
Divide the marginal product of the second input by the marginal product of the first input in order to obtain the marginal rate of technical substitution for the first input with respect to the second. Using the same example, if the marginal product of the first input was 0.8 and the marginal product for the second input was 1.4, then dividing 1.4 by 0.8 results in a marginal rate of technical substitution of 1.75. Thus, a firm would have to reduce 1.75 of the second input in order to use one extra unit of the first input while keeping production constant.