The marginal rate of technical substitution is an economic term that indicates the reason why one input can be substituted for another, keeping total output constant.
The marginal rate of technical substitution is an economic term that indicates the reason why one input can be substituted for another, keeping total output constant. This allows analysts to identify the most profitable production method for a specific item, balancing the competing needs of two separate but equally necessary components. Calculating this relationship is most easily accomplished by plotting the input values on an XY graph to visually represent the rate of change through a series of possible input combinations. It is not a fixed value and requires a new calculation for each change up or down in the continuous variable.
For example, it can be assumed that the production of 100 units of product X requires 1 unit of labor and 10 units of capital. Calculating the marginal rate of technical substitution of labor will tell how many units of capital can be “saved” by adding one additional unit of labor, while holding the total unit of output constant at 100. If 100 units of product X can be produced with two units of labor and only seven units of capital, so the ratio of labor to capital is 3:1.
However, this number is specific to each particular set of input values. Although in this case – going from 1 to 2 units of labor – the replacement ratio was 3:1, this does not mean that it will remain 3:1 for all combinations of labor and capital. If producing 100 units of product X using three units of labor only requires the use of five units of capital, the ratio has changed to 2:1 for that specific labor/capital combination.
This specificity explains why the marginal rate of technical substitution is best represented visually on a graph, using all possible combinations of labor and capital. It enables rapid visual consumption of variable rates across the possible spectrum of labor/capital combinations. This, along with pricing information for the different components, allows you to quickly determine which labor/capital combination provides the most cost-effective method of producing a given quantity of product.
In creating these calculations, it is necessary to assume that units of labor are equally expensive compared to units of capital. The goal then becomes to find the point of production where the combined total units of labor and capital are minimized, saving the most cost. Continuing the previous example, in combination one, one unit of labor and 10 of capital requires 11 combined units of labor/capital to produce 100 of product X. Combination two, consisting of two units of labor and seven of capital, reduces to nine units, while combination three, which employs three units of labor and five units of capital, reduces to seven. Combination three then becomes the cheapest method of producing 100 units of product X.