What Is a Marginal Rate of Technical Substitution?

Marginal rate of technical substitution is an economic term that indicates the ratio at which one input may be substituted for another while holding the total production constant. This allows analysts to identify the most cost-efficient method of production for a specific item, balancing the competing needs of two separate — but equally necessary — component parts. Calculating this ratio is easiest to accomplish by plotting the input amounts on an X-Y graph, in order to visually represent the shifting rate across a number of potential input combinations. It is not one fixed value and requires recalculation for each shift up or down on the variable continuum.

For example, one can assume that producing 100 units of product X requires one unit of labor and 10 units of capital. Calculating the marginal rate of technical substitution for labor will indicate how many units of capital can be "saved" by adding in an extra unit of labor, while keeping the total unit production constant at 100. If 100 units of product X can be produced with two units of labor and only seven units of capital, then the ratio of labor for capital is 3:1.

This number is specific to each particular set of input values, however. Although in this instance — when moving from 1 to 2 units of labor — the rate of substitution was 3:1, that does not mean that it will continue to be 3:1 for all combinations of labor and capital. If producing 100 units of product X using three units of labor only necessitates using five units of capital, the ratio has changed to 2:1 for that specific labor/capital combination.

This specificity explains why marginal rate of technical substitution is best plotted visually on a graph, using all possible combinations of labor and capital. It allows quick visual consumption of the changing rates across the entire possible spectrum of labor/capital combinations. That, in conjunction with pricing information for the different component parts, allows someone to quickly ascertain which combination of labor/capital provides the most cost-efficient method for producing a particular quantity of product.

In creating these calculations, it is necessary to assume that units of labor are equally costly compared to units of capital. The goal then becomes finding the production point where the total combined 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 require 11 combined labor/capital units to product 100 of product X. Combination two, consisting of two units labor and seven of capital, drops that to nine units, while combination three, which employs three units labor and five of capital, drops it to seven. Combination three, then, becomes the most cost-efficient method of producing 100 units of product X.