loss of one unit of . Marginal rate of technical substitution Similarly, sometimes the level set is an isoquant showing various combinations of utilized quantities of labor and of physical capital each of which would result in the production of the same given quantity of output of some good. In this case the absolute value of the implicit derivative is interpreted as the marginal rate of technical substitution between the two factors of production: how much more capital the firm must use to produce the same amount of output with one less unit of labor. Optimization Often in economic theory, some function such as a utility function or a profit function is to be maximized with respect to a choice vector even though the objective function has not been restricted to any specific functional form. The implicit function theorem guarantees that the first-order conditions of the optimization define an implicit function for each element of the optimal vector of the choice vector . When profit is being maximized, typically the resulting implicit functions are the labor demand function and the supply functions of various goods. When utility is being maximized, typically the resulting implicit functions are the labor supply function and the demand functions for various goods. Moreover, the influence of the problem's parameters on — the partial derivatives of the implicit function — can be expressed as total derivatives of the system of first-order conditions found using total differentiation. See also Implicit curve Functional equation Level set Contour line Isosurface Marginal rate of substitution Implicit function theorem Logarithmic differentiation Polygonizer Related rates References Further reading External links Archived at Ghostarchive and the Wayback Machine: Differential calculus Theorems in analysis Multivariable calculus Differential topology Algebraic geometry