Assume the consumer utility function is defined by where U is consumer utility x and y are goods. The law of variable proportions is a new name for the law of diminishing returns a concept of classical economics. Pin On Economics Business Since the indifference curve is convex with respect to the origin and we have defined the MRS as the negative slope of the indifference curve Simple mathematical analysis. . Law of Variable Proportions in terms of TPP and MPP. Any increase in the input will no longer increase the marginal quantity of output. However of the three stages a firm will like to produce up to any given point in the second stage only. But before getting on with the law there is a need to understand the total product TP marginal product MP and average product AP. Therefore producers prefer Stage II the stage of diminishing returns. The law of diminishing marginal utility is a law of economics stating that as a per