What can students possibly learn through impossible examples?

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from Emmanuelle Bénicourt, Sophie Jallais and Camille Noûs and RWER #98

The case of distribution of revenue

Marginal product is a key concept of neo-classical economics, for, in the perfect competition model, it determines inputs’ demands (the quantities chosen by a competitive profit-maximizing firm are such that the value of the input’s marginal product equals the input’s real price). It is then a core concept of neoclassical distribution theory, the so-called ‘marginal productivity theory of income distribution’ (McConnel, Brue & Flynn 2018, chapter 16, 6^th section’s title, 325), in which the price of each input equals its marginal productivity. This is generally what appears in the chapter of beginners’ textbooks which deals with “the markets for the factors of production”, which students read thinking that marginal productivity of an input is the increase in the quantity of output that arises from one additional unit of that input, and “of course” from additional used quantities of all other inputs.

Yet, concerning the presentation of distribution theory, using impossible examples to explain marginal product has two unfortunate pedagogical consequences, consequences that are all the more unfortunate that they happen to be conflicting. On the one hand, (i) it leads to an absurd, and sometimes inconsistent, income distribution theory; on the other hand, (ii) it (more or less explicitly) encourages students to interpret our world through this dubious theory without further questioning.

Our beginner students, to whom the concept of the marginal product (most of the time, labor) has been presented through examples with a fixed-proportion production function and excess quantities of all inputs (except labor), must surely be thinking that an additional unit of labor leads to something similar to the consequences of the withdrawal of one unit of factor, to which Hicks draws attention in the following passage:

“If the proportions are fixed, then […] the withdrawal of one unit will lead to a far greater diminution in the product that can fairly be attributed to that unit alone, since its removal put corresponding units of other factors out of action. If all the factors were paid according to their marginal products calculated in this second manner, their total pay would undoubtedly be far in excess of the value of the goods they produced. Which is absurd.” (Hicks 1932, 81)

For example, if returns to scale are constant, and if we choose units of measure so that the quantity of each of the n inputs needed to produce one unit of output equals 1, if the quantities of n – 1 inputs are sufficiently excessive, then an additional unit of the n^th input will lead to the production of an additional unit of output. If we calculate the marginal product of each input in this manner, for each unit of output produced, the total pay for inputs will be n times greater than the total product!

This ill-defined concept is also clearly inconsistent with the normative content of the marginal productivity theory of distribution, be it implicit — as when Mankiw speaks about the marginal product of a factor as “its marginal contribution to the production of goods and services” (Mankiw 2015, 390, emphasis added) — or explicit — as in McConnel, Brue and Flynn 2018, which claims: “In this marginal productivity theory of income distribution, income is distributed according to contribution to society’s output”, and “To each according to the value of what he or she creates” (McConnel, Brue & Flynn 2018, 325). For, when inputs are complements, their physical productive contributions are impossible to disentangle: it is obviously impossible to separate out the productive contribution of each input.

read more: http://www.paecon.net/PAEReview/issue98/BenicourtJallaisNous98.pdf