Marginal Productivity

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Marginal Productivity

A dominant theme in both the explication and legitimization of a market economy is that if individuals work hard and effectively, they will be appropriately rewarded. Typically understood as the Protestant ethic, the theme provides moral approval for hard work and asset accumulation, even though the terms hard work, effectively, and appropriately require technical specification and thereby a narrower meaning than the theme seems to offer at first glance. The moral injunction is transformed when translated into economic theory.

The foremost attempt to do so was by John Bates Clark (1847–1938) in the late nineteenth century. His ethical marginal productivity theory was an attempt to prove mathematically that people receive what they produce. Correctly formulated, the theory says something much less than that: namely, that the wage rate is only an element in an equilibrium equation and not a uniquely causal factor; indeed, that marginal productivity explains only the demand for labor and not the wage rate. The hold of the Protestant ethic is such that even though economists understand the more limited significance of marginal productivity, an inevitable tendency is for some economists to revert to Clark’s ethical formulation.

That the marginal productivity theory is only a theory of the demand for labor is easily shown. Assuming (eventual) diminishing returns, the marginal product curve for a particular occupation slopes downward to the right. The wage rate is a function of the demand and supply of labor. The marginal product curve represents the demand for labor for the firm: As the wage rate falls, employers will hire more workers, and vice versa. The summation of the individual firms’ marginal product curves yields the market-demand curve for labor. It, together with the labor-supply curve, determines the wage rate. In equilibrium, the intersection of the labor-demand and labor-supply curves will yield the amount of labor hired and the wage rate at which they are hired. The marginal productivity curve enters only into the determination of the labor-demand curve; to determine the wage rate (and employment) one must introduce the labor-supply curve. If, in a particular occupation, the supply of labor shifts to the right, there will be greater employment at a lower wage rate—even though workers are working as hard as before.

Another way of looking at the foregoing is to consider the downward-sloping curve as the value of the marginal product, constructed thusly: The marginal physical product, itself a result of technology, is the immediate cause of the downward slope; the marginal physical product must be multiplied by the price of the product, which is a function of the demand and supply of the product, all of which is separate from or external to the demand for labor. Workers may work as hard as they can, but at best this will only raise slightly the value of the marginal product curve; much more important is technology and the product price. The wage rate is governed largely by nonethical factors.

So, far from proving that people receive (the value of) what they produce, the theory, using the conventional assumptions, proves a tendency toward equal wages. Assume three occupations, each with its respective, negatively inclined marginal productivity curve. Let the three curves start at any three points on the vertical marginal product axis (employment is on the horizontal axis) and let them decline at different rates. The language, “one occupation is more productive than another,” is predicated neither on one curve starting higher than another on the vertical axis, nor on one curve declining less rapidly than the other. It asserts something stronger, something that is analytically false. Assume further a labor-supply curve for each marginal productivity curve; their three respective intersections yield three wage rates, one for each occupation. The conventional assumptions are competition and labor mobility. Labor in the lowest-wage occupations will move to the higher-paying ones. The labor-supply curve shifts to the left in the formerly low-wage occupation, thereby raising the wage; and vice versa in the formerly high-wage occupations. The process, under the postulated static conditions, continues in principle until the same wage rate prevails in all three industries. The theory produces the result, not that one industry has higher wages because it is more productive than another(s), but that there is a tendency toward equal wages. That the tendency is not reached is due to immobility of labor, noncompetitive conditions, wages as not the only remuneration in a job, and evolutionary and dynamic changes in technology, tastes, and so on.

At any rate, marginal productivity theory is only a theory of the demand for labor and is itself dependent in part on technology and on the demand (relative to the supply) of the product of labor. Other marginalist formulations, with the exception of marginal utility as a theory of value, have not been given ethical status: marginal cost, marginal disutility, marginal efficiency of capital or of investment, marginal propensities to consume and to save, marginal rate of substitution, marginal tax rate, marginal revenue, marginal utility of money, and marginal rate of transformation are important and nonethical categories. So too is the marginal productivity theory as a theory of the demand for labor and employment of labor; it is, however, neither a theory of wages nor the Protestant ethic in economic garment.

SEE ALSO Capital; Human Capital; Marginalism; Market Economy