Minimum Wages and the Card--Krueger Paradox.

• Author: Shepherd, A. Ross
• Position: David Card; Alan B. Krueger

1. Ross Shepherd [*]

An apparent paradox perceived by Card and Krueger concerning the relationship between minimum wages, employment, and output prices is resolved by revisiting the economics of minimum wages to show that under monopsonistic conditions in the labor market and competitive price-taking in the market for output, increases in both firm-level and industry employment are compatible with increases in output prices.

1. Introduction

   David Card and Alan B. Krueger (1994) analyzed the experiences of 410 fast-food restaurants in New Jersey and Pennsylvania following the 1992 increase in New Jersey's minimum wage from $4.25 to $5.05 per hour. Their key findings were that (i) employment at stores affected by the increase in the minimum wage grew both absolutely and relative to stores unaffected by the increases (either because they were in Pennsylvania or were New Jersey stores already paying more than the new minimum); (ii) the higher minimum wage was not offset by reductions in nonwage benefits; and (iii) the resultant higher costs were passed through to consumers in the form of higher fast-food prices.

2. The Card--Krueger Paradox

   Card and Krueger (CK) are puzzled by their results because the competitive model predicts lower employment, less output, and hence higher output prices following an increase in the minimum wage, whereas in their view monopsony models that predict greater employment following an increase in the minimum wage predict greater output, and hence lower output prices. In their words:

   "A standard competitive model predicts that establishment-level employment will fall if the wage is exogenously raised. For an entire industry, total employment is predicted to fall, and product price is predicted to rise in response to an increase in a binding minimum wage....

   An alternative to the conventional competitive model is one in which firms are price-takers in the product market but have some degree of market power in the labor market. If fast-food stores face an upward-sloping labor supply schedule, a rise in the minimum wage can potentially increase employment at affected firms and in the industry as a whole....

   Although monopsonistic ... models provide a potential explanation for the observed employment effects of the New Jersey minimum wage, they cannot explain the observed price effects. In these models industry prices should have fallen in New Jersey relative to Pennsylvania..." (Card and Krueger 1994, pp. 790-91).

   The Card--Krueger paradox may be summarized as follows: according to economic theory, an increase in a binding minimum wage (one that changes behavior because it is higher than the prevailing wage) will decrease employment and increase output prices under competition, or under monopsony (perhaps) increase employment and decrease output prices, but it cannot increase both employment and output prices as it did in New Jersey. The purpose of this paper is to revisit the economic theory of minimum wages in order to resolve this paradox. Among other things, I will show that the CK results are not anomalous, as CK evidently believe, but rather are completely consistent with "the alternative to the conventional competitive model" they themselves mention.

3. The Alternative Model

   The alternative to the conventional competitive model mentioned by CK is a blend of perfect competition in the market for output and monopsony power in the market for labor. (In this model the firm is not a true, or pure monopsony--strictly defined as a "single buyer"--in the relevant market for labor. But terms like "monopsony power," "monopsonist," and "monopsony" are used here because our firms, like the pure monopsony, perceive that their behavior affects the going wage. [1]) As in other competitive markets for output, profit-maximizing behavior in the face of free entry and exit is assumed to yield normal profits for firms, with price equal to minimum long run average cost at long run equilibrium. [2] In one or more input markets, including the labor market, the firm is assumed to perceive that a rising supply price causes marginal factor cost to exceed average factor cost. Thus, a hallmark of the model is the firm's perception of rents paid to intramarginal units of factors. This perception is expresse d in the familiar identity,

   [MFC.sub.L] = [AFC.sub.L] + L[d([AFC.sub.L])/dL], (1)

   where [MFC.sub.L], [AFC.sub.L], and L are marginal factor cost, average factor cost, and quantity of a specific factor (L = 1, 2,..., N), respectively, and L[d([AFC.sub.L])/dL] [greater than] 0 is the variation in total rent paid to intramarginal units of the factor, occasioned by a small variation in employment of that factor. (In what follows I focus on the labor market, so L will specifically denote labor.)

   A binding minimum wage affects [MFC.sub.L] in two countervailing ways: it increases average factor cost, while eliminating incremental intramarginal rent up to the level of employment where the minimum wage equals the free market supply price of labor. (If employment expands beyond that point, the minimum wage is no longer binding and incremental intramarginal rent reappears.) The effective marginal factor cost of labor under a binding minimum wage ([[MFC.sup.*].sub.L]) is therefore simply [[MFC.sup.*].sub.L] = [[AFC.sup.*].sub.L] = minimum wage, where [[AFC.sup.*].sub.L] is the effective average factor cost of labor under the minimum wage.

   Profit maximization in this model, where firms are price-takers in the market for output, requires the employer to employ labor up to the point where [MFC.sub.L] equals the market value of labor's marginal product: [MFC.sub.L] = [VMP.sub.L], where [VMP.sub.L] is the arithmetical product of output price and the marginal physical product of labor. At the equilibrium level of employment under the minimum wage,

   [[MFC.sup.*].sub.L] = [[AFC.sup.*].sub.L] = [[VMP.sup.*].sub.L], (2)

   if this occurs within the relevant range, that is, the range over which the minimum wage is binding; otherwise it obtains at the end of the relevant range, where

   [[MFC.sup.*].sub.L] = [[AFC.sup.*].sub.L] = [AFC.sub.L] [less than] [VMP.sub.L] [less than] [MFC.sub.L] (3)

   The foregoing points are illustrated in Figure 1, where [AFC.sub.L], [MFC.sub.L], and [VMP.sub.L] curves of the typical firm are shown. (Note that the diagram is "opened up" for viewing by an overly steep [MFC.sub.L] curve.) Profit-maximizing employment obtains initially at [L.sub.1], where [MFC.sub.L1] = [VMP.sub.L1] = [L.sub.1]B. At this level of employment, the supply price of labor (free market wage) is = [AFC.sub.L1] = [L.sub.1]A. [3] The difference between [MFC.sub.L] and [AFC.sub.L] at [L.sub.1]--distance AB--measures the increase (decrease) in rents paid to intramarginal workers as a result of a small increase (decrease) in employment in the neighborhood of [L.sub.1].

   Now let a minimum wage be established at [[MFC.sup.*].sub.L]. Profit-maximizing employment increases to [L.sub.2] at the end of the relevant...