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Product and resource markets: points of symmetry.

Abstract

For an introductory-level course, one useful teaching strategy is to regularly make students aware of the connections and symmetries between results established in different parts of the course. For example, in the introductory microeconomics course, it is straightforward to connect the behavior of a product price-maker and a resource price-maker. After identifying a number of general points of symmetry between them, this paper more carefully examines the connection between the mark-up pricing behavior of a product seller and the mark-down pricing behavior of a resource hirer. It then illustrates the connection between third-degree price and wage discrimination for one particular case.

Introduction

For an introductory-level course, one useful teaching strategy for greater understanding is to regularly make students aware of the connections and symmetries between results established in different parts of the course. [1] For example, in the introductory microeconomics course, an understanding of firm behavior in resource markets can be enhanced by reminding students of the results established for firm behavior in product markets. Because the logic of marginal reasoning developed in order to explain the latter is quite similar to that used to explain the former, by making such connections clear, not only may understanding resource market results be easier to achieve, understanding product market results is reinforced. After identifying a number of general points of symmetry between them, this paper more carefully examines the close connection between the mark-up pricing of a product seller and the mark-down pricing behavior of a resource hirer. It then illustrates the connection between third-degree price and wage discrimination for one particular case.

General Points of Symmetry

It is straightforward to connect the behavior of a product price-taker (ppt), a firm that is assumed powerless to affect the market-determined product price, and a resource price-taker (rpt), a firm that is assumed powerless to affect the market-determined resource price, or wage; whereas the former faces a horizontal product demand schedule, the latter confronts a horizontal resource (labor) supply schedule, both suggesting the absence of price-making ability. While the market-determined product price for a ppt equals marginal revenue regardless of quantity sold (because the firm can sell as much as it chooses at that price), the market-determined wage for a rpt equals marginal labor cost regardless of amount of labor hired (because the firm can hire as much labor as it chooses at that wage).

In addition, while the market-determined product price equals marginal cost at the profit-maximizing quantity of output for a ppt, the market-determined wage equals marginal revenue product at the profit-maximizing amount of labor for a rpt, with the logic of marginal reasoning behind these results quite similar for either decision. That is, over the range of output for which product price exceeds marginal cost for a ppt, increased production will increase total profit since total revenue will increase by more than total cost; similarly, over the range of labor for which marginal revenue product exceeds labor's wage for a rpt, the hire of additional labor will increase total profit for the same reason. Over the range of output for which product price is less than marginal cost for a ppt, decreased production will increase total profit since total cost will fall by more than total revenue; similarly, over the range of labor for which marginal revenue product is less than labor's wage, the hire of less labor will increase total profit for the same reason.

A final point of symmetry regarding price-takers is that just as the market-determined product price must at least equal the value of minimum average variable cost to insure an incentive for a loss-minimizing ppt to remain open, the market-determined wage must be no greater than the value of maximum average revenue product to insure the same for a loss-minimizing rpt; only if these conditions hold will the firm--ppt or rpt--be able to cover its total variable cost and thus be able to insure its loss (or negative total profit) is less by remaining open than shutting down. It is also straightforward to connect the behavior of a product price-maker (ppm), a firm that is assumed able to influence/determine the product price buyers are willing to pay (by varying the quantity it offers to sell), and a resource price-maker (rpm), a firm that is assumed able to influence/determine the resource price (wage) that workers are willing to accept (by varying the amount of labor it offers to hire); whereas the ppm faces a down-sloping product demand schedule, the rpm faces an up-sloping resource (labor) supply schedule, both implying the ability of the firm to alter price.

Whereas the firm-determined product price exceeds marginal revenue at every quantity beyond the first unit for a ppm (because product price must fall in order to sell additional units of output), marginal labor cost exceeds the firm-determined wage at every amount of labor beyond the first unit in the case of a rpm (because the wage must rise in order to hire additional units of labor). While the firm-determined product price exceeds marginal cost at the profit-maximizing quantity of output for a ppm, marginal revenue will equal marginal cost there; similarly, although the firm-determined wage is less than marginal revenue product at the profit-maximizing amount of labor for a rpm, marginal labor cost will equal marginal revenue product there. The logic of marginal reasoning is quite similar for either decision; with respect to choosing the profit-maximizing quantity of output, over the range of output for which marginal revenue exceeds marginal cost for a ppm, increased production will increase total profit because total revenue will increase more than total cost; over the range of output for which marginal revenue is less than marginal cost, decreased production will increase total profit because total revenue will decrease less than total cost.

Similarly with respect to choosing the profit-maximizing amount of labor; over the range of labor for which marginal revenue product exceeds marginal labor cost for a rpm, the hire of additional labor will increase total profit because total revenue will increase more than total cost; over the range of labor for which marginal revenue product is less than marginal labor cost, the hire of less labor will increase total profit. Having identified a number of general points of symmetry for price-takers and price-makers, in both product and resource markets, this paper will now address two particular points of symmetry. The complexity of them should not preclude their being presented in an introductory course, in light of recent offerings of introductory microeconomics textbooks. In a number of them [2], (third-degree) price discrimination--until recently a topic reserved for courses beyond the introductory level--is discussed; the economic logic behind the behavior of such a price discriminator is easily developed as a straightforward extension of the result we turn to now.

Mark-up and Mark-down Pricing

The first issue elaborated on is the general similarity that exists between a profit-maximizing ppm marking up marginal cost to determine the optimal price to charge consumers, and a profit-maximizing rpm marking down marginal revenue product to determine the wage to offer workers, labor assumed to be the firm's one variable resource. Just as a ppm equates marginal revenue (MR) and marginal cost (MC) to determine the optimal quantity of output to produce, and finds the maximum price consumers are willing to pay by noting the price on its demand schedule corresponding to that quantity, a rpm equates marginal revenue product (MRP) and marginal labor cost (MLC) to determine the optimal amount of labor to hire, and finds the lowest wage that workers will accept by noting the wage on its (labor) supply schedule corresponding to that amount. Just as a ppm may be said to "mark-up" the MC of its optimal output to determine the price to charge consumers, a rpm may be said to "markdown" the MRP of its optimal amount of labor to determine the wage to offer workers. Taking a closer look at the symmetry of this conclusion [3], the reader is alerted that the focus is short-run, and that the firm produces a single product using one variable resource, labor. Looking first at a ppm, equating MR and MC (second-order conditions are ignored) implies the firm sets a price that is a multiple of the MC of its optimal output; more specifically, the firm's optimal price is equal to the MC of its optimal output multiplied by an expression equal to: the absolute value of the price elasticity of demand at its optimal output divided by that absolute value minus 1. [4]

A quite analogous result is valid for the case of a profit-maximizing rpm. To see this, assume the firm confronts a labor supply curve which describes the wage (W) as a simple function of the quantity of labor supplied, whose first derivative is positive. Multiplying both sides of that function by quantity of labor yields an expression for total labor cost. Differentiating, manipulating the resulting expression, and equating same to MRP (in order to satisfy the necessary condition for maximum profit), we obtain an expression that implies the firm's optimal wage is equal to the MRP of its optimal amount of labor multiplied by an expression equal to: the wage elasticity of supply at its optimal amount of labor divided by that elasticity plus 1. This result implies that a profit-maximizing firm should offer/set a wage that is some fraction of the MRP of its optimal amount of labor. Just as our previous result associates with the firm "marking up" its MC to determine the price to charge consumers, this result suggests a firm "marking down" its MRP to determine the wage to offer workers. Note how the size of the fraction, which the wage is of MRP, depends on the value of the wage elasticity of supply (e): if the value e equals 1, the fraction is .5; if it is less than 1, the fraction is less than .5, and if it is more than 1, the fraction is more than .5.

The higher e is at the firm's point of operation, the larger the fraction that the offered wage will be of the MRP of the last worker hired, i.e., the smaller the "mark-down.". [5] If, for whatever reason, the elasticity of supply is greater so that labor is more sensitive to wage changes, indicating that workers will more dramatically reduce the quantity of their service supplied to the firm when the wage is reduced, the firm will be less inclined to offer a wage as low as it otherwise might, in light of its desire to attract the number of workers it wants to hire in order to maximize profit. Just as the ability of a ppm to raise price above MC is constrained by the size of the price elasticity of demand of its consumers, so the ability of a rpm to lower the wage it offers below MRP is similarly constrained by the wage elasticity of supply of its workers. (The reader may note that if e equals [], which it would if the firm's labor supply schedule is horizontal, the optimal wage is equal to MRP at the point of maximum profit, the result we associate with the behavior of a wage-taker.)

Second-degree Price Discrimination

Turning now to another matter, in the special case of a firm operating at its shut-down point, the optimal mark-up/mark-down, respectively, will result in the firm being just able to cover its Total Variable Cost (TVC); a graphical description of these similar situations is offered in Figures 1a and 1b. In Figure la, tangency between the ppm's demand and AVC schedules insures the best the firm can do is operate at the tangency and earn total revenue equal to TVC. In Figure 1b, tangency between the rpm's (labor) supply and average revenue product (ARP) schedules insures the same. (The reader may note that ARP Lequals total revenue, and W Lequals TVC; since W = ARP at the tangency, it is just worthwhile for the firm to remain open and hire the amount of labor supplied at the wage W[o].) Let us now consider one similarity related to this last point. Just as the ppm described in Figure 1 a below can do better than simply cover its TVC by engaging in second-degree price discrimination, the rpm described in Figure 1b below can do better than simply cover its TVC by engaging in second-degree price wage discrimination. See website http://rapidintellect.com/AEQweb/win2004.htm

Second-degree price discrimination entails a price-maker using more than one price, in selling its product (ppm) or hiring labor (rpm). Typically, a firm would associate different blocks of units (of product or labor) with different prices, consistent with product demand and labor supply schedules, respectively. For example, a product seller might charge one price for each of the first ten units it sells and a lower price for each of the next ten units sold, assuming a total of twenty units are sold. Similarly, an employer might offer a representative employee a certain wage for each unit of labor up to "half-time", with a higher wage for each unit up to "full-time". The simplest illustration of second-degree price discrimination involves the use of two prices only. These scenarios are now illustrated graphically; Figure 2a below modifies Figure 1a by introducing the price P'. See http://rapidintellect.com/AEQweb/win2004.htm

If Q' units are sold at the price P', and (Q'Q[o]) are sold at the price P[o] (a two-price scheme consistent with second-degree price discrimination), total revenue equals P'Q' plus {P[o](Q'Q[o])}, which is greater than TVC, equal to p[o]Q[o], so that the firm has a clear incentive to remain open, vice being indifferent (in terms of its negative total profit) to remaining open or shutting down. Figure 2b below modifies Figure 1b by introducing the wage W'. If L' units of labor are offered at the wage W' and (L'L[o]) units are offered at the wage W[o] (a two-wage scheme consistent with second-degree wage discrimination), TVC equals W'L' plus W[o](L'L[o]), less than total revenue, which is equal to W[o]L[o]. Thus, as in Figure 1b, the firm has a clear incentive to remain open, vice being indifferent, per above.

Conclusion

Because of the advantages of making students aware of the connections and symmetries between results established in different parts of a course, this paper has identified the important links regarding analysis of firm behavior in product and resource markets which are suitable for presentation in an introductory microeconomics course. By making a conscious effort to tie these results together, students will be able to achieve a greater understanding of them.

Endnotes

[1] See [Ausubel, 1963], Ch. 8, for a rigorous discussion, from a cognitive science perspective, of how "practice", or repetition, can promote learning.

[2] See [Colander, 2001], [Baumol and Blinder ,2003], and [Frank and Bernanke, 2004].

[3] [Robinson, 1965] points out this symmetry in her classic study.

[4] See [Baye, 2003].

[5] See [Cain, 1986] and [Sharir, 1995] for more rigorous investigations of this point in terms of gender differences; [Ransom, 1993] examines the issue in terms of seniority in the context of the academic labor market.

References

Ausubel, D.P. 1963. The Psychology of Meaningful Verbal Learning. London: Grune & Stratton.

Baumol, W.J. and Blinder, A.S. 2003. Microeconomics: Principles and Policy. 8th ed. Orlando, Fl: Dryden Press

Cain, G.G. 1986. The economic analysis of labor market discrimination: a survey. In Handbook of labor economics, Volume 1, ed. O. Ashenfelter and R. Layard. Amsterdam: North-Holland.

Colander, D. 2001. Microeconomics. 4th ed. NYC, NY: Irwin/McGraw-Hill.

Frank,R. and Bernanke, B. 2004. Principles of Microeconomics. McGraw- Hill/Irwin.

Ransom, M.R. 1993. Seniority and monopsony in the academic labor market. American Economic Review 83 (March): 221-33.

Robinson, J. 1965. Economics of imperfect competition. London: Macmillan.

Sharir, S. 1995. Is discriminatory monopsony by sex a viable model? Journal of Economics 21 (Fall): 87-94.

David W. Weber, U.S. Coast Guard Academy

Weber, Ph.D., is Professor in the Department of Leadership & Management.
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Author:Weber, David W.
Publication:Academic Exchange Quarterly
Geographic Code:1USA
Date:Dec 22, 2004
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