Effects of wage discrimination on employment and firm's location.

• Author: Shieh, Yeung-Nan

1. Introduction

   In his famous book, The Economics of Welfare [6], Pigou showed graphically that the third degree price discrimination does not change total output of a monopoly if the demand curves in two separate markets are linear. Later, Robinson [7] confirmed Pigou's proposition mathematically. Recently, Ekelund, Higgins and Smithson [2], Mai and Shih [4] extended Pigou-Robinson's analysis to the hiring of labor by a monopsony. They showed that the wage discrimination doesn't change total employment of a monopsony if the supply curves of labor in two separate markets are linear, and that Pigou-Robinson's proposition applies to the input markets. However, their analysis is based on the traditional non-spatial setting in which transportation cost and location decision are insignificant and negligible. It would be interesting and important to investigate the effect of wage discrimination on employment in a spatial world.

   The purpose of this paper is to investigate the effects of wage discrimination on total employment and plant location of a monopsony in the Weber-Moses triangle. It will be shown that in the spatial economy the Pigou-Robinson proposition holds if the plant location is predetermined. However, if the plant location is a choice variable, the wage discrimination may change total employment even if the supply curves are linear. This indicates that location decision and transportation cost play an important role in the determination of wage discrimination on total employment.

2. The Basic Model

   Our analysis is based on the well-known Weber-Moses triangular model with the following assumptions:

   (a) A monopsonist employs a single input (labor) located at two separate markets, A and B, to produce a single output which is sold in a monopolistic market C. The Weber-Moses triangle in Figure 1 depicts the location problem of the firm, [9; 5]. In Figure 1, the distances a and b and the angle [Pi]/2 [greater than] [Alpha] [greater than] 0 are known, and [Theta] [less than] [Alpha]. The distance between the plant and the output market, h, is held constant, thus all points along the arc IJ are the only ones which are considered as possible plant locations for the monopsony.(1) The plant location is determined if the value of [Theta] is chosen.

   (b) The production function is specified as:

   q = f(L) = f([L.sub.1] + [L.sub.2]), [f.sub.L] [greater than] 0, [f.sub.LL] [less than] 0 (1)

   where [L.sub.1] is located at A and [L.sub.2] is located at B.

   (c) The workers charge f.o.b. prices for labor and the producer charges c.i.f. price for output. The firm has monopsony power and faces two upward sloping supply curves at sources A and B, i.e.,

   [w.sub.1] = [a.sub.1] + [b.sub.1][L.sub.1], [w.sub.2] = [a.sub.2] + [b.sub.2][L.sub.2] (2)

   where [a.sub.1], [a.sub.2], [b.sub.1] and [b.sub.2] are constant.

   (d) The cost of hiring a worker at the plant is the wage rate at source plus the cost of transporting one unit of labor to the plant, i.e.,

   [c.sub.1] = [w.sub.1] + [ts.sub.1], [c.sub.2] = [w.sub.2] + [ts.sub.2] (3)

   where t is the constant transportation rate of labor.(2) By the law of cosines the distance variables [s.sub.1] and [s.sub.2] can be defined as:

   [s.sub.1] = [([a.sup.2] + [h.sup.2] - 2ah cos [Theta]).sup.1/2] (4)

   [s.sub.2] = [[[b.sup.2] + [h.sup.2] - 2bh cos([Alpha] - [Theta])].sup.1/2]. (5)

   The price of output at the plant is the market price minus the cost of transporting one unit of output from the plant to the market,

   p - rh (6)

   where p = p(q) = p[f(L)], and r is the constant transportation rate of output.

   (e) The objective of the firm is to choose the profit-maximizing employment...