Industrial Organization and the Labor Market

Abstract

This chapter makes a deeper investigation into the interactions between the industry and labor with various facets of the market structures and industrial labor. We consider the well-known duopolistic models, the wage bargaining frameworks, the wage competition, short-run and long-run general equilibrium effects of reforms, and the possibility of labor as a Giffen input. We show in terms of a Cournot quantity competition model that if the firms differ in their production function, possibility of Giffen input cannot be negated. It may so happen that the total demand of the industry for the input may exhibit a perverse positive relation with input price, although this possibility is absent in the standard case of linear demand and Cobb–Douglas production functions. In addition, the economic slowdown of the 1970s prompted deregulation in product and labor market, and it was hoped that it would reduce unemployment and increase the rate of economic growth. Liberalization had reduced the bargaining power of the trade union as well as the entry barriers in the product market. We capture many such effects in this chapter and provide support with worked-out examples.

Appendix I

Cost minimization and comparative statics

$$ z=wL+rK+\mu (Q-f(k.L)) $$

The first-order conditions are

$$ \frac{\partial z}{\partial L}=w-\mu {{f}_{L}}=0 $$

$$ \frac{\partial z}{\partial K}=r-\mu {{f}_{K}}=0 $$

$$ \frac{\partial z}{\partial \mu }=(Q-f(k.L))=0. $$

The comparative static effects are calculated from

$$\left[ {\begin{array}{*{20}{c}}{ - \mu {f_{LL}}}&{ - \mu {f_{LK}}}&{ - {f_L}}\\{ - \mu {f_{LK}}}&{ - \mu {f_{KK}}}&{ - {f_K}}\\{ - {f_L}}&{ - {f_K}}&0\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{{\rm{d}}L}\\{{\rm{d}}K}\\{{\rm{d}}\mu }\end{array}} \right] = \begin{array}{*{20}{c}}{ - {\rm{d}}w}\\{ - {\rm{d}}r}\\{ - {\rm{d}}Q}\end{array}$$

Input substitution effect

${{\left| \frac{\text{d}L}{\text{d}w} \right|}_{SE}}=$, determinant: $\frac{f_{K}^{2}}{D}<0$

$$ {{\left(\frac{\text{d}L}{\text{d}Q} \right)}_{\text{Outputeffect}}}=\frac{-\mu {{f}_{LK}}{{f}_{K}}+{{f}_{L}}\mu {{f}_{KK}}}{D}=\frac{\text{d}\mu }{\text{d}w}. $$

Sign is indeterminate. On the other hand, the input demand function is

$$ L=L(w,r,Q(w,r)) $$

$$ \frac{\text{d}L}{\text{d}w}=\frac{\partial L}{\partial w}+\frac{\partial L}{\partial Q}\frac{\partial Q}{\partial w}=\frac{\partial L}{\partial w}+\frac{\partial L}{\partial Q}\frac{\partial Q}{\partial \mu }\frac{\partial \mu }{\partial w} $$

Input demand function in the context of Cournot model

$$ L=L(w,r,{{q}_{1}}(w,r,{{q}_{2}}(w,r)) $$

$$ \frac{\text{d}L}{\text{d}w}=\frac{\partial L}{\partial w}+\frac{\partial L}{\partial {{q}_{1}}}\frac{\partial {{q}_{1}}}{\partial \mu }\frac{\partial \mu }{\partial w}+\frac{\partial L}{\partial {{q}_{1}}}\frac{\partial {{q}_{1}}}{\partial {{q}_{2}}}\frac{\partial {{q}_{2}}}{\partial w} $$