A minimum‐wage model of unemployment and growth: The case of a backward‐bending demand curve for labor

• DOI: http://doi.org/10.1111/ijet.12168
• Author: Till Gross,Richard A. Brecher
• Published date: 01 September 2019
• Date: 01 September 2019

A minimum-wage model of unemployment and growth:

The case of a backward-bending demand curve for labor

Richard A. Brecher



and Till Gross



We add a minimum wage and hence involuntary unemployment to a conventional two-sector

model of a perfectly competitive economy with optimal saving and endogenous growth. Our

resulting model highlights the possible case of a backward-bending demand curve for labor,

along which a hike in the minimum wage might increase total employment. This theoretical

possibility complements some controversial empirical studies, in challenging the standard

textbook prediction of an inverse relationship between employment and the minimum wage.

Our model also implies that a minimum-wage hike has negative implications for both the growth

rate and lifetime utility.

Key words optimal growth, minimum wage, learning by doing, involuntary unemployment

JEL classification E24, O41

Accepted 15 May 2017

1 Introduction

This paperintroduces a minimum wageand hence involuntary unemploymentinto the Ramsey–Cass–

Koopmans (Ramsey 1928;Cass 1965; Koopmans 1965) two-factor model of optimal growth over an

infinite horizon, as extendedby Srinivasan (1964) and Uzawa (1964) to the two-goodcase.

1

To avoid

an inherent problem of overdetermination, our minimum-wage model incorporates an endogenous

rate of growth,

2

fueled by technological improvements due to learning by doing. Within this

framework, weinvestigate how a hike in the minimum wage affectsemployment, growth, and welfare.

Contrary to conventional academic wisdom, our analysis shows that a minimum-wage hike can

(under specified conditions) increase total employment, because of what may be called a backward-

bending demand curve for labor. Notably, this outcome is possible even though we consider a

perfectly competitive economy, in which firms are wage takers (not setters).

3

This theoretical result



Department of Economics, Carleton University, Ottawa, Ontario, Canada. Email: richard.brecher@carleton.ca

We gratefully acknowledge helpful comments and suggestions from Lawrence F. Katz and an anonymous Associate Editor.

1

For an alternative approach to modeling growth with unemployment, see Cahuc and Michel (1996), who add a minimum

wage to an overlapping-generations model with only one good (produced in two technologically different sectors) and

three factors of production.

2

As discussed below, the minimum wage fixes (via the conditions for profit maximization) the interest rate, which then

determines the balanced-growth rate (needed to satisfy the household’s Euler equation). For an alternative solution to the

overdetermination problem in the absence of long-run growth, see Brecher et al. (2013).

3

It is well known that with wage-setting firms, minimum wages may increase employment, as first established by Stigler

(1946) in the case of a monopsonist. Alternatively, if firms set wages optimally for efficiency-wage reasons, Manning

(1995) shows that a minimum-wage hike may lead to a rise in employment. Flinn (2006) obtains this same result when the

wage is determined instead by bargaining in the presence of search and matching frictions.

doi: 10.1111/ijet.12168

International Journal of Economic Theory xxx (2018) 1–13 ©IAET 1

International Journal of Economic Theory

International Journal of Economic Theory 15 (2019) 297–309 © IAET 297