The present note examines the effect of minimum wage noncompliance on the sub-minimum wage rate in a competitive labor market. The note shows that noncompliance shifts leftward the demand curve of labor and shifts rightward the supply curve of labor, unambiguously leading to a fall in the equilibrium sub-minimum wage rate. Two implications follow: first, contrary to a major result in the minimum wage literature, noncompliance must not necessarily reduce employment (as compared to the pre-law level) it may even increase employment if the deterrent effect of the expected penalty is more than offset by the inducement effect of a lower wage rate. Secondly, and more importantly, if the minimum wage law aims at improving low wages, workers are better off without a law than with one which is not accompanied with sufficient inducement to ensure compliance.

Joachim RosenmÃ¼ller

English

Research Papers in Economics

Minimum wage noncompliance and the sub−minimum wage
rate 
Gideon Yaniv
College of Management National Insurance Institute, Israel
Abstract
The present note examines the effect of minimum wage noncompliance on the sub−minimum
wage rate in a competitive labor market. The note shows that noncompliance shifts leftward
the demand curve of labor and shifts rightward the supply curve of labor, unambiguously
leading to a fall in the equilibrium sub−minimum wage rate. Two implications follow: first,
contrary to a major result in the minimum wage literature, noncompliance must not
necessarily reduce employment (as compared to the pre−law level); it may even increase
employment if the deterrent effect of the expected penalty is more than offset by the
inducement effect of a lower wage rate. Secondly, and more importantly, if the minimum
wage law aims at improving low wages, workers are better off without a law than with one
which is not accompanied with sufficient inducement to ensure compliance.
Citation: Yaniv, Gideon, (2004) "Minimum wage noncompliance and the sub−minimum wage rate." Economics Bulletin, Vol.
10, No. 9 pp. 1−7
Submitted: July 28, 2004.  Accepted: September 10, 2004.
URL: http://www.economicsbulletin.com/2004/volume10/EB−04J30002A.pdf1. INTRODUCTION 
 
The economic literature on minimum wage noncompliance focuses mainly on the 
conditions under which a competitive employer would opt not to comply with the 
minimum wage law (henceforth, MWL) and on the effects that noncompliance may 
have on his optimal employment level [e.g., Ashenfelter and Smith (1979), Grenier 
(1982), Chang and Ehrlich (1985), Chang (1992), Yaniv (1994, 2001)]. A major result 
of this literature is that the optimal employment level when not complying with the 
MWL is not the same as the optimal level in the absence of a MWL. The reason for 
this is that noncompliance entails the risk of getting caught and punished. 
Consequently, as first pointed out by Chang and Ehrlich, noncompliance increases the 
marginal cost of labor for the employer, therefore inducing him to reduce employment 
below the level he would choose in the absence of a MWL. An implicit assumption 
underlying this result is that the sub-minimum wage paid by the non-complying 
employer is identical to the free market wage prevailing in the absence of a MWL. In 
other words, an implicit assumption is that noncompliance has no effect on the 
competitive sub-minimum wage rate.  
 
In a recent note, Yaniv (2004) has translated Chang and Ehrlich's result into graphical 
terms, showing that noncompliance shifts leftwards the labor demand curve. The 
present note further investigates the effect of noncompliance in the labor market, 
demonstrating that noncompliance also shifts the supply curve rightwards, therefore 
unambiguously leading to a fall in the competitive sub-minimum wage rate. This 
surprising result implies first that noncompliance must not necessarily result in 
reduced employment (as compared to the pre-MWL level), and more importantly, that 
if the MWL is not accompanied with sufficient inducement to ensure compliance, 
low-wage workers are better off without a MWL. Section 2 begins with reviewing the 
effect of noncompliance on the demand curve of labor; section 3 examines the effect 
of noncompliance on the supply curve of labor; section 4 considers the labor market 
equilibrium, and section 5 concludes. 
    
 
2. THE LABOR DEMAND CURVE 
 
    Following Yaniv (2004), consider a profit-maximizing employer who produces a 
single product with labor input, L, only. Suppose that the employer operates in a 
perfectly competitive labor market where he hires labor input at a given wage rate, w, 
per hour. His profits, π, are given by V(L) − wL, where V(L) denotes the market value 
of output and, by assumption, V′(L) >0 and V″ (L)< 0. The first-order condition for 
profit maximization is V ′(L0)  − w  = 0, hence the number of hours hired by the 
employer is determined at the point where the value of the marginal product of labor 
equals the competitive wage rate. Totally differentiating the first-order condition with 
respect to L and w yields dL/dw = 1/V ″(L) < 0, implying that the employer’s demand 
curve for labor is negatively sloped: a rise in the market wage rate will decrease the 
number of labor hours demanded by the employer.  
 
  Suppose now that a MWL is enacted, requiring the employer to pay a minimum wage, 
m ( > w), per each hour of labor employed. However, the employer may choose not to 
comply with the MWL, therefore paying each hour of labor the free market wage. 
Noncompliance exposes the employer to the risk of being detected and punished. Suppose that the probability of being detected violating the MWL is independent of 
the employer’s activity level, given exogenously at the rate of p (<1). Suppose further 
that in case of detection the employer will be obliged to pay back, for each hour of 
labor he has employed, a multiple λ(>1) of the wage underpayment, m − w . The 
expected profits of the employer, if not complying with the MWL, will be 
 
                             Ep V L w L p V L w L m w L π λ =− − + − − − ( ) [() ] [() ( )] 1 .            (1) 
 
  The first-order condition for the maximization of expected profits is  
 
                                      
dE
dL
VL wpmw
()
'( ) [ ( )]
π
λ =− + − 0 = ,                          (2) 
 
implying that employment will be determined at the point where the value of the   
marginal product of labor equals the expected wage rate, w + pλ(m− w ). As first 
pointed out by Chang and Ehrlich (1985), a MWL will reduce employment not just in 
case of compliance but in case of noncompliance as well: by increasing the marginal 
cost of labor, the expected penalty, pλ(m− w), acts as a deterrent to labor employment. 
 
Because profits vary inversely with the wage rate, the profit-maximizing employer 
would choose not to comply with the MWL if the expected wage when not 
complying, w + pλ(m− w), is lower than the statutory minimum, m. It immediately 
follows that the employer would not comply if pλ < 1 and comply otherwise. That is, 
the employer would comply with the MWL only if the level of enforcement 
(represented by pλ) is sufficiently high. Totally differentiating the first-order 
condition (2) with respect to L and w reveals now that for any w < m  
 
                                                          
dL
dw
p
VL
=
− 1 λ
"( )
 ,                                                (3) 
 
which is negative as long as the employer is not complying with the MWL. This 
means that a fall in the market wage rate below the statutory minimum will still 
increase the quantity of labor demanded by the employer, yet by a lesser amount than 
it would in the absence of a MWL. Hence, the labor demand curve, in its part below 
the statutory minimum, becomes dependent on the level of enforcement and steeper 
than the labor demand curve in the absence of a MWL. Noncompliance will therefore 
shift the labor demand curve clockwise below the statutory minimum. The greater the 
level of enforcement, the steeper will be the labor demand curve, hence the stronger 
its clockwise shift. When pλ is raised to unity, the labor demand curve will become 
vertical below the statutory minimum (its slope with respect to the vertical axis will 
fall to zero). The employer, who will now be complying with the MWL, will employ 
the quantity of labor demanded at the statutory minimum regardless of the market 
wage rate. 
 
 
3. THE LABOR SUPPLY CURVE 
 
Consider now a utility-maximizing individual who offers her labor services, L, in a 
perfectly competitive market where she faces a given wage rate, w, per hour of labor. Suppose that her utility function is given by U  =  – φ (L) + wL, where φ (L) denotes 
the disutility of labor (reflecting forgone utility of leisure) and, by assumption, φ ′(L) 
> 0 and φ ″(L) > 0. The first-order condition for utility maximization is  − φ ′(L) +  w 
= 0, hence the number of labor hours offered by the individual is determined at the 
point where the marginal disutility of labor equals the competitive wage rate. Totally 
differentiating the first-order condition with respect to L and w yields dL/dw =1/φ ″(L) 
> 0, revealing that the individual's supply curve of labor is positively sloped: a rise in 
the market wage rate will increase the number of labor hours supplied by the 
individual.         
 
Suppose now that a MWL is enacted, requiring employers to pay a minimum wage, m 
( > w) per each hour of labor employed. Suppose, however, that pλ < 1. 
Consequently, employers opt not to comply with the law, therefore paying each hour 
of labor the free market wage. Still, with probability p, the individual's employer will 
be detected and obliged to pay her back, for each hour of labor employed, a multiple λ 
(>1) of the wage underpayment, m – w. The individual's expected utility is thus given 
by 
 
                  ] ) ( ) ( [ ] ) ( )[ 1 ( L w m wL L p wL L p EU − + + − + + − − = λ φ φ .          (4) 
     
The first-order condition for the maximization of expected utility is 
 
                                       , 0 )] ( [ ) ( '
) (
= − + + − = w m p w L
dL
EU d
λ φ                     (5) 
 
implying that the individual will supply labor up to the point where its marginal 
disutility equals her expected wage rate, w + pλ(m – w). Totally differentiating the 
first-order condition (5) with respect to L and w reveals now that for any w < m 
            
                                                           
) ( "
1
L
p
dw
dL
φ
λ −
=  ,                                                 (6) 
 
which is positive as long as the employer is not complying with the MWL. This 
means that a fall in the market wage rate below the statutory minimum will still 
decrease the quantity of labor supplied by the individual, yet by a lesser amount than 
it would in the absence of a MWL. Hence, the labor supply curve, in its part below the 
statutory minimum, becomes dependent on the level of enforcement and steeper than 
the labor supply curve in the absence of a MWL. Noncompliance will therefore shift 
the labor supply curve counter-clockwise below the statutory minimum. The greater 
the level of enforcement, the steeper will be the labor supply curve, hence the greater 
its counter-clockwise shift. When pλ is raised to unity, the labor supply curve will 
become vertical below the statutory minimum.           
 
Noncompliance will also push down the individual's reservation wage. To see this 
notice that a prerequisite for the individual to supply a positive number of hours in the 
labor market is that  d(EU)/dL > 0 at L = 0. In the absence of a MWL, this requires 
that the market wage rate, w, exceed φ ′(0). However, when employers do not comply 
with the MWL, it is sufficient for w to exceed [φ ′(0) – pλm] / [1– pλ], which is less 
than φ ′(0), as φ ′(0) < w < m. Because the individual expects a raise in case of detection, she will be willing to join the labor market at a lower wage rate. The greater 
the level of enforcement, the lower will be the reservation wage. When pλ = φ ′(0)/ m, 
the individual will be willing to work for no pay at all (i.e., accept a zero wage) and as 
enforcement increases further, she will even be willing to pay (i.e., accept a negative 
wage) for the opportunity to work. When pλ is raised to unity, the reservation wage 
will drop to minus infinity, hence the labor supply curve will become vertical below 
the statutory minimum.           
 
 
4. LABOR MARKET EQUILIBRIUM 
 
Figure 1 now depicts the equilibrium wage rate in the labor market before and after the 
introduction of a MWL. In the absence of a MWL, the aggregate demand curve, D0, 
and the aggregate supply curve, S0, intersect each other at the wage rate of w0 per hour 
(point a). The introduction of a MWL, which requires employers to pay workers at 
least m (> w 0) per hour, shifts the labor demand and supply curves clockwise and 
counter-clockwise, respectively, below the statutory minimum. Given that 
enforcement is insufficient to induce compliance (pλ < 1), the labor demand curve 
would maintain its negative slope whereas the labor supply curve would maintain its 
positive slope, shifting to   and , respectively. Consequently, and contrary to an 
implicit assumption in the noncompliance literature, the equilibrium sub-minimum 
wage rate would not remain at its pre-MWL level, but would rather drop to (point b). 
The greater the level of enforcement, the stronger would be the shift of each curve, 
thus the greater the fall in the sub-minimum wage rate.  
$ D $ S
$ w
 
When pλ is raised to unity, which is the level of enforcement sufficient to induce 
compliance, the labor demand and supply curves would become vertical below the 
statutory minimum at the level of employment demanded and supplied at the statutory 
minimum, respectively (curvesD and  S ). Consequently, an equilibrium at a sub- 
minimum wage rate would no longer be possible. Employers would now be complying 
with the MWL, demanding less than the amount of labor supplied at the statutory 
minimum. The market would stabilize at the statutory (non-equilibrium) wage rate, m, 
implying that S −D  hours of labor remain unemployed.   
 
 
5. CONCLUSIONS 
     
Examining the effect of minimum wage noncompliance on the sub-minimum wage 
rate, the present note has shown that noncompliance shifts leftward the labor demand 
curve of the non-complying employer and shifts rightward the labor supply curve of 
the underpaid worker. As long as enforcement is insufficient to induce compliance, 
these shifts will lead to a fall in the equilibrium sub-minimum wage rate. Two 
important implications follow: first, if the MWL aims at improving wages, workers 
are better off without a MWL than with one which is not accompanied with sufficient 
inducement to ensure compliance. Secondly, contrary to a major result in the 
minimum wage literature, which implicitly assumes that the free-market wage rate is 
not affected by the introduction of a MWL, noncompliance must not necessarily 
reduce employment; it may even increase employment if the deterrent effect of the 
 expected penalty is more than offset by the inducement effect of a lower free-market 
wage rate. 
 
 
 
 
 
R E F E R E N C E S 
 
Ashenfelter, O., and R.S. Smith. 1979. Compliance with the minimum wage law. 
Journal of Political Economy  87: 333-350. 
 
Chang, Y-M, and I. Ehrlich. 1985. On the economics of compliance with the 
minimum wage law. Journal of Political Economy 93: 84-91. 
 
Chang, Y-M. 1992. Noncompliance behavior of risk-averse firms under the minimum 
wage law, Public Finance Quarterly 20: 390-401. 
 
Grenier, G. 1982. On compliance with the minimum wage law. Journal of Political 
Economy 90: 184-187. 
 
Yaniv, G. 1994. Complaining about noncompliance with the minimum wage law, 
International Review of Law and Economics 14: 351-62. 
 
Yaniv, G. 2001. Minimum wage noncompliance and the employment decision. 
Journal of Labor Economics 19: 596-603. 
 
Yaniv, G. 2004. Minimum wage compliance and the labor demand curve. Journal of 
Economic Education 35: 290-294.  
 
 

Minimum wage noncompliance and the sub-minimum wage rate

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Minimum wage noncompliance and the sub-minimum wage rate

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