On the Welfare Effects of a Wage Floor - Application to Minimum

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On the Welfare Effects of a Wage Floor - Application to Minimum

    USBIG Discussion Paper No. 77, February 2004

    Work in progress, do not cite or quote without author’s permission

    On the Welfare Effects of a Wage Floor

     in a Two-Sector Labor Market with Impoverished Workers

    *Dr. David L. Wetzell


    That a wage floor, such as the minimum wage, lowers employment has been extensively empirically confirmed. However, among poorer workers the relatively inelastic nature of labor demand may permit an increase in the minimum wage to have a positive wage spill-over into the uncovered sector if covered sector employees' need to "moon-light" in the uncovered sector is reduced. The model indicates that wage floors may be a more appropriate instrument for reducing poverty when workers are impoverished and also affirms the need to empirically test for their impact on the income and hours worked by directly and indirectly affected workers.

     * Dr. David Wetzell is at Universidad de Las Americas-Puebla. He can be contacted through email address at and his address is Universidad de las Americas, Puebla; Departamento de Economia; Ex-hacienda de Santa Catarina Mertir; Cholula, Puebla, 72820.


    The following is an “ideal-type” situation where a wage floor, such as a minimum

    wage or a living wage, may be justified despite how it causes a reduction in the level of

    1employment in the covered sector. As with Mincer(1976), the model considers that

    displaced workers will be able to find work in the uncovered sector. Unlike Mincer (1976), the model abstracts from unemployment or search for covered-sector jobs and, instead, allows employed workers to supplement their income by “moon-lighting” in the

    2uncovered or informal sector. Also, unlike Mincer (1976), the model derives labor-

    supply directly from utility-maximizing labor supply decision. For simplicity, it is assumed that the hours of workers employed in the covered sector are determined exogenously by work-week restrictions. As such, the relevant choice is the time supplied to the uncovered sector. It is also assumed that workers are poor and that, as shown in

    3Wetzell(2001), “leisure” requires money or purchasable inputs.

    Here, the difference between consumption and leisure is that leisure consists of more time-intensive activities and consumption consists of more money-intensive activities. This is like the difference between reading a book and going to the movies. This alters the model by adding a pecuniary cost of leisure, p, to the budget constraint so L

     1 It is taken as given that an increase in the wage floor will induce a modest decline in the number of jobs as shown by an extensive empirical literature. 2 If worker is interpreted as a household then this could be interpreted as how other members of the household besides the head working for money in the uncovered sector. 3 For simplicity, for workers to be “poor” is taken to mean that they have no other source of income besides

    working. This assumption could be relaxed some without changing the results.

    If utility is defined over consumption and leisure then consumption can also have a time-cost. However, inasmuch as the time-cost of consumption complicates the analysis and tends to matter more for higher wage levels, the time-cost of consumption is omitted from the model. It is important to emphasize that from a time-allocation perspective, leisure is time-intensive consumption and consumption is money-intensive consumption.

    4now money is needed for any form of utility-producing activities. This implies workers

    need some source of money and if they lack non-earned income, they may need to work somehow regardless of their received wage offer. Or, they may not be able to afford a

    5positive reservation wage with respect to all forms of work. The absence of a positive

    reservation wage can make labor supply curves negatively-sloped. That is when they are offered a lower wage, the worker will likely respond by trying to work more hours. Generally, the introduction of a money/pecuniary cost of leisure into a labor-supply model tends to lower the observed elasticity of labor supply by increasing the need for money and correspondingly the hours worked. This alteration to the labor-supply model can help to explain the observed inelastic labor supply of welfare-recipients in many

    6studies, as is summarized in Moffit(2003). The vulnerability of workers in such a

    situation sets out labor-market regulations as ideally attempts to reduce the level of cut-throat competition between workers who may have very little bargaining power on their own accounts. However, regulations are usually imperfect and never cover all forms of work and, in reducing competition between workers they tend to favor some workers at the expense of others, potentially increasing inequality. If these short-comings are taken into account then do regulations still reduce poverty? This paper sets out an ideal-type

     4 The pecuniary or money cost of leisure is assumed a constant with the cost of consumption normalized for simplicity. Likewise, the time cost of leisure is normalized to keep the model simple; a virtue that will come into play through-out the model-building-process. 5 Work is here defined as activities engaged in primarily for pecuniary gain. 6 Moffit(2003) writes that substitution and income elasticities from the pre-1995 literature fell into the general range of those elasticities obtained from the literature on substitution and income effects estimated from wage and nonincome variation. However, as shown by Heckman (1993), the latter literature was flawed due to the negative bias caused by pervasive non-classical measurement error in reported hours of work. One would generally expect the non-adjusted labor supply elasticities to be more positive on average. A working paper of the author shows that when one removes observations likely to be measured with error with a quantile-based trim of a log-wage regression that the empirical labor-supply elasticities are uniformly higher. As such, the near zero and often negative labor-supply elasticities from policy-variation for poorer people probably genuinely reflect that this group tends to have less elastic labor supply than the majority of workers.

    situation where a wage floor and work-hour restrictions combine to improve the welfare of most workers in both covered and uncovered sectors.

    The model is a simple one with two sectors, one covered by a wage-floor and work-hours restriction. To simplify the model, the number of workers, or households, is

    7normalized to one with a time endowment of one. A worker can only work half of their

    time-endowment in the covered sector and is assumed to be working half of their time-endowment in the covered-sector by the model. Additionally, it is also assumed that the wage floor in the covered-sector is so low that covered workers work additional hours in the uncovered sector.

    The model then proceeds as follows: there are no skill-differences between workers, but a fraction of workers work half their endowment in the covered sector and, taking their covered sector income as exogenous, then choose how many hours to supply to the uncovered sector. Similarly, the other workers choose how many hours they will supply to the covered sector. The fraction of workers in each group is exogenously determined by labor demand in the covered sector and the wage floor value, or minimum wage. Labor demand in the covered sector has a negative elasticity proportional to the minimum wage level, or

    cwme8L(1) . The uncovered sector wage is inversely proportional to the total d2

    hours worked in the uncovered sector, or

     7 It is trivial to show that assuming these values do not affect the comparative-statics of the model. 8 This assumption guarantees that Labor Demand will never exceed the amount of labor legally available, given the work-week restriction.

    (2)wH, where is the total hours worked in the uncovered sector, and u,tuHu,t

    (3)H2LH;(12L)HL, where is the formal sector’s labor demand u,tdu,cdu,ud

    HHand and are the hours worked in the uncovered sector by covered sector and u,cu,u

    9non-covered sector workers, respectively.

    Hence, it follows that

    w(4) . ucwcwmm He+ H(1- e )u,cu,u

    1CLFor simplicity, Workers’ have uniform Cobb-Douglass preferences, U(C, L) = ee

    and take as exogenous the uncovered-sector wage, w. The only difference between the u

    two groups is the constraint they face for their uncovered-sector labor-supply decision.

    1CLCovered-sector workers maximize subject to H+ Le=1/2 and pLe+C=w u,cl ue

    1CLH+w/2. Uncovered-sector workers, on the other hand, must maximize subject u,cme

    to H+ Le=1 and pLe+C = w H. u,ul uu,u

    The above two maximization problem give us:

    p;(1)wwp;w(w;w)(w;w)1LumLuumum(5) H== for u,c2(p;w)2(p;w)22(p;w)LuLuLu

    wwworkers employed in the covered sector, so long as H>0 and , u,cuc

    p;(1)wwpLuuL11;(6) H= and u,u(p;w)(p;w)(p;w)LuLuLu