Person-Specific Labor Costs and the Employment Effects of. Minimum Wage Policy

Transcription

1 Person-Speciic Labor Costs and the Employment Eects o Minimum Wage Policy Gilbert L. Skillman Department o Economics Wesleyan University Middletown, CT gskillman@wesleyan.edu

2 Person-Speciic Labor Costs and the Employment Eects o Minimum Wage Policy Abstract Economic debates over minimum wage policy are typically premised on the assumption that raising a binding wage loor must reduce long-run employment i the aected markets are competitive and complete. It is shown here to the contrary that employment eects o raising the minimum are indeterminate i competitive employers incur person-speciic labor costs, which vary with the number o employees rather than with hours worked per employee, and there are diminishing returns in the contribution o individual hours to eective labor input. This conclusion is robust to extensions o the basic model incorporating various orms o input substitutability. In addition, the qualitative impact o varying non-labor inputs is shown to depend critically on how they interact with labor in the production unction. (JEL D21,J23, J32, J38) 1

3 The employment consequences o minimum wage legislation have been the subject o renewed attention in the labor economics literature, due both to recent policy initiatives and to controversial new evidence suggesting instances o zero or even positive employment eects rom increasing wage loors. David Card and Alan Krueger, who have contributed signiicantly to this literature, discuss the relevant issues and evidence in their recent and controversial work, Myth and Measurement (1995). Both Card and Krueger and their critics (see, or example, the Industrial and Labor Relations Review review symposium devoted to their book (Ehrenberg, 1995)) argue as though the sides o the debate are dictated by a strict analytical dichotomy with respect to the structure o labor markets, such that increasing an eective wage loor necessarily reduces longrun employment i the aected markets are competitive and complete. As Card and Krueger note, it is readily demonstrated that imposing or raising a binding wage loor may increase employment i irms enjoy monopsony power, or i labor markets are characterized by asymmetric inormation with respect to work eort (Rebitzer and Taylor, 1995) or the quality o job applicants (Stiglitz, 1987). But what i none o these departures rom ideal market conditions obtain? Does it necessarily ollow that competitive irms reduce long-run employment when a wage loor is raised? This note answers that question in the negative given that the aected markets are characterized by quasi-ixed or person-speciic labor costs, 1 which vary with the number o employees rather than the number o hours worked. Person-speciic labor costs arise, or 1 Although the ormer term is used more requently in the literature (dating back at least to Oi (1962)), the latter is given preerence here as being more transparently descriptive o the phenomenon under study. 2

4 example, in providing employees with oices or other work spaces, certain ringe beneits, sanitary acilities and other workplace amenities, speciic training, and equipment. These costs are evidently pervasive, and they oten constitute a signiicant proportion o total labor costs (Hart, 1984). Faced with person-speciic costs, proit-seeking employers are not indierent to the mix o number o workers and hours per worker utilized in generating given magnitudes o eective labor input. Donaldson and Eaton (1984) study the implications o such costs or irms choice o hours, labor orce size, and employment contract provisions given diminishing marginal returns o individual labor hours to eective labor inputs. However, they do not consider the implications o minimum wage policy in the presence o person-speciic labor costs. Based on a simpliied version o their model, it is demonstrated here that increasing a binding minimum wage will lead employers to substitute employees hired or hours worked by each employee, resulting in an increase in employment or any given quantity o desired labor input. In addition, the utility o any worker who remains employed must increase, although wage income per employee may decline. The net change in employment is determined by combining the positive substitution eect and the more amiliar negative scale eect o increasing unit labor costs, the sum o which cannot be signed a priori. Consequently, under the stated conditions, the conventional view that raising the minimum wage lowers employment (measured by the number o workers hired) cannot be considered a presumptive, let alone a necessary, outcome o competitive market behavior. 3

5 I. A Basic Model o Labor Demand with Person-Speciic Costs Imagine that a proit-maximizing irm supplies a competitive product market using a technology summarized by the twice continuously dierentiable production unction x = G( l), where x denotes quantity o output, l represents units o eective labor input, and G is strictly increasing and strictly concave in its argument. Let p denote output price. Eective labor input depends on the number o workers n and hours per worker h according to the multiplicatively separable unction l = A( h) n. Assume that A is thrice continously dierentiable, strictly increasing, and strictly concave in h, suggesting diminishing marginal returns to increasing an individual s work hours. 2 Note that although the production unction is strictly concave in l, it may not be concave in the constituent elements n and h. Consequently, standard concave programming analysis may not be validly applied to the irm s proit-maximization problem with respect to these choice variables. One method o dealing with this diiculty, utilized by Donaldson and Eaton and emulated below, is to break the problem into two parts, involving irst cost minimization with respect to hours and then proit maximization given the resulting minimized unit cost o labor. The irm aces two types o costs in engaging labor inputs. First and amiliarly, its labor costs vary with hours worked; in the standard model o competitive labor markets the marginal cost o hours worked is simply given by the market wage rate w. In addition, however, the irm incurs a person-speciic cost c per worker hired, regardless o the hours expended per worker. 2 This is slightly stronger than necessary; it is only required that the unction A(h) exhibit eventually diminishing returns. 4

6 For the sake o simplicity in deriving the main result, non-labor inputs in production, work eort, and unit person-speciic labor costs c are initially treated as constant. The consequences o taking each o these as choice variables are considered in section V. Since the irm is not indierent as to how eective labor inputs are provided when aced with person-speciic labor costs, it may be inappropriate to depict the competitive labor-buying irm as a wage-taker who allows its workers reely to determine their respective working hours. For each worker, the irm instead chooses a bundle o income and hours worked rom a rontier derived rom the worker s preerences and reservation utility level. Assuming or a moment that the minimum wage constraint is not binding on the irm s choices, and letting y represent compensation per employee, its labor supply constraint is (1) U ( y, t h) u, where U is a twice continously dierentiable, strictly quasiconcave utility unction in income and leisure, t is the endowment o hours and u the reservation level o utility or each prospective employee. Assume that U is strictly increasing in income and leisure. The labor supply constraint can be more conveniently written as (2) y Y( h), where the worker s income-hours rontier Y(h) (equivalent to the indierence curve in (h, y) space corresponding to utility level u ), given the oregoing assumptions, is twice continuously dierentiable, strictly increasing and strictly convex in h. Without loss o generality, suppose the reservation level o utility ensures that Y(h) > 0 or all h > 0. 5

7 Note, again ignoring the minimum wage constraint, that the irm s desire to maximize proits ensures that the labor supply constraint (2) will hold with equality. The irm s total labor costs are thereore given by the expression ( ) c + Y( h) n, and the irm s optimizing choice o labor hours corresponds to a point such as that illustrated at point A in Figure 1, involving a tangency between the income-hours rontier and the irm s highest attainable isoproit curve π*. Donaldson and Eaton study this problem in detail. [Figure 1 about here] One implication o their analysis is that the irm enjoys some leeway in its choice o a compensation scheme to implement the optimal outcome. The irm might or example pay workers by a straight hourly wage w* = Y( h*) h, corresponding to line 0B in Figure 1, but * with the consequence that each worker s desired marginal tradeo between hours and income diers rom that o the irm, so that the latter might be compelled to speciy hours inputs by contract. Alternatively, the irm might oer a two-part compensation scheme such as 0CD in Figure 1, which aligns irm and worker incentives at the margin. But now suppose there exists a minimum wage policy which requires that eective hourly compensation not all below some legislatively determined loor. This introduces an additional constraint o the orm (3) y h w, where w is the stipulated wage loor. I the wage loor is eective, thenw > w*, and the new constraint, illustrated by line 0F in Figure 1, is binding, with a constrained optimum or the irm such as at point E. The original labor supply constraint will typically not be relevant, but even i 6

8 it were, the irm s total labor costs now take the orm C( h, n; c, w ) = ( c + w h) n. 3 Note that each employed worker receives economic rent under the minimum wage except or the boundary case in which both constraints bind simultaneously. The irm s optimization problem given the minimum wage constraint is explored in the next two sections. II. The irm s labor cost minimization problem Consider irst the irm s problem o minimizing the cost o a given quantity o eective labor input ~ l. The irm seeks to minimize C( h, n; c, w ) subject to ~ (4) A( h) n = l. This is equivalent to choosing h to minimize unit labor cost, equal to c w h (5) B( h; c, w ) = +, A( h) and then choosing n to satisy (4). Assume that a strictly interior solution to this programming problem obtains. The constrained optimum h must satisy the corresponding irst-order condition (6) B ( h ) = A( h ) w ( c + w h ) = ( 0. ) 2 [ A h ] The unction B(h) is strictly pseudo-convex, which is to say that given B ( h ) = 0, B is strictly convex in a neighborhood o h, so that 3 A semicolon is used in deining objective unctions to separate choice variables rom parameters. The latter may be suppressed in subsequent discussion i no ambiguity is thereby created. 7

9 (7) = c + w B h h A ( ( ) ) > ( 0 ) 2 [ A h ] by virtue o the strict concavity o A. As a consequence, ulillment o the irst-order condition (6) is suicient or h to be a local optimum, assuming an interior solution. On the basis o (6) and (7) the standard apparatus o comparative static analysis can be applied. Invoking the implicit unction theorem, we can write h = H( c, w ) such that (8) B ( H( c, w ); c, w ) 0 or some neighborhood o initial values o the parameters. Totally dierentiating this identity with respect to w and rearranging yields (9) h ( A( h ) h A ( h )) = w A( h ) B ( h ) [ ] 2, which is strictly negative by the irst- and second-order conditions (6) and (7). 4 From (4) and (9) it ollows that (10) n w > 0, where n is the cost-minimizing number o workers hired or a given level o desired labor input ~ l. Finally, a procedure similar to that ollowed above establishes that h c > 0, as might be expected intuitively. 4 Given an eective wage loor and person-speciic labor costs, the model yields an unambiguous test or the assumption o (eventually) diminishing marginal returns in the contribution o individual hours to eective labor input (i.e., that A < 0, at least at the optimum). It is readily shown that in the absence o diminishing returns, the reservation utility constraint (1) on individual labor supply is always binding i the wage loor is, with the implication that the irm increases rather than decreases hours per worker in response to the imposition or elevation o a binding minimum wage rate. 8

10 The economic logic o results (9) and (10) is illustrated in Figure 2. The eect o an increase in the minimum wage is to increase (in absolute value) the slope o labor isocost curves at any given (h,n) combination, which induces the irm to substitute employees or hours worked per employee. Consequently, the number o employees engaged to generate any given level o eective labor input unambiguously increases. [Figure 2 about here] Expressing (9) as an elasticity gives (11) η hw = c c + w h < α( h 0, ) where η hw = w h h w is the wage elasticity o the irm s cost-minimizing choice o labor hours per worker, evaluated at the wage loor, and α( h) = A ( h) h A ( h) is an elasticity expression indicating the degree o diminishing returns in the per-capita eective labor unction A(h). Similar calculations show that the elasticity o cost-minimizing hours with respect to changes in c, denoted η hc, is just equal to -η hw. Allowing h to vary optimally, the absolute value o the elasticity expressed in (11) is nondecreasing in c and non-increasing in w i α is non-decreasing in h and η hw < 1 and only i one or the other o the latter two conditions holds. For example, i A( h) = h β, β ( 01, ), thenα ( h ) = ( β 1) and η hw = -1 or all values o c and w such that the irm desires to produce. 9

11 Since the cost-minimizing quantity o labor hours h is independent o p and ~ l, the minimized level o unit labor cost can be written q = Q( c, w ). This is the eective unit cost which determines the irm s proit-maximizing choice o labor, considered next. III. Implications o the Firm s Proit-Maximizing Labor Choice Given the cost-minimizing level o unit labor cost q, the irm chooses the level o total labor input l to maximize proit, expressed as (12) Π( l; q, z) = pg( l) ql z, where z denotes ixed non-labor costs. Since G is strictly concave, the optimal choice l* is unique. Again assuming an interior solution, the necessary and suicient condition or an optimum is (13) Π l ( l*; q) = pg ( l*) q = 0. By the implicit unction theorem, the optimum can be written as a dierentiable unction l* = L( p, q) or some neighborhood o the initial values o p and q. Substituting this unction into (13) transorms the expression into an identity. Total dierentiating this identity with respect to q gives (14) l * 1 =, q pg which is negative as might be expected. Using the irst-order condition (13), the corresponding elasticity expression or (14) can be written 10

12 (15) η = ( γ ( l*) ) lq q 1 = < 0, pg l * where η lq ln l * G l * =, and similar to α(h), γ ( l*) = lnq G is an elasticity measure o the degree o diminishing returns, in this case with respect to the production unction G. It is readily checked that dη dq has the same sign as γ ( l ), so that, or instance, η lq becomes less lq negative as q increases i γ ( l ) > 0. Moreover, comparative static analysis parallel to the oregoing reveals that η lp l = ln *, an elasticity expression representing the responsiveness o ln p individual labor demand to changes in output price, is just equal to - η lq. It s now possible to consider the total impact o an increase in the minimum wage on the proit-maximizing size o the irm s labor orce. Recall that minimized unit cost q is itsel a unction o w, as is the cost-minimizing magnitude o hours per worker h. Based on equation (4) and the oregoing optimization conditions, the irm s quantity demanded o workers (ignoring that its labor orce must be measured in integers) can be written (16) n* = N( c, w ) = L( Q( c, w )) A( H( c, w )) Totally dierentiation o (14) with respect to w, evaluated at the proit-maximizing solution while holding output price p constant, gives n * = w l * q A q w l A * * hw A 2 = l * * q ha l w h * * c + w h * w A 11

13 (applying the envelope theorem with respect to q and irst-order condition (6)), yielding, ater some substitution and rearrangement, n * w (17) η = = nw ω ( η lq ηhw) w n *, where ω = w h * c + w h, the ratio o wages to total labor cost. Expression (17) is a relative o * the well-known Slutsky equation with respect to household demand. It shows that the net eect o an increase in the wage loor on the number o workers demanded by the irm, expressed as an elasticity, is the sum o a negative labor-speciic scale eect ωη lq and a positive laborspeciic substitution eect ωη hw. Note critically that in the presence o person-speciic labor costs, the net eect on irm-level employment o an increase in the minimum wage cannot be signed a priori without urther conditions. This is also true with regard to the impact o c on the magnitude o the employment elasticity. For example, i negative, η nw is increasing in c i in addition α ( h) and γ ( l) are non-negative and η hw 1. Note urther that so long asη nw 0, the eect o raising the wage loor is unambiguously (at least in the context o partial equilibrium analysis) to redistribute welare rom capital to labor, so that workers employed under the original wage loor receive higher economic rents. However, labor income per worker, given by y* = w h*, may decline with an increase in the minimum wage. There is in act a direct tradeo between the irm-level employment and income eects o a wage loor hike: other things equal, the larger in absolute value is the wage elasticity o hours demand η hw, the larger is the employment eect and the smaller is the change in wage 12

14 income per worker. O course, the latter change is negative or absolute values o the elasticity greater than one. IV. Industry-Level Employment Eects o Raising the Minimum Wage The employment eect recorded in expression (17) is derived treating output price p as a parameter. However, i most or all irms in a given product market ind their costs increased when a wage loor is raised, one would expect a corresponding increase in output price and a consequent reduction in equilibrium market output. Thereore net employment eects o increasing the minimum wage must be calculated at the industry level. Note, however, that the term industry should be interpreted loosely, since it is possible that workers covered by minimum wage legislation may be employed in the production o a wide array o goods. I output price is understood to vary with the wage rate, the irm-level employment eect o raising the minimum wage becomes d n* d w p (18) η = = nw ω( ( 1 η pq ) η lq ηhw ) w n* (making use o the result that η lp = η, and using the total rather than the partial derivative lq operator with respect to n* to indicate the endogeneity o p), where η pq d ln p d lnq I = 0 measures the responsiveness o industry equilibrium price p I to changes in labor cost q. This elasticity measure embodies two separate considerations, the impact o rising q on the irm s average cost, and the response o equilibrium price to this change in cost. For example, a nondiscriminating monopolist will, other things equal, increase its price less than a competitive industry in response to a given cost increase. 13

15 Note that equation (18) is larger in value than its counterpart in (17), i all common terms are equated. This is the case because each irm which remains in the aected industry will, ceteris paribus, increase its output, and consequently its demand or labor, in response to the price increase occasioned by the higher minimum wage. However, increasing the wage rate will also typically alter the number o irms in a given market, so these industry-level changes must also be taken into account. To accomplish this, assume or convenience that all aected irms are identical and operate in the same industry, and thus write industry-level employment as n = m n *, where n* as beore denotes each irm s proit-maximizing demand or employees, and m I represents the equililibrium number o irms in the industry. This can in turn be expressed as the ratio o equilibrium quantity demanded in the market to equilibrium irm output, or (19) m I = X ( P( q)) G( L( P( q), q)), where xi = X ( p) denotes market quantity demanded as a unction o the equilibrium price, and pi = P( q) denotes equilibrium market price as a unction o labor cost. Given (19), the industry-level employment eect o raising the minimum wage is dn dw m dn I * dw n dmi = I + * (ignoring that numbers o irms and employees can in practice take dw only integer values), which ater some substitution and rearrangement yields I I dn dw w I I I (20) ηnw = = ω η pq η xp + ( 1 η pq ) n I ( p x * ql*) η I p I x * lq η hw 14

16 (again using total rather than partial derivative operators to indicate that both direct and indirect I eects on employment arise when output price is endogenous), where η xp is the elasticity o market demand, assumed or the sake o discussion to be strictly negative, and other variables are deined as beore. The labor-speciic scale eect deined earlier is shown to correspond at the industry level to a weighted average o two negative terms governed by essentially dierent microeconomic considerations inorming the elasticities o irm-level labor demand and marketlevel product demand. As with its irm-level counterparts in (17) and (18), the net industry-level employment eect expressed in (20) cannot be signed a priori. Thus, depending on speciic technological and market conditions, increasing the minimum wage may reduce, increase, or leave unchanged total employment o workers aected by the change. V. Extensions o the Basic Model The paper s central result, expressed in equation (20), that the net employment eect o raising the minimum wage cannot be determined a priori when person-speciic labor costs are present, was derived on the basis o a simple model in which non-labor inputs, work eort, and the magnitude per worker o person-speciic costs are in eect held constant. This qualitative assessment is not aected by incorporating these elements as choice variables in the irm s optimization problem. However, as indicated below, doing so potentially alters the magnitude and even the sign o the employment eect. Variable non-labor inputs 15

17 Suppose we represent non-labor inputs in production by introducing a new argument k, capital services, into the production unction, thus writing x = G(l,k). Let r denote the parametric unit price o capital services. Assume that G is increasing and strongly concave in its arguments (so that the corresponding Jacobian matrix is negative deinite or all positive values o the inputs), and indicate irst and second partial derivatives by subscripts, with G i denoting the marginal product o input i and G ij the marginal impact o increasing input j on the marginal product o i, i,j = l,k. Let the notation used in the basic model be correspondingly modiied so that γ ij (l,k) represents an elasticity expression measuring the responsiveness o i s marginal product to changes in input j. When i=j, this expression is interpreted similarly to γ as a measure o the degree o diminishing returns. When i j, this is instead a measure o the degree o complementarity among actors. (Note that γ lk and γ kl are not necessarily equal, but must have the same sign.) In this scenario the irm chooses inputs l and k to maximize (21) Π( l, k; q, r) = pg( l, k) ql rk. Standard optimization analysis yields, with some substitution and rearrangement, k γ lkγ (22) ηlq = γ ll γ kk kl 1, where the superscript k indicates that the irm s elasticity o eective labor demand is now derived taking the capital input as variable. The term in parentheses is guaranteed to be negative by the strong concavity o G. Comparison with the corresponding expression (15) 16

18 shows that the newly derived elasticity is larger in absolute value (i.e., more negative) than its short-run version, i γ ll is equated to γ, its counterpart in the basic model. The counterpart to expression (20) becomes much more complicated when there are multiple variable inputs in production. However, or the special case o constant returns to scale technology with two inputs (i.e., given that G is homogeneous o degree one in inputs l and k), a amiliar characterization o long-run labor demand elasticity (see, or example, Hamermesh (1993), p. 24) can be adapted to yield [ hw ] I I (23) nw ( xp ( ) ) η = ω λη + 1 λ σ η, whereσ is the elasticity o substitution o k or l and λ is labor s share o total production cost. Note that the sign o the net employment eect remains indeterminate. Moreover, a subtle distinction must be noted with respect to the impact o variability in nonlabor inputs. As suggested by the examples given in the introduction, certain o these inputs may vary directly with the number o workers employed and thus contribute to unit person-speciic costs c. This is particularly signiicant i these inluence the marginal contributions to eective labor o individual hours, the case considered next. Variable unit person-speciic costs Now consider a scenario in which the magnitude o unit person-speciic cost c is itsel a choice variable which inluences the eective labor contribution per worker. 5 Accordingly, let 5 Firm-speciic training activities are an obvious example o this phenomenon. Other possibilities: specialized clothing might render service personnel more immediately identiiable and thus less likely to be impeded in perorming their work; proximate sanitary acilities may reduce undue interruptions; on-site lockers may reduce startup costs. Outside the ramework o competitive and complete markets, search and screening expenditures may increase the average quality o workers, while person-speciic monitoring may boost individual work eort. 17

19 this contribution be written A(h, c) and assume that it is strongly concave in its arguments. Let subscripts be used to represent partial derivatives, so that A i denotes the marginal contribution o variable i to a worker s eective labor input and A ij represents the eect o increasing labor variable j on the marginal contribution to eective labor o variable i, i,j = h,c, supposing that A hc > 0. Since c thus provides beneits as well as costs to the irm, there is no loss in assuming that A is strictly increasing in its arguments. Let the notation used in the basic model be modiied accordingly so that α ij denotes an elasticity measure o the responsiveness o argument i s marginal contribution to individual labor input to changes in argument j. Thus, as with the term α in the basic model, α ii < 0 measures the intensity o diminishing returns to argument i, while α ij > 0, j i, is a measure o the degree o complementarity between the two arguments. c w h The irm in this case chooses both h and c in minimizing B( h, c; w ) = +. Standard A( h, c) analytical procedures, again assuming an interior solution, yield (24) η c hw = α ch w 1 1+ α cc α chα hc α hh α ( ω ) cc, where the superscript-c indicates that unit person-speciic costs are taken as variable. Noting the correspondence o α hh and α and that A cc < 0, the sign o (24) cannot be determined a priori, nor can its magnitude be unambiguously compared with that o (11), its counterpart in the simpler model. However, i A ch = 0, implying in turn that α ij = 0, i j, then 18

20 this term is strictly more elastic than its counterpart in the basic model, i corresponding terms are equated. It can by parallel steps be shown that (25) c ηcw dc / dw = = w h h α hh c + α α h cc α α chα α hc hh α ( ω 1) cc ch cc, which is similarly indeterminate in sign. Consequently the impact o raising the wage loor on productivity-enhancing person-speciic labor costs is also ambiguous. Note, however, that c is strictly increasing in w i A ch = 0. Evaluated at the proit-maximizing solution, the net impact o raising the minimum wage on irm-level employment in this scenario, again treating output price p as parametric, can be expressed as (26) η c nw n * w c c * η = = ω ηlq ηhw + w n * h * w cw. In general, neither the sign o expression (26) nor its magnitude relative to that o (17) can be established. However, one can veriy using (24) and (25) that, other things equal, expression (26) is larger in magnitude (i.e., less negative) than (17) i A ch = 0. In any event, the net employment eect o raising the minimum wage remains indeterminate. Work eort Finally, suppose the model were altered to incorporate a third dimension o labor input, work eort e, and thus write eective labor contribution per worker as A(h, e). Let A be 19

21 strongly concave in its arguments, with A he > 0. Assume urther that A is strictly increasing in h, and increasing in work eort or values o e (0, e ~ ]. Suppose that the irm optimizes with respect to h, e, and l. The counterpart to (16) representing the dependence o proit-maximizing employment on the parameters is L( Q( c, w e e ) (27) n * = N ( c, w ) =, A( H( c, w ), E( c, w )) where the superscript e indicates that n* is determined given that e is a choice variable, and e* = E( c, w ) indicates proit-maximizing eort as an implicit unction o the parameters. This implies the comparative static expression (28) A dl * q dn dq dw l A * e * * A e h + e * hw w = dw A 2. Note that there is no direct or indirect price o eort to the irm, so long as the worker s reservation utility is more than satisied by the terms o employment. As a result, the irm may, i it wishes, and contractual conditions permit, set eort so that the reservation utility constraint is just binding. Consequently, two cases must be considered in evaluating expression (28). In the irst case, suppose that the marginal contribution o eort to eective labor input reaches zero (that is, A e = 0) beore the reservation utility constraint is engaged. In this case, adjusting work eort so that each worker just receives the reservation utility level is not optimal, so cost minimization implies that A e = 0 at the optimum, since the inramarginal cost o eort to the irm is zero. In addition, standard comparative static analysis can be invoked to demonstrate that 20

22 (29) η e hw = α hh ( 1 ω) α heα α ee eh is strictly negative due to the strong concavity o A in its arguments. Comparison o (29) to its counterpart in (11) demonstrates that the negative responsiveness o hours to an increase in wages is unambiguously greater when eort is also a choice variable, other things equal, given A e = 0 and A eh > 0. This implies, via (28), with other things equal, that allowing optimal variation in eort increases (i.e. makes more positive or less negative) the value oη nw, thus expanding the scope or employment gains. Suppose alternatively that ~ e exceeds the magnitude o work eort at which each worker receives just the reservation utility or a given combination o wage rate w and hours h. This implies that the inramarginal contribution o work eort to eective labor input is strictly positive, and the reservation utility constraint will consequently be binding at the optimum. Accordingly, let e = E( h, w ) denote the level o work eort which aords the reservation level o utility given the minimum wage and hours expended per employee. It is readily veriied that e is increasing in w and decreasing in h given that the minimum wage constraint is also binding. In this case, allowing eort to vary has an ambiguous impact on the irm-level employment eect o raising the minimum wage. Evaluated at the proit-maximizing solution, expression (28) takes the speciic orm e (30) η = dn * w e Ae q de nw ω ηlq ηhw dw n = + h * * dw, 21

23 e where η hw e diers indeterminately rom η hw as expressed in (28). Consequently the precise impact o allowing work eort to vary cannot be determined in this scenario. In sum, incorporating variable work eort in the model does not alter the indeterminacy o employment eects, and make increase the scope or positive employment eects rom raising the wage loor, other things equal. VI. Discussion and Conclusion Opponents o minimum wage policies have oten, i not typically, argued as though it were presumptive that raising a wage loor must curtail employment, particularly in the long run. O course, no such presumption can be established on theoretical grounds i the aected labor markets are subject to certain imperections. It is shown here that in addition negative employment eects may not obtain even i the aected labor markets are competitive and complete, given that they are characterized by person-speciic labor costs and diminishing returns to eective labor inputs o individual work hours. Under the stated conditions, the conventional wisdom may in act be completely reversed, with employment rising and income per worker alling as a result o a hike in the wage loor. These results are shown to be robust to extensions o the basic model which incorporate various orms o input substitutability. Moreover, under the conditions studied here raising a wage loor may encourage more rather than less productivity-enhancing expenditures per worker, and may additionally serve as a policy instrument in allocating work hours more evenly across an economy s labor orce. 22

24 At least in a partial equilibrium context, it remains the case that raising a binding wage loor must incur additional dead-weight losses, although there will be an unambiguous redistribution o welare rom capital to labor so long as the employment eect is non-negative. Workers who remain employed under a minimum wage regime receive economic rents unless irms are willing and able to adjust individual eort levels to eliminate them. In a general equilibrium context, however, unambiguous eiciency judgments cannot be made given that there is any other deviation rom ideal conditions. In light o the results presented here, the impact o minimum wage policy on employment is essentially an empirical issue, with no presumption assignable to any particular market response. Furthermore, employment eects may vary across economies or over time as technologies or market conditions change. O course, the results presented here cannot o themselves establish a case or wage loors as an instrument o government policy with respect to poverty or income inequality, and it may be that the contingent nature o employment eects argues against a universal minimum wage policy. However, the considerations studied here may serve to reset the terms o ongoing debates and provide a basis or more nuanced investigations o this policy instrument. 23

25 REFERENCES Card, David and Krueger, Alan B. Myth and Measurement: The New Economics o the Minimum Wage. Princeton, NJ: Princeton University Press, Donaldson, David and Eaton, B. Curtis. Person-Speciic Costs o Production: Hours o Work, Rates o Pay, Labor Contracts. Canadian Journal o Economics, August 1984, 17(3), pp Ehrenberg, Ronald G., ed. Review Symposium: Myth and Measurement: The New Economics o the Minimum Wage. Industrial and Labor Relations Review, July 1995, 48(4), pp Hamermesh, Daniel S. Labor Demand. Princeton, NJ: Princeton University Press, Hart, Robert A. The Economics o Non-Wage Labour Costs. London, UK: George Allen & Unwin, Oi, Walter Y. Labor as a Quasi-Fixed Factor. Journal o Political Economy, December 1962, 70(6), pp

26 Rebitzer, James B. and Taylor, Lowell J. The Consequences o Minimum Wage Laws: Some New Theoretical Ideas. Journal o Public Economics, February 1995, 56(2), pp Stiglitz, Joseph E. The Causes and Consequences o the Dependence o Quality on Price. Journal o Economic Literature, March 1987, 25(1), pp