BLS WORKING PAPERS

U.S. DEPARTMENT OF LABOR 

Bureau of Labor Statistics 

OFFICE OF PRICES AND LIVING

CONDITIONS 

 

Minimum Wages, Employment and Monopsonistic Competition 

V. Bhasker, University of Essex 

Ted To, U.S. Bureau of Labor Statistics 

 Working Paper 369

 December 2003 

All views expressed in this paper are those of the authors and do not necessarily reflect the views or policies of the 

Bureau of Labor Statistics. 
Minimum Wages, Employment and

Monopsonistic Competition∗

V. Bhaskar

University of Essex

Ted To

Bureau of Labor Statistics

August 2003

Abstract

We set out a model of monopsonistic competition, where each employer competes

equally with every other employer. The employment effects of minimum wages depend on the degree of distortion in the labor market. If fixed costs per firm are high

then the labor market is relatively non-competitive and minimum wages increase employment. Conversely, low fixed costs make for a more competitive labor market

where minimum wages reduce employment. This contrasts with the results of a Salop style model with localized employer competition where a minimum wage unambiguously raises employment. We also find that the welfare effect of a small minimum

wage is unambiguously positive.

Keywords: monopsonistic competition, labor theory, minimum wages, monopsony

JEL classification codes: J23, J42, L13

∗We thank Greg Kurtzon, Randy Verbrugge and seminar participants at the 2003 Western Economic Association meeting in Denver for helpful comments and suggestions. V. Bhaskar is grateful to the Economic

and Social Research Council, UK for its support under research grant L138251029. The views expressed are

not to be attributed to the Bureau of Labor Statistics or to the Department of Labor.
1 Introduction

The view that labor markets are imperfectly competitive, with employers possessing

some market power, has gained prominence in recent years. Empirical studies have come

up with many findings, such as the positive employment effects of minimum wages (Card

and Krueger, 1995), that are inconsistent with models of perfect competition. Two alternative approaches to modelling imperfect competition are search models (Burdett and

Mortensen, 1998) and models of monopsonistic competition (Bhaskar and To, 1999).1

In this paper, we provide a simple model of monopsonistic competition in the labor

market. Workers have heterogeneous preferences over employer characteristics, and each

employer competes equally with every other employer in seeking to attract workers. This

may be contrasted with the circle model of monopsonistic competition in Bhaskar and To

(1999), where each employer effectively competes only with her two immediate neighbors. Our model may be viewed as a Dixit-Stiglitz type model, since each firm competes

with every other firm, and when the number of firms is large, yields establishment labor supply curves with approximately constant wage elasticity. However, we emphasize

that it is not a representative worker model—rather, it is based on heterogenous workers,

each of whom chooses to work for at most one employer. Our model is an adaptation of

Sattinger’s (1984) model of consumer choice to the labor market. This adaptation results

in some technical difficulties, since a realistic model of labor markets must allow for the

possibility that some workers may be unemployed.

We use this model to study the effects of a minimum wage upon employment in a free

entry equilibrium. As in other models of monopsonistic competition, a minimum wage

has two conflicting effects. First, it has the standard monopsony effect whereby a moder1Bhaskar et al. (2002) provide a discussion of the empirical evidence, and argue that models of oligopsony/monopsonistic competition provide a parsimonious explanation for much of this evidence. Manning

(2002) is a textbook on labor economics with an approach centered on models with employer market power.
ately chosen minimum wage reduces the marginal cost of labor, increasing labor supplied

to individual firms. Second, it has a first order negative effect on profits, causing firms

to exit, thus reducing employment. We find that the net effect of a small minimum wage

can be either positive or negative, depending upon parameter values. If fixed costs are

high, so that the equilibrium number of firms is small, and the labor market is relatively

non-competitive, then a small minimum wage increases employment. On the other hand,

if fixed costs are low, so that the labor market is relatively competitive, a minimum wage

reduces employment. In other words, the employment effect of a minimum wage is related to the extent to which the labor market is distorted. These results may be contrasted

with those obtained in the context of the circle model of the labor market used by Bhaskar

and To (1999). Walsh (2001) shows that in the circle model, the effect of a small minimum

wage upon employment is unambiguously positive.2

Interestingly, under some parameter configurations with the current model, minimum

wages can increase employment even when the labor market has many employers or

when the establishment level labor supply elasticity is high. This is of importance because one common argument is that even if there are labor market distortions, these distortions become insignificant in industries like fast food, where many employers compete

for workers. Our results show that even when a labor market appears to be competitive,

minimum wages can increase employment.

Finally, extensive numerical computations suggest that welfare unambiguously increases when a minimum wage is imposed just above the equilibrium wage rate. That

is, the welfare gain due to increased wages outweighs the welfare loss resulting from the

reduction of job choices due to employer exit and from (potential) disemployment.

2Walsh corrects and clarifies the formulation in Bhaskar and To. Although Walsh shows that it is possible

to modify the circle model to produce negative employment effects, these modifications require somewhat

unreasonable parameter restrictions. Further, these restrictions do not have an intuitive interpretation in

terms of the extent of labor market distortions.

2
2 The Model

To ensure that labor supply is imperfectly elastic, we assume that different jobs have different non-wage characteristics. These include the job specification, hours of work, distance of the firm from the worker’s home, the social environment in the workplace, etc.

The importance of non-wage characteristics has been recognized in the theory of compensating differentials, which is a theory of vertical differentiation. Some jobs are good

while other jobs are bad, and wage differentials compensate workers for these differences in characteristics. We assume that jobs are horizontally differentiated so that workers

have heterogenous preferences over these characteristics. McCue and Reed (1996) provide survey evidence of horizontal heterogeneity in worker preferences. Heterogeneous

preferences over non-wage characteristics ensures that each employer has market power

in wage setting, even if it competes with many other employers.

Our modelling of the labor market is inspired by Sattinger’s (1984) model of the product market. The key difference is that we allow for unemployment (“home production”).

Let us suppose that the individual worker has the following utility function:

U = W1−γL

γ

(1)

where W is the worker’s job-adjusted income (defined below) and L is time spent at

leisure activities. Let firms be indexed by j ∈ {1, 2, . . . , n}. Each firm offers a “job” that has

characteristics that differ from its rivals and workers have heterogeneous preferences over

these characteristics. We shall also assume that the alternative to outside employment is

home production which we denote as job 0.

The worker’s preferences over this set of n + 1 alternatives are parameterized by the

n + 1 vector r whose generic component rjis a measure of the worker’s disutility from

activity j. In particular, a larger value of rj reduces the value of working for employer j,

3
at the offered wage wj

. More specifically, we model this as follows. If a worker works hj

hours for wage wj and has disutility rj for working at job j then her disutility-adjusted

earnings from job j are wjhj/rj and her total job-disutility-adjusted income from all jobs

is W =

Pn

j=0 wjhj/rj

. Workers have likes and dislikes over job characteristics and an

unpleasant job (i.e., one for which rjis large) reduces the pleasure that a worker gets from

her income. We assume that the return to home production, w0, is exogenously specified.

If L ̄ is the total amount of leisure time available then she enjoys L = L ̄ −

Pn

j=0 hj hours of

leisure.

Taking the first order conditions yield:

∂U

∂hj

= (1 − γ)

wj

rj



L

W

γ

− γ



W

L

1−γ

≤ 0 (2)

for j = 0, 1, . . . , n. For generic values of r, this condition will hold with equality for exactly

one employer and with strict inequality for all other employers. This implies that individual workers will work for at most one employer. Let j = arg maxk{wk/rk} represent

the employer for whom the first order condition holds with equality. Solving equation

(2), the worker’s labor supply to employer j is hj = (1 − γ)L ̄ and for all employers k 6= j

is hk = 0. If j happens to be home production, the worker will be unemployed.

Suppose that there is a unit mass of workers and that for each worker, her disutilities,

rj, are independently and identically distributed with a continuous distribution function

F and corresponding probability density function f. The conditional probability given rj

that the worker prefers employer j to employer k is 1 − F(rjwk/wj ). Thus the conditional

probability given rj that the worker prefers employer j to all other employers and to

staying at home is Q

k6=j

[1 − F(rjwk/wj )]. Multiplying individual labor supply by this

4
probability and integrating over all rj yields labor supply to firm j

Lj = (1 − γ)Ls ̄

j (3)

where sjis firm j’s share of total labor supplied (either for work or for home production)

and is given by:

sj =

Z Y

k6=j



1 − F



rjwk

wj

 f(rj )drj

. (4)

For the case when all firms but j offer wage w−j, this becomes:

sj =

Z 

1 − F



rjw−j

wj

n−1 

1 − F



rjw0

wj

 f(rj )drj

. (5)

Suppose that F is the Pareto distribution so that F(x) = 1−(b/x)

a and f(x) = aba/xa+1

where a, b > 0 and x ≥ b. Consider employer j’s labor supply when all rival employers

offer wage w−j and wj, w−j > w0. The equation for firm j’s share of labor supplied can be

written as:

sj =







h

1 −



w−j

wj

ai

+

1

n



w−j

wj

a

−



w0

w−j

a(n−1) 

w0

wj

a



+

1

n+1 

w0

w−j

a(n−1) 

w0

wj

a

if wj ≥ w−j

1

n



wj

w−j

a(n−1)

−



w0

w−j

a(n−1) 

w0

wj

a



+

1

n+1 

w0

w−j

a(n−1) 

w0

wj

a

if wj ≤ w−j

(6a)

For the case when wj, w−j < w0, sj can be written as:

sj =







1

2

h wj

w0

a

−



w−j

w0

a 

w−j

wj

ai

+

1

n+1 

w−j

w0

a 

w−j

wj

a

if wj ≥ w−j

1

n+1 

wj

w−j

a(n−1) 

wj

w0

a

if wj ≤ w−j

. (6b)

These expressions are rather complicated, however, for the case with symmetric wages

(i.e., wj = w−j = w), the establishment level elasticity of labor supply is given by the

5
following, relatively simple expression:

ε =







a((n+1)(n−1)+(

w0

w )

an)

(n+1)−(

w0

w )

an if w ≥ w0

an if w ≤ w0

. (7)

This is a weakly decreasing, continuous function of w and is bounded by a(n − 1) and

an. That is, as the market wage rate rises, the elasticity of labor supply falls. This is what

should be expected since if the wage is high relative to the return from home production, home production becomes a less attractive substitute. Moreover, ε is an increasing

function of the number of firms, n. Differentiating ε with respect to n we get:

∂ε

∂n =







a((n+1)2−(2n+1)(

w0

w )

an+(n+1)(

w0

w )

an ln(

w0

w )

an)

(n+1−(

w0

w )

an)

2 if w ≥ w0

a if w ≤ w0

. (8)

Consider the case when w ≥ w0. Since −(2n+1)x+(n+1)x ln x is strictly decreasing for all

x ≤ 1, it follows that the minimum value of numerator is an2. Thus we can conclude that

∂ε/∂n > 0. As should be expected, establishment level labor supply becomes more elastic

as the number of employers increases. In particular we have the desirable result that as

the number of firms, n, grows large, the labor market approaches perfect competition

with establishment labor supply curves becoming perfectly (infinitely) elastic.

For a fixed number of firms in a symmetric equilibrium, wages will be set according

to the rule,

w(n) = φ

ε

1 + ε

(9)

where φ is the marginal revenue product of labor.3 Thus wages are a strictly increasing

3The assumption, that the marginal revenue product of labor is constant, is not really necessary. If

both capital and labor are required, and there is constant returns to scale and a competitive capital market,

Bhaskar and To (1999) show that when the capital labor ratio adjusts optimally, the “net revenue product”

6
function of the labor supply elasticity. This implies that there is a unique, symmetric

equilibrium wage, w

∗

(n), satisfying equations (7) and (9).4 Moreover, since labor supply

elasticity rises with the number of employers, equilibrium wages do so as well.

Given the equilibrium wage rate, w

∗

(n), the equilibrium share of labor per firm is

given by

s

∗

(n) =







1

n

h

1 −



w0

w∗(n)

ani

+

1

n+1 

w0

w∗(n)

an

if w

∗

(n) ≥ w0

1

n+1 

w∗(n)

w0

a

if w

∗

(n) ≤ w0

. (10)

As should be expected, if w

∗

(n) = w0 then each of the n + 1 activities garners an equal

share of labor supplied—i.e., s

∗

(n) = 1/(n + 1).

The equilibrium profits of the firm are given by

π

∗

(n) = (φ − w

∗

(n))L

∗

(n) (11)

where L

∗

(n) = (1 − γ)Ls ̄ ∗(n). This is decreasing in the number of firms for two reasons.

First, labor supply per firm is decreasing in n, and second, the wage is also higher with

n. To see the former, examine equation (13). The numerator is a scalar multiple of the

numerator of (8) and by similar argument we can show that εn < 0. Since labor supply

falls and wages rise with n, profits must fall with n. The free entry number of firms is an

n

∗

such that π

∗

(n

∗

) − c = 0 where c is the fixed cost of production.

3 The effects of a minimum wage

When a minimum wage is imposed, establishment level employment rises due to the

monopsony effect, but total employment may fall because of induced firm exit. Recall

is constant.

4As noted by Sattinger (1984), there may well exist other, asymmetric equilibria. For tractability, we

focus only on the symmetric equilibrium.

7
that establishment level employment is given by:

L(n) = (1 − γ)Ls ̄

j

where sjis as given in equations (6a) and (6b).

Let E denote total employment, Ln. In order to work out the employment effect of a

minimum wage under free entry, we utilize the following decomposition, due to Walsh

(2001):

dE

dwm

=

Ln

w



ε −

ε−j

εn



where ε is the elasticity of firm labor supply with respect to the own wage, ε−jis the

elasticity with respect to competitor firm wages, and εn is the elasticity with respect to n.

The own wage elasticity of labor supply is given by equation (7). From the equation

for labor supply, ε−j and εn are as follows:

ε−j = −a(n − 1) (12)

εn =







−

(n+1)2−(2n+1)(

w0

w )

an+(n+1)(

w0

w )

an ln(

w0

w )

an

(n+1){n+1−(

w0

w )

an}

if w ≥ w0

−

n

n+1 if w ≤ w0

. (13)

It is straightforward to show that there exist parameter values such that the employment effect of a minimum wage is positive. For example, consider parameter values such

that w

∗ ≤ w0.5

In this case, ε = an and εn = −n/(n + 1), so that

dE

dwm

=

L

w

a

That is, if the equilibrium wage is sufficiently small relative to the return from home

5Since the equilibrium wage, w∗

, is bounded above by φ, we may choose φ so that w

∗

is smaller than w0.

8
production, a minimum wage increases employment.

Unfortunately, general conditions for negative employment effects are not possible

because of the non-linearity of the equilibrium system of equations. For this reason, we

numerically compute the equilibria for a wide range of parameters to establish that minimum wages can lower employment. We present a selection of these results in Table 1.

These results show that fixing other parameter values, the minimum wage effect depends

upon the fixed cost c. When fixed costs are relatively low, a minimum wage reduces employment. When the fixed cost is large, minimum wages increase employment. Since

fixed costs are the factor which prevent perfect competition from occurring, our results

have an intuitive interpretation—minimum wages raise employment when the labor market is distorted, but reduce employment when the market is relatively competitive. Note

however that even for labor markets that appear to be highly competitive to a casual observer (e.g., n > 850 or ε > 90), a minimum wage can still have a positive employment

effect. That is, even if a labor market appears, prima facie, to be competitive, a minimum

wage may increase employment under monopsonistic competition.

3.1 Welfare Effects

Let us now consider the utility of an individual with disutilities r = (r0, r1, . . . rn). Suppose the equilibrium wage profile is w = (w0, w1, . . . wn). This worker will spend (1 − γ)L ̄

hours at activity j where j = arg max wj/rj and γL ̄ hours at leisure activities. Her indirect

utility can be written as:

U(w, r) = K max 

wj

rj

1−γ

(14)

9
Table 1: Employment and welfare effects

a w0 c n w

∗

l ε

employment

effect

welfare

effect

0.01 0.90 0.00002 1531.9 0.939 0.00033 15.3 −0.003379 0.016

0.01 0.90 0.00004 1068.8 0.914 0.00047 10.7 −0.001426 0.023

0.01 0.90 0.00006 863.7 0.896 0.00058 8.6 0.000012 0.028

0.01 0.90 0.00008 741.5 0.881 0.00067 7.4 0.000014 0.032

0.01 0.95 0.000005 3112.6 0.969 0.00016 31.1 −0.00332 0.0081

0.01 0.95 0.000010 2186.2 0.956 0.00023 21.9 −0.00124 0.0114

0.01 0.95 0.000015 1775.9 0.947 0.00028 17.8 0.00001 0.0140

0.01 0.95 0.000020 1531.3 0.939 0.00033 15.3 0.00001 0.0161

0.25 0.90 0.0005 61.2 0.94 0.008 15.2 −0.0809 0.023

0.25 0.90 0.0010 42.2 0.91 0.012 10.6 −0.0285 0.033

0.25 0.90 0.0015 34.0 0.89 0.014 8.5 0.0073 0.040

0.25 0.90 0.0020 29.1 0.88 0.017 7.3 0.0086 0.045

0.25 0.95 0.0001 139.5 0.972 0.0036 34.7 −0.0884 0.011

0.25 0.95 0.0003 79.2 0.952 0.0062 19.8 −0.0065 0.018

0.25 0.95 0.0005 60.7 0.938 0.0081 15.2 0.0041 0.023

0.25 0.95 0.0007 50.8 0.927 0.0096 12.7 0.0049 0.027

0.25 0.99 0.000005 630.4 0.994 0.0008 157.5 −0.0812 0.0024

0.25 0.99 0.000010 444.8 0.991 0.0011 111.2 −0.0265 0.0033

0.25 0.99 0.000015 362.6 0.989 0.0014 90.7 0.0007 0.0041

0.25 0.99 0.000020 313.6 0.987 0.0016 78.4 0.0008 0.0047

1.00 0.90 0.002 15.3 0.94 0.032 14.8 −0.280 0.045

1.00 0.90 0.004 10.3 0.91 0.045 10.2 −0.019 0.062

1.00 0.90 0.006 8.1 0.89 0.054 8.1 0.124 0.075

1.00 0.90 0.008 6.8 0.87 0.062 6.8 0.148 0.084

1.00 0.95 0.0005 31.1 0.968 0.0158 30.6 −0.303 0.023

1.00 0.95 0.0010 21.5 0.955 0.0224 21.4 −0.064 0.032

1.00 0.95 0.0015 17.2 0.945 0.0273 17.2 0.058 0.039

1.00 0.95 0.0020 14.7 0.936 0.0314 14.7 0.068 0.045

1.00 0.99 0.00002 157.6 0.994 0.0032 157.1 −0.321 0.0047

1.00 0.99 0.00004 110.9 0.991 0.0045 110.8 −0.097 0.0067

1.00 0.99 0.00006 90.2 0.989 0.0055 90.2 0.011 0.0081

1.00 0.99 0.00008 78.0 0.987 0.0063 78.0 0.013 0.0094

Notes: The employment and welfare effects are elasticities with respect to

the minimum wage. For these computations, we fix various scale parameters as follows: γ = 0.5, b = 1, φ = 1 and L ̄ = 1. These numeric results were

computed using a FORTRAN program employing the non-linear equation

solver from the Argonne National Laboratory’s collection of optimization

subroutines, MINPACK-1.

10
where K = (1 − γ)

1−γγγL ̄. For symmetric wage profiles where wj = w for j = 1, 2, . . . n,

indirect utility can be rewritten as:

U(xe, xu) = K (max{xe, xu})

1−γ

(15)

where xe = max{w/rj}

n

j=1 and xu = w0/r0. Each ratio, xj = wj/rj has cumulative distribution 1 − F(wj/xj ). The random variable xe is an order statistic with cumulative distribution [1 − F(w/x)]n

. Thus x = max{xe, xu} is a random variable that has cumulative

distribution G(x) = [1 − F(w/x)]n[1 − F(w0/x)]. Differentiating yields density function:

g(x) = nw

1 − F



w

x

n−1

1 − F



w0

x

f

w

x



+ w0



1 − F



w

x

n

f



w0

x



x

2

(16)

Average utility is equal to a typical worker’s expected utility and can therefore be written

as

EU = K

Z

x

1−γ

g(x)dx. (17)

As before, consider the case when F is the Pareto distribution. If w ≥ w0 then we can

write g as

g(x) =







a(n+1)

x



bx

w

an

bx

w0

a

if x ≤

w0

b

an

x



bx

w

an

if w0

b ≤ x ≤

w

b

. (18)

If w ≤ w0 then g can be written as:

g(x) =







a(n+1)

x



bx

w

an

bx

w0

a

if x ≤

w

b

a

x



bx

w0

a

if w

b ≤ x ≤

w0

b

. (19)

11
Thus

EU = K







a(n+1)

a(n+1)+1−γ



w0

w

an 

w0

b

1−γ

+

an

an+1−γ

h

w

b

1−γ

−



w0

w

an 

w0

b

1−γ

i

if w ≥ w0

a(n+1)

a(n+1)+1−γ



w

w0

a 

w

b

1−γ

+

a

a+1−γ

h

w0

b

1−γ

−



w

w0

a 

w

b

1−γ

i

if w ≤ w0

(20)

where n = n

∗ and w = w∗

(n

∗

).

Given the complexity of this expression, analytic welfare calculations are not possible.

However, numeric computations can be used to evaluate the welfare consequences of

a minimum wage. Some of these results are presented in Table 1. What appears to be

true is that for this model, assuming that the rj are distributed Pareto, minimum wages

unambiguously increase welfare. Since as is common with monopsonistic competition,

minimum wages have opposing welfare effects (increasing wages vs declining job choices

and potentially declining employment), we do not believe that this unambiguous welfare

result is robust to modelling changes or even changes in the assumed distribution of the

rj. Nevertheless, it is useful to observe that welfare can increase even as employment falls

so that the literature’s preoccupation with the employment effects of minimum wages

may be misguided.

4 Concluding Comments

We have developed a simple model of monopsonistic competition, where each employer

competes equally with all other employers for workers. This is similar to a Dixit-Stiglitz

style model, although it is based on heterogeneous workers, each of whom only works for

one employer. We find that the effect of a small, binding minimum wage is ambiguous: it

will be positive if the labor market is relatively distorted, and negative otherwise.

One point worth emphasizing is that even for labor markets that to all appearances

is competitive, a moderately chosen minimum wage can increase employment. For ex12
ample labor market concentration might be considered a useful statistic for judging the

competitiveness of the labor market. However, as we have demonstrated, even for quite

large n, a minimum wage can still increase employment.

References

Bhaskar, V., A. Manning and T. To, “Oligopsony and Monopsonistic Competition in Labor

Markets,” Journal of Economic Perspectives, 16(2):155–174, 2002.

Bhaskar, V. and T. To, “Minimum Wages for Ronald McDonald Monopsonies: A Theory

of Monopsonistic Competition,” Economic Journal, 109:190–203, 1999.

Burdett, K. and D. T. Mortensen, “Wage Differentials, Employer Size, and Unemployment,” International Economic Review, 39(2):257–273, 1998.

Card, D. and A. B. Krueger, Myth and Measurement: The New Economics of the Minimum

Wage, Princeton, New Jersey: Princeton University Press, 1995.

Manning, A., Monopsony in Motion, London, UK: London School of Economics Press, 2002.

McCue, K. and W. R. Reed, “New Empirical Evidence on Worker Willingness to Pay for

Job Attributes,” Southern Economic Journal, 62(3):647–653, 1996.

Sattinger, M., “Value of an Additional Firm in Monopolistic Competition,” Review of Economic Studies, 51:321–332, 1984.

Walsh, F., “Comment on: ‘Minimum Wages for Ronald McDonald Monopsonies: A Theory of Monopsonistic Competition’,” Economic Journal, 113(489):718–722, 2001.

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