Chapter 7 Wages and Employment in a Single Labor Market
LO1: THE COMPETITIVE FIRM’S INTERACTION WITH THE MARKET
We first examine the case in which the firm is a competitive seller of its output in the
prod- uct market and a competitive buyer of labour in the labour market. The firm is both
a price- and a wage-taker: it cannot influence either the product price or the wage rate.
Their supply schedules for a given homogeneous type of labour are perfectly elastic
(horizontal) at the market wage rate, W c
The firms are wage-takers, not wage-setters, and consequently can employ all of the
labour they want at THIS market wage rate.
The demand schedules determine the level of employment in each firm: in this case, N
and N u2its of labour
The demand schedules for labour in the two firms are the schedules of the value of the
marginal products of labour, defined as the marginal physical product of labour times the
price at which the firms can sell their products.
Only if the firms are selling the same output would their product prices have to be the
same; otherwise, p n1ed not equal p . 2* Chapter 7 Wages and Employment in a Single Labor Market
The market demand curve is the
summation of the demand curves of the
The market demand curve can be
obtained as follows.
For any specific wage rate, such as W 0
in Figure 7.1, determine the quantity of
labor that each firm in the market would
wish to employ.
For the two firms depicted in Figures
7.1(a) and (b), these quantities are N 0
and N , 2espectively. Adding these
quantities gives the total market demand
at that wage rate.
In summary, when the firm is a competitive buyer of labour, it faces a perfectly elastic
supply of labour at the market wage.
When the firm is a competitive seller of its output on the product market, it regards the
price at which it sells its output on the product market as fixed, and its derived demand
for labour schedule is the value of the marginal product of labour, defined as the marginal
physical product of labour times the fixed price at which the firm sells its output.
The intersection of the firm’s labour supply and demand schedules determines the
employment level of the firm for that particular type of labour.
This analysis was based on the long-run assumption that the firm could get all of the
labour it needed at the market-determined wage rate
Wages are determined elsewhere (In the aggregate labour market for that particular type
In the short run, however, even a firm that is competitive in the labour market may have
to raise its wages in order to attract additional workers This is referred to as dynamic
monopsony. Chapter 7 Wages and Employment in a Single Labor Market
In such circumstances, the
firm’s short-run labour
supply schedule could be
upward sloping, as S s
In the short run, in order to expand its workforce so as to meet an increase in the demand
for labour from D to D”, the firm may have to pay higher wages, perhaps by paying an
overtime premium to its existing workforce, or by paying higher wages to attract local
workers within the community.
The resultant expansion of the workforce can be depicted as a movement up the short-
run supply curve in response to the new higher wage of W , occassoned by the increase in
the demand for labour from D to D’.
Due to wages higher than the market wages, there will be a supply influx of other
workers, which shifts the supply Ss to S ’, sepress the temporarily high, short-run wage
of W bsck to its long-run level W c
Thus, the long-run supply of labour schedule to the firm, S , can be thought of as a locus
of long-run equilibrium points Chapter 7 Wages and Employment in a Single Labor Market
IMPERFECT COMPETITION IN THE PRODUCT MARKET
In the case of monopoly in the product market, the firm is the industry, and therefore
there is no need to distinguish between the firm’s labour demand and that of the industry
as a whole.
its output price is not fixed. For the monopolist, marginal revenue is the relevant factor.
- when the monopolist hires more labour to produce more output, not only does the
marginal physical product of labour fall (as is the case with the competitor), but also the
MR from an additional unit of output falls.
- Monopolist can sell more output only by lowering the product price and this, in turn,
- Both MPP anN MR fallQwhen N increases in (7.1), then the monopolist’s demand for
labor falls faster than it would be if it behaved as a competitive firm in the product
market, in which case only MPP woNld fall, as in (7.2)
Since MR 0
N = N D
Substituting W* into either the supply or demand equation yields the equilibrium
It is easy to add other variables (shifters) like the X or Z, to our models to make them
where Z, X represent other supply and demand factors that shift the position of the supply
and demand functions.
If we know how policy changes affect the position of the demand or supply function (i.e.,
how they affect a or c), then, given estimates of the other parameters, we can simulate the
effect of the policy change on the equilibrium. Chapter 7 Wages and Employment in a Single Labor Market
The equilibrium wage and
The slope of the supply function is
1/f, and the intercept is –c/f.
The demand function, after its axes
are switched the slope is 1/b, and
the intercept is -1/b.
In order to match the form of the above supply and demand equations with the
unconventional economists’ reverse representation of functions, it is worth re-expressing
these equations in terms of W as
These are equations for straight lines.
Slope 1/b. Intercept -a/b
Note that for these linear demand and supply functions, the absolute change or the slope
is constant, so the elasticity varies.
Since the elasticity is given by , if the slope is constant, the elasticity will vary
with W/N. Chapter 7 Wages and Employment in a Single Labor Market
It is sometimes useful to work with log-linear instead of simple linear functions.
The functional form for the supply and demand functions is given by
The convenience of the log-linear functional form
- the slope parameters 𝛽 and 𝜂 are the demand and supply elasticities.
- The slopes of the log-linear functions are constant, and so too are the elasticities.
Because economists often have estimates of these elasticities, the reduced form turns out
to be easier to use for simulating the impact of changes in policy.
𝑛 = 𝑙𝑜𝑔𝑁 𝑆
𝑛 = 𝑙𝑜𝑔𝑁
𝑤 = 𝑙𝑜𝑔𝑊
An equilibrium n* and w* will occur as before, where n = n , and implicitly N = N
Application: Incidence of a Unit Payroll Tax
A common use of these equilibrium models is in the evaluation of tax policy.
A payroll tax is a tax levied on employers, based on the level of employment, usually
proportional to the firm’s payroll
These taxes are often viewed as taxes on employers, rather than on workers.
As such, they are often attacked as taxes on jobs, or “job killers.”
By investigating the possible impact of such taxes on wages and employment, we can
evaluate the truth to these claims.
We will consider a simple per-unit tax, T, applied on a per-employee basis to firms.
We will use the linear system of equations to further simplify the analysis. Chapter 7 Wages and Employment in a Single Labor Market
Workers are paid the wage W for a unit of work, while firms pay W + T per unit hired—
W to the employee, and T to the government.
This is likely to reduce employment because it raises the cost of hiring labour. This
common sense ignores the impact of the tax on the labour market and the adjustments
that might occur.
The initial equilibrium is A, with equilibrium employment N and 0age W . 0
The imposition of the tax shifts the demand schedule N down by T units for every
The initial demand curve gives the optimal labour demanded at a cost of W per unit,
whereas the shifted curve accounts for the fact that the price of labour is now W + T.
If there were no other changes in the labour market (i.e., the wage stayed the same)
demand would fall from N to 0’.
However, as long as the supply curve is not horizontal, the equilibrium wage drops to
W , and employment falls only to N .
The lower wage effectively means that the workers pay some portion of the tax. Chapter 7 Wages and Employment in a Single Labor Market
In fact, at the new level of employment1 N , we can account for who pays the tax.
- Workers’ wages are lowered by W0 – W1 (BC), this represents their share.
- The remainder of T CD is paid by the firm.
Therefore, the incidence of the tax does not necessarily fall only on the party that
physically pays the tax or fills in the forms.
Algebraically, we can see this by substituting the appropriate post-tax prices into the
demand and supply equations:
𝑁 = 𝑎 + 𝑏 𝑊 + 𝑇 = 𝑎 + 𝑏𝑊 + 𝑏𝑇
𝑁 = 𝑐 + 𝑓𝑊
Set N = N S
𝑎 + 𝑏𝑊 + 𝑏𝑇 = 𝑐 + 𝑓𝑊
𝑎 − 𝑐 𝑏
𝑊 1 ( 𝑓 − 𝑏) − 𝑏 − 𝑓×𝑇 < 𝑊 0
With T, the worker’s wage is reduced from the original level by×T
This is the worker’s share of the taxes.
The worker’s share will depend on the relative slopes of the supply and demand
Note that the effect of a payroll tax may differ in the short and long run.
For example, if labour supply is perfectly inelastic in the long run (f =0), workers will
end up paying the entire tax and the employment level will be unaffected.
In the short run, with more elastic labour supply, firms will pay part of the tax, and
employment will be lower than before the tax. Chapter 7 Wages and Employment in a Single Labor Market
LO3 MONOPSONY IN THE LABOUR MARKET
In this section the assumption of being a competitive buyer of labour is relaxed.
So as to trace out the implications of this single change, termed monopsony, the firm is
still assumed to be a competiti