Labour and Labour Markets
- Text: Chapter 14
Introduction
- Importance of labour markets:
- most income is from wages and salaries;
- patterns of pay and employment: determined inlabourmarkets.
- Some key questions: who works, who doesn’t? what kind of work?
why are some people paid more than others?
- Modeling approach:
- typical micro approach: what would rational, self-interested
decision-makers do?
- Decision-makers: Supply – households/workers
Demand – businesses/employers.
- Main topics:
- labour supply decision and consumer theory;
- labour demand and the hiring decision;
- imperfect competition in labour markets: monopsony and unions.
(won’t do unemployment or search approaches: usually macro)
Supply of Labour
- An application of consumer theory.
- Assume people act rationally to maximize their own welfare (“utility”).
- Rationally: actions are consistent.
- Labour supply decision: decision to allocate time between uses.
- Uses?
- Work
- Leisure (any non-work use of time)
- house work
- raising children
- school
- entertainment etc.
- The decision to work (supply labour) involves a cost-benefit comparison:
- Benefit: value of labourincome earned
- Cost:value of the foregone non-work activities
disutility of work.
- Measure these values in terms of "utility"
- Valuation will depend upon the person's preferences.
- Captured in the form of the person's “utility function” (hypothetical
thinking tool)
Preferences: How the person values choices
- Utility function:
U = U(Y ,h)
Y - incomeh - leisure (hours)
- more Y or more h raises utility: both are goods.
- indifference curve: combinations of Y and hthat give exactly the
same amount of U.
- Shape of indifference curves:
- Negatively sloped: if Y is reduced the person must be given more
h if U is to remain the same.
- Convex shape: curve becomes flatter as you move down it.
-impliesvalue of a good is high when scarce and low when
abundant.
- practical importance of this assumption?
- interior solutions more likely.
- Marginal rate of substitution (MRS) between leisure and income.
- minus the slope of the indifference curve.
- measures value of an extra unit of leisure in terms of income.
- An indifference curve goes through each h, Y combination.
- Higher indifference curve means higher utility.
- Indifference curves cannot cross if the person is rational (otherwise ranking of
outcomes is contradictory)
Budget Line: What Choices are Possible?
- Shows the labour market tradeoff between h and Y.
- Time Constraint:T = J + h
T = total number of hours available
(text assumes focus is on a day then T=24 hours)
J = number of hours on the job (working)
h = hours of leisure
Note: choices to the right of h=T make no sense.
- Budget line shows what combinations of Y and h are attainable.
- Shows constraints the person faces.
- Income :Y = w J + N
w = wage rate (per unit of time worked)
J = time worked
N = non-labour income (interest, rental income, government
Transfers, etc.)
= 0 in the textbook examples.
- Combining the income and time constraints gives:
Y = wJ+ Nsubstitute: J= T - h
Y = w (T-h) + N
- Graph this: Y - vertical axis, leisure (h - horizontal axis
intercept (h=0): wT + N
slope:-w
- Hours of leisure (h): measured left-to-right.
- Hours of work (J): measured right-to-left.
- Attainable Y, h combinations: anything on the budget line.
Best Choice?
- The attainable Y,h combination that puts the person on the highest
indifference curve, i.e. that maximizes utility.
- Two types of solution:
(a) Interior solution: some time is allocated to h and some to J.
- Indifference curve tangent to budget line.
- marginal value of leisure time (measured in
income) equals the marginal of time at work.
MRS of leisure for income = w
($ value of leisure) ($ value of time at work)
(marginal value of leisure is the Marginal Rate of
Substitution (MRS) – slope of indifference curve)
- if not? Individual shifts more time into the higher
value use and becomes better off.
- Most people opt for the interior solution (labour force participants).
(Statistics Canada: January 2018, 64.6% of Canadian adults are labour force participants)
(b) Corner solution:
- All time is allocated to one use, either: h=T or J=T.
- Not-in-labour force: h=T , J =0 (non-participant)
- person chooses to not supply labour
- why? Value of time in leisure is always higher than w.
- this is not uncommon (about 1/3 of Cdn. adults).
- Other extreme: all work! T=J
- possible if wage is high relative to value of leisure.
- not of much practical importance.
What determines the best choice? (exogenous variables)
(1) Preferences
e.g. indifference curves become steeper: work less (more leisure).
(2) Non- labour income:
- rise in N:- work less if leisure is anormal good.
- work more if leisure is an inferior good.
(3) Wage rate: a rise in W has two effects
- income effect: richer so raise h if leisure normal, reduce le
if leisure is inferior.
- substitution effect: work time is more valuable so
substitute toward work.
Total effect = Income effect + Substitution effect
- Wage rise raises J if leisure is inferior (upward sloping labour
supply curve)
- Wage rise could raise or lower J if leisure is normal
i.e., is income or substitution effect stronger?
(diagram above: leisure is normal)
An Individual’s Labour Supply Curve
- Start at the best choice for given Non-labour income, preferences and wage.
- plot the value of W vs. J : one point on the labour supply curve.
- Let the wage change and find the new best choice.
- plot the new value of W vs. J: a second point on the labour supply curve.
- Continue: eventually trace out the entire labour supply curve:
- Shape of an individual’s labour supply curve?
- substitution effect and income effect of a wage change conflict (assuming
leisure is a normal good).
- labour supply curve could slope upward, downward or be backward
bending (as in Fig. 14-6 or above)!
Market labour supply curve:
- Horizontal sum (across hours worked) of labour supply curves of
individuals in that labour market.
Some Implications of the theory of labour supply:
(1)Provides a framework for thinking about labour supply behavior:
- a given pattern of behavior between people, times, places reflects:
(a) wage rates
(b) non-labour income
(c) preferences
- changes in labour supply behavior reflect these same factors.
(2)Suggests a tie between the decision-maker’s value of time and the wage
rate.
For a worker: value of time at the margin = wage rate
Complications and realism: is this a sensible model?
- It can be extended to allow for many uses of time (not just work and
leisure).
e.g. housework, education, etc.
- similar logic applies: allocate time to its highest value use.
- Is the budget line really just few points (part-time job, full-time job,
not working)?
- model works much the same!
- adjustments at a given employer limited, is choice
realized by moving between employers with different work-weeks?
- Unemployment: doesn’t it imply constraints on choice?
or is unemployment a decision to not work?
(voluntary vs. involuntary unemployment)
(model can be made more complex and realistic: but follows same
basic logic)
- Here worker chooses hours given the wage. Can build models
where different jobs offer different wage-hours packages.
Labour Demand: a Model of the Hiring Decision
Hiring Decision:
- Assume a profit maximizing employer.
- Hire another unit of labour if:
Benefit > Cost
- Cost of labour (per unit):
- all compensation costs: wage/salary, benefits, payroll tax, etc.
- call this the “wage” (W)
- Benefit of an extra unit of labour to the employer?
- value of output produced by the extra unit of labour.
e.g. if an extra worker raises output by 10 units and
sellingeach extra unit of output raises revenues by $20:
worker’s time is worth $200 to the employer
($20 x 10 units of output)
- This is “Marginal Revenue Product” (MRP) of the extra labour.
MRP = (Marginal Revenue) x (Marginal Product of labour)
Marginal product (MP) = extra output from the hiring of extra labour
(10 units of output in the example)
Marginal revenue (MR) = extra revenue from the sale of extra output
($20 in the example)
Note:
- if the output market is competitive firm is a price taker
- then: MR = Price
- so:MRP = Price x MP
= Value of marginal product (VMP)
(VMP is just a special case of MRP: text often uses VMP)
Shape of the MRP (or VMP) Curve in the Short-run:
- Short-run: there are fixed inputs used in combination with labour to
produce output.
- say that physical capital (machines, factory or store size) is fixed.
(Classic example of fixed factor: land)
- Plotting MP vs. units of labour (L):
- could slope upward initially (specialization, division of labour:
Smith’s pin factory).
- Law of Diminishing Returns (see Ch. 9) suggests that MP
eventually declines as more labour is added.
Why? Each unit of labour will have less fixed input towork with.
MP: downward sloping at higher L due to diminishing returns.
- So maybe:
- Note: MP is slope of the production function (last term: Figure 9-6)
- MRP curve:
- multiply MP curve by MR;
- if output market is competitive MR is a constant (price): MRP curve
has same shape of MP curve.
- if output market is imperfectly competitive:
- more L, more output, move down MR curve.
- Result? MRP has a more negative slope than if MR was
constant.
- Average Revenue Product (ARP):
- ARP is the average of the MRPs. For first unit of L ARP=MRP.
- ARP rising as long as MRP>ARP.
- ARP falling as long as MRP<ARP.
- ARP at maximum when ARP=MRP.
MRP Curve is the Short-run Labour Demand Curve:
- Say that the labour market is competitive:
- many small employers on the demand side;
- many workers supplying labour of this type.
- Each employer will be a “price taker”:
- must match the wage of competing employers;
(otherwise no one works for the employer)
- cost of labour: - flat line at the going wage rate.
- individual employer can hire as much as it likes
at this wage: flat labour supply to firm.
- Employer decision:
- Hire more workers if : MRP > W
- Lay off marginal workers if: MRP < W
- Optimal hiring level is where: MRP = W .
- The downward sloping part of MRP that is below ARP is the short-run
labour demand curve!
- given the wage hire where MRP = W (L* in the diagram)
(whyMRP below ARP? if MRP=W >ARP lose money!)
- Diagram: - Value of output: area under MRP up to L* (area A+B)
- Total wages paid: rectangular area W L* (area B)
- Area A?goes to the employer and other factors of production.
- Higher wage will means less labour demanded (move along MRP).
- Labour demand model:
- quantityof labourhired (L*) is endogenous;
- exogenous variables? wage, determinants of MRP.
Market Labour Demand Curve:
- Horizontal sum of the firm labour demand curves.
i.e. sum over quantities.
Implications of the Short-Run Theory of Labour Demand:
(1) Key determinants of labour demand are the determinants of MRP:
- Factors affecting Marginal productivity:
e.g., technology, organization of production, quantity and quality of other inputs.
- Factors affecting Marginal Revenue:
i.e., output market conditions --- level of demand for output (via
price of output produced).
- Explaining rising employment? (↑MRP)
- Rise in output price
- More or better non-labour inputs
- Better technology or organization.
- Explaining shifts in employment between firms, industries, occupations, regions? (determined by shifts in MRP)
If Industry A is drawing workers from Industry B then MRP in
A is higher than MRP in B at current employment levels.
- allows employers in A to pay higher wages and
bid workers away from industry B.
(see also textbook Figure 14.9)
(2) Wages and Productivity are linked:
- employers hire up to the point where W = MRP.
- competition between employers enforces this.
- explaining wage differences between people and jobs?
- theory says look at differences in productivity determinants.
- So the model implies: an NHL player, movie star or CEO are paid
a lot because their MRP is very high;
a fast-food worker, or textile worker is paid
little because MRP is low.
(differences in wages between countries: can they be explained in
terms of differences in determinants of MRP?)
- “Winner-take-all” markets and “Superstars” (see pp. 488 new edition,
section 14.14 old edition):
- in some cases small differences in skill or ability lead to
much different MRPs and wages.
- the“best” are paid massively more than the next best.
- thiscan occur even though the “best” is only slightly “better”
than the next best.
i.e. small differences in skill are magnified into large
differences in value and pay.
- Rooted in the nature of the service being provided.
- actor, author, athlete: large audience and a consumer taste for
the best.
- competitive situation: winner does far better than others.
(text: lawyer example. CEOs?)
Long-run Demand for Labour:
- Labour demand in the long-run (long-run: employer can vary all inputs)
- can change the amount of fixed inputs in the long-run (affects MRP)
- firm may change the labour intensity of production in the long-run.
e.g., substitute physical capital for labour if wages rise.
- the possibility of substitution can make long-run labour demand
curves more elastic than short-run labour demand curves.
- prices of non-labour inputs are also determinants of labour demand.
(see Ch. 9 (new) Ch. 10 (old): using isoquant-isocost framework)
Supply-Demand in Labour Markets
- Wage determination in a competitive labour market?
- Usual Supply-Demand story:
- wages rise if excess demand ; wages fall if excess supply.
- Equilibrium wage?Labour supply = Labour demand
- At this outcome:
- time is allocated to its highest value use.
- if MRP > value of leisure time the wage offered will be high
enough to induce the person to work.
(efficient: time is allocated to its highest value use; workers-
employers split the surplus;surplus maximized)
- Supply shifts reflect: changing value of time, non-labour income, #people.
- Demand shifts reflect: changes in determinants of MRP, number of
employers.
- Usual Supply-Demand comparative statics
e.g. demand shift right W and L rise.
Monopsony
- Monopsony: “one buyer”
- chapter discusses this as a labour market model.
- monopsony can arise in goods markets as well.
- Focus of the chapter is on a “single-price” monopsonist.
- like monopoly, price discrimination (wage discrimination) is an attractive
option if possible.
- Only one employer of a type of labour
- The employer is not a wage-taker: hiring decisions affect the
wage that must be paid.
i.e. faces the supply curve for that type of labour.
- Cost of an extra unit of labour = marginal factor cost of labour = MFC
- For monopsony:
MFC >W
Why? - The employer must raise the wage to hire one more unit of L.
- So MFC is:
- the wage paid, PLUS
- the increase in wages paid to all other units of labour
MFC = W + L x W/L > W
Where W/L is the rise in W needed to attract more L.
- So:
- Hiring decision with monopsony?
- Hire more L as long as the benefit (MRP) exceeds cost of more L
(MFC).
- L will be at the level where:
MRP = MFC (LM in diagram below)
- What wage is paid? (W=WM in diagram)
- height of labour supply curve at value of L where:
MRP = MFC.
- Note: W< MRP
- The worker is paid less than the value of their
contribution to output
- Wage will be less than in a competitive labour market.
i.e. competition ensures W = MRP where MRP=Labour Supply.
(Wcomp with employment Lcomp below)
- L exchanged is less than in the competitive case:
- some workers for whom MRP > W are not hired.
- outcome is inefficient:
- some jobs for which MRP > value of worker’s time
don’t exist.
- why? Restricting hiring keeps monopsonist wage down.
- Size of underpayment (gap between MRP and W)?
- depends on the elasticity of labour supply
- Hire until:
MRP =W + L x W/L
MRP = W { 1 + (L/W) x W/L) }
= W { 1 + 1/ }
where: = (L/L) = wage elasticity of labour
(W/W) supply
- pay is closer to MRP the more elastic is labour supply (high ).
i.e. monopsonist is most powerful if workers are immobile.
- Algebraic example:
MRP = a – b L
Labour supply: W = c + v L
MFC = W + L x W/L
= (c + v L) + L x v = c + 2v L
Hire until: MRP =MFC
a-bL = c + 2vL
L = (a-c)/(b+2v)
Wage: W = c + v x (a-c)/(b+2v) (subst. L into labour supply)
Wage Discrimination in Monopsony:
- Modeling wage discrimination is similar to modeling price discrimination.
- Wage discrimination faces information problems:
- employer needs to know wage at which different workers are willing
to work.
- workers have no incentive to reveal that they are willing to work for
a low wage.
- Employer’s ideal: “Perfect wage discrimination”
- pay each worker the minimum they require to supply labour
i.e. height of the labour supply curve at each L.
- result: hire until MRP = labour supply curve
- each L paid different wage.
- outcome is efficient but all surplus to employer.
- requires a lot of information in practice!
- Wage discrimination between broad groups of workers:
- say employer knows two groups have different supply curves
- groups will have different MFC curves as well (say MFC1 and
MFC2).
- hiring decision:
- hire more as long as: MRP > MFC for one of the groups.
- at the margin always hire worker from the group with lower
MFC.
- at the profit maximizing outcome (if hiring from both groups):
MRP = MFC1 = MFC2
- wages will differ between the two groups
- difference related to the form of the labour supply
curve.
- elasticity of labour supply important to wage paid:
W1 { 1 + 1/ }= W2 { 1 + 1/ }
W1, W2 = wage of group 1,2
= labour supply elasticities of 1,2
So wage is lower the lower is the elasticity (more
inelastic is labour supply).
- can this explain differences in pay between groups e.g.
men vs. women?
- Wage discrimination by number of hours worked: is overtime pay an
example of wage discrimination?
Effects of a Minimum Wage Law
- A minimum wage is an example of a price floor.
- government makes it illegal to pay wages below the minimum.
(a) Effects in a competitive labour market:
- To have any effect the minimum wage (M) must be above the
competitive wage (Wc).