Labour and Labour Markets

Labour and Labour Markets

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).