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 in labour markets.

- 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.

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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?

- Paid Work (just call it work below)

- 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 labour income earned

- Cost: value of the foregone non-work activitiesdisutility 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)

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Preferences: How the person values choices

- Utility function:U = U(Y , h)

Y - income h - leisure (hours)

- more Y or more h raises utility: both are goods.

- indifference curve: combinations of Y and h that 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.

-implies value of a good is high when scarce and low when abundant.

- practical importance of this assumption?- interior solutions more likely.

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- 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)

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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 are impossible.

- Budget line shows what combinations of Y and h are attainable.

- 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.

(ASIDE: This assume the person is an employee. We could allow for self-employment then wJ is replaced with some function G(J) determined by rate at which time can be turned into self-employment income)

- Combining the income and time constraints gives:

Y = wJ+ N substitute: J= T - h

Y = w (T-h) + N

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- 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.

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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.

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- 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).

( Another extreme: all work! T=J. Possible if wage is high relative to value of leisure. Of no practical importance )

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What determines the best choice? (exogenous variables)

(1) Preferencese.g. indifference curves become steeper: work less (more leisure).

(2) Non- labour income:- rise in N: - work less if leisure is a normal good.

- work more if leisure is an inferior good.

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(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 normali.e., is income or substitution effect stronger?

(diagram above: leisure is normal)

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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:

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- 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.

- Is the market curve more likely to slope upward due to wage effects on non-participation?

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 changes in 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

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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)

- Here worker chooses hours given the wage. Can build models where different jobs offer different wage-hours packages.

- similar underlying logic: choose the package that makes you happiest.

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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 selling each 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)

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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 to work with.

MP: downward sloping at higher L due to diminishing returns.

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- 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.

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- 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.

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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.

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- 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)

(why MRP 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.

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- Higher wage means less labour demanded (move along MRP).

- Labour demand model:

- quantity of labour hired (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.

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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.

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- 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)

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(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?)

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- “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.

- this can 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?)

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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)

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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

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e.g. demand shift right W and L rise.

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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

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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

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- 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.

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- 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 + 2vLL = (a-c)/(b+2v)

Wage: W = c + v x (a-c)/(b+2v) (subst. L into labour supply)

Wage Discrimination in Monopsony:

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- 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 labouri.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):

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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?

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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).

- Effect?

- employment falls along the demand curve (Lc to Lmin).

- excess supply of labour (unemployment: Ls-Lmin).

- Welfare effects:

- Efficiency loss (A+B) results due to the decline in employment (value of time to employer was

greater than value in non-work uses)

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- Employers are worse off:

- pay more for workers they still hire.

- lose former profits on jobs that no longer exist.

- Low-skill workers:

- overall whether total wages rise or fall depends on the elasticity of labour demand.

(total rises if inelastic)

- those with jobs gain (C), those without lose.

(b) Monopsony and Minimum Wage:

- Strange result is possible.

- With a minimum wage marginal factor cost (MFC) is flat up to the point where M hits the labour supply curve.

- over some range MFC is actually lower than with no minimum wage.

(why? Initially there is no need to raise the wage when hiring more)

- it is possible that a minimum wage could raise employment (diagram)

- but if set too high employment still falls.

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- Case where minimum wage is low enough that employment rises:

- Low-skill labour markets seem unlikely to be monopsonies.

- retail, fast-food, services: typical minimum wage industries.

- many employers.

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Models with Labour Unions

- Common approach:

- model a union as a cartel or monopoly.

- controls the supply of labour to the firm.

- Text: unions raise wages in the union sector.

(like a monopolist raising the price of their good)

- You could model union effects as like those of a minimum wage.

- so: likely to lower employment in the union sector.

- A complication?

- minimum wages raise wages for almost all low-skill workers.

- unions: directly raise wages of union sector worker

- If this lowers employment in the union sector workers those who lose jobs may move to the non-union sector and depress wages there.

- Other approaches?

- Assume a union utility function: U(W, E) union cares about wage levels and employment levels of its members.

- union negotiates a contract (values of W and E) with a profit maximizing employer.

- bargain reflects different W,E tradeoffs the of the employer and union and relative bargaining power.

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