Week 4: Labour Markets

Working-age population (WAP)

The population within the age range used as the base for labour market statistics (e.g. 15-64 years); the denominator for participation and employment rates.

Labour force (L)

The sum of employed and unemployed people; those who are either working or actively seeking work. L = E + U.

Employed (E)

People who currently have a job (working for pay or profit, including unpaid work in a family business under most classifications).

Unemployed (U)

People without a job who are actively looking for work and available to start.

Unemployment rate (UR)

U/L, the share of the labour force without a job.

Labour force participation rate (LFPR)

L/WAP, the share of the working-age population that is in the labour force (employed or unemployed).

Employment rate / absorption rate (AR)

E/WAP, the share of the working-age population that is employed.

Not economically active

WAP - L; people of working age who are neither employed nor counted as unemployed (not actively seeking work).

Discouraged workers (DW)

People who want a job and would take one if offered, but are not counted as officially unemployed because they are not actively searching.

Expanded unemployment rate (EUR)

(U+DW) / (L+DW); an unemployment measure that includes discouraged workers as part of both the numerator and an expanded labour force.

Reservation wage

The wage that would make a worker indifferent between working and remaining unemployed.

Efficiency wage theory

The idea that paying workers more than the reservation wage can raise their productivity and effort, and reduce costly turnover.

Collective bargaining

Wage negotiation between firms/employers and organized groups of workers (unions), rather than individual bargaining.

Labour productivity (A)

Output per worker, Y/N; in the production function Y=AN, A is exactly labour productivity.

Production function (this chapter)

The relationship between labour input and output; this chapter assumes the simple form Y = AN.

Markup (m)

The amount by which firms price above marginal cost; in the price-setting relation P=(1+m)W (with productivity A=1), a higher m means firms charge more relative to their labour cost.

Wage-setting (WS) relation

The relationship W = P^e F(u,z) between the nominal wage chosen in wage bargaining, the expected price level, the unemployment rate, and other factors z; F is decreasing in u and increasing in z.

Price-setting (PS) relation

The real wage implied by firms' pricing decisions, W/P = 1/(1+m); independent of the unemployment rate, so it is a horizontal line in (u, W/P) space.

Natural rate of unemployment

The unemployment rate at which the real wage chosen in wage-setting equals the real wage implied by price-setting: F(u_n,z) = 1/(1+m).

Natural level of employment

The level of employment consistent with the natural rate of unemployment: N_n = L(1 - u_n).

Natural level of output

The level of output produced at the natural level of employment: Y_n = A x N_n.

Employment protection

Regulations that make it more costly for firms to lay off workers; one of the factors bundled into the catch-all variable z.

Unemployment insurance/benefits

Payments made to workers who lose their jobs; a factor bundled into the catch-all variable z in the wage-setting relation.

Catch-all variable (z)

A variable in the wage-setting relation standing for all factors other than the expected price level and the unemployment rate that affect wage setting (e.g. unemployment benefits, employment protection); higher z raises wages.

Active vs sclerotic labour market

An "active" labour market has many separations and hires (workers frequently entering/exiting unemployment) at a given unemployment rate; a "sclerotic" one has few separations and hires and a stagnant pool of unemployed people.

Henry Ford's 1914 "$5 day" wage experiment

Ford raised pay for qualified workers to $5 for an 8-hour day (up from roughly $2.30 for a 9-hour day); turnover and layoff rates fell dramatically afterward, and it is widely cited as early evidence for efficiency wage theory.

Why the unemployment rate alone can be misleading about labour-market dynamics

A given UR can arise in an active market (lots of flows in/out of unemployment) or a sclerotic one (few flows, unemployed people stay unemployed a long time); the UR number alone doesn't reveal which situation an economy is in.

Why the official UR can understate labour-market distress

Discouraged workers who want a job but stop actively searching are not counted as unemployed (they fall into "not economically active"), so a rise in discouraged workers can make the official UR look better than the true state of the labour market; this is why the EUR is used alongside it.

Why the nominal wage depends on the expected price level, not the actual price level

Wages are typically set in advance (via contracts/agreements) before the actual price level for that period is known, so bargainers must use their best expectation, P^e, rather than the (unknown) actual P.

If expected prices rise by X%, holding u and z fixed, what happens to the nominal wage and the real wage implied by wage-setting?

Since W = P^e x F(u,z) and F(u,z) is unchanged (u and z fixed), the nominal wage W rises by exactly the same X% as P^e (they are proportional); the real wage W/P^e = F(u,z) stays exactly the same, unaffected by the change in expected prices.

Why higher unemployment lowers wages

Higher unemployment weakens workers' bargaining power (it's easier for firms to find replacement workers and harder for workers to find another job), so firms can pay lower wages and still keep enough workers.

What determines a worker's bargaining power

How costly it is for the firm to find other workers, and how easy it is for the worker to find another job if they left the firm.

Why efficiency wages can be individually rational for a firm even though they pay above the reservation wage

Paying more than the minimum needed reduces costly turnover and can raise effort/productivity, especially where morale and commitment matter for output quality; the resulting productivity and retention gains can offset the extra wage cost.

Why the wage-setting relation is ultimately about the real wage, not the nominal wage

Both workers and firms care about what the wage can actually buy (W/P), not the nominal currency amount, so the economically meaningful relation is expressed in real terms.

Why the price-setting relation is a horizontal line in (u, W/P) space

Firms set P=(1+m)W based on their markup over cost, which does not depend on the unemployment rate; so the real wage implied by pricing, 1/(1+m), is the same regardless of u.

Why the WS curve is downward sloping in (u, W/P) space

As unemployment rises, wage-setters accept a lower real wage because their bargaining power weakens, so the real wage chosen in wage setting falls as u rises.

Why the natural rate of unemployment is where WS and PS intersect

It's the unique unemployment rate at which the real wage that wage-setters demand exactly equals the real wage that price-setters are willing and able to pay; at any other u, the two real wages are inconsistent and there is pressure for wages/prices to adjust.

Why an increase in the markup (m) raises the natural rate of unemployment

A higher m lowers the price-setting real wage 1/(1+m), shifting the PS line down; the WS curve is unchanged, so the new equilibrium is at a higher u, because it now takes more unemployment (weaker bargaining power) to make wage-setters accept the lower real wage firms are offering.

Why an increase in unemployment benefits (part of z) raises the natural rate of unemployment

Higher unemployment benefits make being unemployed less costly, so at any given u workers/unions can hold out for a higher real wage (F increases), shifting the WS curve up; since PS is unchanged, equilibrium moves to a higher natural rate of unemployment.

Why a minimum wage above the market-clearing wage raises the natural rate of unemployment

A binding minimum wage effectively raises the real wage demanded at low unemployment rates, so it takes a higher unemployment rate to bring the wage-setting real wage down to what price-setting implies.

What "natural" means in natural rate of unemployment, natural employment, and natural output

It does not mean fixed forever or optimal — it means the rate/level consistent with wage-setting and price-setting being mutually consistent, holding structural factors (z, m) constant; it changes if those structural factors change.

Why economists sometimes look at the employment rate instead of the unemployment rate

Because many people classified as "not in the labour force" are actually discouraged workers who would take a job if offered one, the unemployment rate can miss part of the picture; the employment rate (E/population) avoids relying on the labour-force classification.

Why, in the labour supply/demand appendix, the WS relation becomes upward-sloping in employment (N) rather than downward-sloping

Since unemployment u = L - N, higher employment N corresponds to lower unemployment u; because the real wage in wage-setting falls as u rises, it rises as N rises, so plotting against N (instead of u) flips the slope to upward.

Unemployment rate vs expanded unemployment rate

UR = U/L uses only the official labour force (employed + unemployed actively searching); EUR = (U+DW)/(L+DW) also counts discouraged workers as both unemployed and part of the labour force, giving a higher and arguably more complete picture of labour underutilization.

Labour force participation rate vs employment (absorption) rate

LFPR = L/WAP measures how many working-age people are engaged with the labour market at all (working or seeking work); AR = E/WAP measures how many are actually employed; the gap between them is driven mainly by unemployment.

Wage-setting relation vs price-setting relation

The WS relation describes the real wage workers/unions can obtain given the unemployment rate (downward sloping in u); the PS relation describes the real wage firms are willing to pay given their pricing behaviour (horizontal, set by the markup); their intersection pins down the natural rate of unemployment.

Natural rate of unemployment vs actual unemployment rate

The natural rate is the medium-run equilibrium rate consistent with WS=PS; the actual rate can differ from it in the short run (e.g. if P differs from P^e), but tends to return to the natural rate over the medium run as expectations adjust.

Unemployment rate formula

UR = U / L = U / (E+U), expressed as a percentage.

Labour force participation rate formula

LFPR = L / WAP = (E+U) / WAP, expressed as a percentage.

Employment (absorption) rate formula

AR = E / WAP, expressed as a percentage.

Expanded unemployment rate formula

EUR = (U + DW) / (L + DW) = (U+DW) / (E+U+DW), expressed as a percentage.

Wage-setting relation (general form)

W = P^e F(u,z), or in real terms W/P^e = F(u,z), where F is decreasing in u and increasing in z.

Price-setting relation (with productivity A=1)

P = (1+m)W, which implies the real wage from pricing: W/P = 1/(1+m).

Natural rate of unemployment condition

Setting the WS and PS real wages equal (using P^e=P): F(u_n, z) = 1/(1+m). Solve this equation for u_n once you're given a specific functional form of F.

Natural level of output formula

Y_n = A x N_n, where N_n = L(1 - u_n) is the natural level of employment implied by the natural rate of unemployment.

Labour market stats calc: WAP=60m, E=30m, U=6m, DW=4m. Find UR, LFPR, AR, EUR, and the number not economically active.

L=E+U=36m. UR=6/36=16.7%. LFPR=36/60=60.0%. AR=30/60=50.0%. EUR=(6+4)/(36+4)=10/40=25.0%. Not economically active = WAP-L = 60-36=24m.

Labour market stats calc: WAP=300m, E=140m, U=20m. Find the unemployment rate and the labour force participation rate.

L=140+20=160m. UR=20/160=12.5%. LFPR=160/300=53.3%.

Natural rate calculation: F(u,z)=z-u, with z=0.9 and m=20%. Find the natural rate of unemployment.

1/(1+m)=1/1.2=0.8333. Set z-u_n=1/(1+m): 0.9-u_n=0.8333, so u_n=0.9-0.8333=0.0667, i.e. u_n ~= 6.67%.

Natural rate calculation: F(u,z)=z-u, with z=1.1 and m=10%. Find the natural rate of unemployment.

1/(1+m)=1/1.1=0.9091. Set z-u_n=1/(1+m): 1.1-u_n=0.9091, so u_n=1.1-0.9091=0.1909, i.e. u_n ~= 19.09%.

Production function calc: Y=AN with A=25 and N=8 million workers. Find output Y and confirm labour productivity.

Y = A x N = 25 x 8 = 200 million (units of output). Labour productivity = Y/N = 200/8 = 25 = A, confirming that in Y=AN, A is exactly output per worker.

Natural output calc: A=20, labour force L=50 million, natural rate of unemployment u_n=8%. Find the natural level of employment and natural level of output.

N_n = L(1-u_n) = 50 x (1-0.08) = 46 million. Y_n = A x N_n = 20 x 46 = 920 million.

Expected-inflation calc: expected prices are set to rise by 8% next year, with u and z unchanged. Using W=P^e F(u,z), find the resulting change in the nominal wage and the real wage.

Nominal wage W rises by exactly 8% (since W is proportional to P^e). Real wage W/P^e = F(u,z) is unchanged (0% change), since F(u,z) did not change.

Labour market stats family: WAP=80m, E=45m, U=5m, DW=6m. Compute UR, LFPR, AR, and EUR (1 d.p.), and explain what the gap between UR and EUR tells you.

L=45+5=50m. UR=5/50=10.0%. LFPR=50/80=62.5%. AR=45/80=56.3%. EUR=(5+6)/(50+6)=11/56=19.6%. The gap (10.0% vs 19.6%) shows that once discouraged workers are counted, labour-market slack is roughly double what the official rate suggests.

Using the WS and PS relations, explain and sketch the effect of a decrease in the markup on the equilibrium real wage, the natural rate of unemployment, natural employment, and natural output.

A lower m raises the price-setting real wage 1/(1+m), shifting the PS line up; the WS curve is unchanged, so the new intersection has a higher equilibrium real wage and a lower natural rate of unemployment u_n; since N_n=L(1-u_n), natural employment rises, and since Y_n=A x N_n, natural output rises too.

Given W=P^e F(u,z) and P=(1+m)W, with P^e=P, derive the general condition that defines the natural rate of unemployment (do not assume a specific F).

From wage-setting: W/P=F(u,z) (using P^e=P). From price-setting: P=(1+m)W, so W/P=1/(1+m). Setting the two expressions for W/P equal gives F(u_n,z)=1/(1+m), the condition that implicitly defines the natural rate u_n.

If Y=BN, what does labour productivity equal, and why are 1/B and N/Y not correct answers?

Labour productivity is output per worker, Y/N; substituting Y=BN gives Y/N=B, so labour productivity equals B. 1/B and N/Y are the inverse of this and don't mean "output per worker" (N/Y would be "workers per unit of output", the reciprocal of productivity).

Under perfect competition, price equals marginal cost, so in P=(1+m)W (with labour productivity A=1) the markup m must equal 0. What real wage does this imply?

If m=0, then P=(1+m)W=W, so W/P=1: the real wage equals 1, i.e. firms pay workers the full value of what they produce, with no markup taken.

Which of these people counts as "unemployed" in the standard definition: (a) works part-time, (b) works unpaid in a family business, (c) has no job, isn't looking, and isn't available to start, (d) has no job, is actively looking, and is available to start?

Only (d): someone with no job who is actively searching and available to work. (a) and (b) count as employed; (c) is not economically active (or a discouraged worker if they'd take a job when offered one), not officially unemployed.

A fall in the unemployment rate occurs. Does this change the real wage implied by the price-setting (PS) relation? Explain.

No change — the PS relation, W/P=1/(1+m), depends only on the markup m, not on u; a change in unemployment moves the economy along the (unchanged) PS line without shifting it or being affected by it. Only the WS relation's real wage responds to u.

Explain the effect of a fall in the unemployment rate on the real wage, from the perspective of (1) the wage-setting relation, and (2) the price-setting relation.

(1) Via wage-setting: a lower u strengthens workers' bargaining power, so the real wage implied by WS (F(u,z)) rises - movement along the downward-sloping WS curve to a higher real wage. (2) Via price-setting: no effect - the PS real wage, 1/(1+m), does not depend on u at all, so it stays exactly the same.

Explain what the labour force participation rate represents, and give one plausible reason it might rise over a 10-15 year period in an economy.

LFPR = (E+U)/WAP, the share of the working-age population that is either working or actively looking for work. A plausible reason for a rise: more women entering the labour force over time, rising education levels increasing job-market engagement, or economic necessity (e.g. household income pressures) pushing more working-age people to seek work.

Explain how a rise in each component (E, U, WAP considered separately) would change the unemployment rate, holding the others fixed.

A rise in E (holding U fixed) lowers UR, since L=E+U grows while U (the numerator) is unchanged. A rise in U (holding E fixed) raises UR, since both the numerator and L rise, but the unemployed share increases. A change in WAP alone does not directly change UR, since WAP doesn't enter the UR formula (U/L) at all - it only affects LFPR and AR.

Define the reservation wage and explain, using efficiency wage theory, why a firm might rationally choose to pay above it.

The reservation wage is the wage at which a worker is indifferent between working and being unemployed. Efficiency wage theory argues that paying above this wage can reduce costly employee turnover and increase effort/productivity/morale, particularly where the quality of work depends on commitment; the resulting productivity and retention gains can outweigh the extra wage cost, especially when unemployment is low and quitting is easy.

Sketch and explain, using the WS-PS diagram, the effect of a rise in the minimum wage on the natural rate of unemployment, assuming it binds above the wage that would otherwise prevail at low unemployment.

A binding minimum wage effectively raises the real wage floor at low unemployment rates, above what F(u,z) alone would generate; since firms' pricing behaviour (the PS line) is unchanged, equilibrium moves along the PS line to a higher u - the natural rate of unemployment rises, because it now takes more slack in the labour market to bring wage demands down to the level compatible with firms' pricing.

Briefly explain three distinct types of policy that could lower an economy's natural rate of unemployment, using the WS-PS framework.

(1) Reducing the generosity of unemployment benefits (lowers z, shifting WS down, lowering u_n); (2) increasing product-market competition to reduce firms' market power and markup m (shifts PS up, lowering u_n); (3) improving labour-market matching and training programmes to reduce structural mismatch between available jobs and workers' skills (reduces frictional/structural unemployment without necessarily hurting worker bargaining power).

An economy has A=15, L=40 million, and a natural rate of unemployment of 7%. If a policy reform lowers u_n to 5% with A and L unchanged, calculate the resulting change in the natural level of output.

Before: N_n=40x0.93=37.2m, Y_n=15x37.2=558m. After: N_n=40x0.95=38.0m, Y_n=15x38.0=570m. Natural output rises by 570-558=12 million (about 2.2%), purely from more people being employed at the same productivity.

A country's official UR is low (5%) but its EUR is much higher (18%), while its LFPR has been falling for a decade. What does this combination most likely indicate about the labour market?

It suggests substantial hidden slack: many working-age people have given up actively searching (becoming discouraged workers or dropping out of the labour force) rather than finding jobs, so they don't show up in the official UR but do show up in the EUR and the falling LFPR - the low official UR is likely overstating labour-market health.

Common mistake: using WAP as the denominator for the unemployment rate

UR = U/L (the labour force), not U/WAP; using WAP would understate the unemployment rate because it includes people not in the labour force (e.g. students, retirees) who aren't part of the relevant base.

Common mistake: treating "not economically active" and "unemployed" as the same thing

Being unemployed requires actively searching for and being available for work; someone who isn't looking (and isn't a discouraged worker who would take a job if offered) is "not economically active," not "unemployed" - this distinction is exactly why the official UR can differ from EUR.

Common mistake: assuming labour productivity is N/Y instead of Y/N

Labour productivity is output per worker (Y/N); N/Y is its reciprocal (workers needed per unit of output) and represents something different.

Common mistake: forgetting that the PS relation doesn't depend on u

Students sometimes try to plug u into the price-setting relation W/P=1/(1+m); the PS line is horizontal in (u, W/P) space precisely because it has no u term - only the markup m determines it.

Common mistake: mixing up which curve shifts for a wage-side vs a pricing-side shock

Changes to z (e.g. benefits, employment protection) shift the WS curve; changes to m (markup/competition) shift the PS curve. Shifting the wrong curve when asked to analyse a specific shock (e.g. "an increase in the markup") is a common exam error - always check whether the shock affects wage-setting (z) or price-setting (m).

Common mistake: assuming a higher natural rate of unemployment always means a "worse" or badly-managed economy

The natural rate reflects structural features of the labour market (bargaining power, benefits generosity, markups) - it isn't a business-cycle indicator, and a change in it doesn't necessarily mean short-run mismanagement; short-run deviations of the actual rate from the natural rate are the business-cycle concern.

Integrated: Explain the full chain from an increase in the markup (m) to a change in the natural level of output (Y_n), naming every relation involved.

A higher m lowers the price-setting real wage 1/(1+m), shifting the PS line down in (u, W/P) space; with the WS curve unchanged, the new WS-PS intersection occurs at a higher natural rate of unemployment u_n (F(u_n,z)=1/(1+m) requires higher u_n to lower F to the new, lower 1/(1+m)); a higher u_n means lower natural employment N_n=L(1-u_n); with productivity A unchanged, natural output Y_n=A x N_n falls.

Integrated: A country simultaneously experiences rising unemployment benefits (z rises) and increased product-market competition (m falls). What happens to the natural rate of unemployment, and why is the net effect ambiguous without knowing the relative sizes of the shocks?

Rising z shifts the WS curve up (raises u_n, all else equal); falling m shifts the PS curve up (lowers u_n, all else equal). The two shocks push the natural rate in opposite directions, so the net effect on u_n depends on which effect dominates - without knowing the magnitudes of the shift in z versus the shift in m, the direction of the net change cannot be signed.

Integrated: Using both the unemployment-rate statistics (UR, LFPR, EUR) and the WS-PS model, explain why a fall in u_n (a "good" structural change) might not immediately show up as a fall in the measured UR.

The WS-PS model determines the natural (medium-run equilibrium) rate, but the measured UR reflects the actual rate, which can deviate from the natural rate in the short run (e.g. during a cyclical downturn, or if prices differ from what was expected when wages were set); also, if LFPR rises at the same time (e.g. previously discouraged workers start actively searching again), the measured UR could rise briefly even as the underlying natural rate falls, since newly-searching entrants are initially counted as unemployed until they find work.