Principles of Economics and Management I
Session 9 ยท Unemployment, Inflation and the Labor Market
Introduction
๐ Where We Came From
We already know how to measure a countryโs output and what makes it grow in the long run.
Today we look at the two variables central banks watch most closely: unemployment and inflation. ๐
And at the end, at the relationship between them: the Phillips curve. ๐
๐บ๏ธ Todayโs Map
- ๐ฅ Measuring unemployment
- ๐ท Supply, demand and wage rigidity
- ๐งฉ Types of unemployment and the natural rate
- ๐ถ Measuring inflation: the HICP
- ๐ The Phillips curve
Part 1 ยท The Labor Market and Unemployment
๐ฅ Splitting the Population
Not everyone who is not working is unemployed. First, we split the adult population.
๐ท Employed: they have a job.
๐ Unemployed: they have no job, but are actively looking.
๐๏ธ Out of the labor force: they neither work nor look (students, retirees).
๐ The Unemployment Rate
The labor force is the employed plus the unemployed.
\[ \text{Unemployment rate} = \frac{\text{Unemployed}}{\text{Labor force}} \times 100. \]
Note: those outside the labor force do not enter. Anyone who gives up looking drops out of the calculation. ๐ค
โ ๏ธ An Important Detail
If many people give up looking, they leave the labor force.
The unemployment rate can fall without anyone having found a job.
That is why we also look at the participation rate: what fraction of the adult population is in the labor force. ๐
๐ Source: OpenStax Macro 3e, ยง8.1 โHow Economists Define and Compute Unemployment Rateโ, โHidden Unemploymentโ, โLabor Force Participation Rateโ and โCriticisms of Measuring Unemploymentโ.
๐ท Labor Supply and Demand
Just as in micro: the demand for labor comes from firms, the supply from households.
Demand depends on the marginal productivity of labor; supply, on the choice between work and leisure.
In a flexible market, the wage adjusts until there is no involuntary unemployment. But the real world does not work that way. ๐ค
๐ง Why Wages Are Rigid
If wages were fully flexible, there would be no persistent unemployment. But there is rigidity:
๐ผ Efficiency wages: paying above market raises productivity and reduces turnover.
๐ Contracts and unions: wages set for fixed periods, hard to lower.
๐งฑ Minimum wage and social norms: legal floors and resistance to nominal cuts.
๐ Source: OpenStax Macro 3e, ยง8.3, โWhy Wages Might Be Sticky Downwardโ, which gives the same reasons and adds the insider-outsider and relative wage arguments.
๐ Rigidity Generates Unemployment
A wage above equilibrium: more people want to work (7) than firms hire (3).
๐งฉ Types of Unemployment
โณ Frictional: between jobs, searching for the next one. It is normal and even healthy.
๐๏ธ Structural: skills do not match the vacancies (technological change, declining sectors).
๐ก๏ธ Cyclical: the kind that rises in recessions, when aggregate demand falls.
๐ฏ The Natural Rate of Unemployment
Even in a healthy economy, unemployment is never zero.
Natural rate: frictional plus structural unemployment, when there is no recession.
Cyclical unemployment is the deviation from this natural rate. ๐ก๏ธ
๐ Unemployment Is a Flow, Not a Stock
A useful way to see why the natural rate is positive. Let \(s\) be the rate at which the employed lose jobs and \(f\) the rate at which the unemployed find them.
In steady state, the flow in equals the flow out: \[s\,(1 - u) = f\,u \quad \Longrightarrow \quad u = \frac{s}{s + f}\]
Unemployment is positive whenever \(s > 0\), however efficient the market is. A pool with water flowing in and out is never empty.
And it tells you what policy can actually move: the separation rate \(s\) (employment protection, restructuring) and the finding rate \(f\) (matching, training, benefit design). ๐ฏ
๐ช๐บ Portugal and the Euro Area
Portugal started much higher in 2015 and converged. Source: Eurostat. ๐
๐ Review ยท Part 1
Two multiple choice questions and one exercise. โ๏ธ
โ Multiple Choice 1
A long spell of bad news leads many jobseekers to give up looking. Employment does not change. The measured unemployment rate:
A. Falls, because those people leave the labor force entirely.
B. Rises, because more people are without work.
C. Does not move, because employment did not move.
D. Cannot be computed without the participation rate.
โ A. They stop being counted in both the numerator and the denominator, so the rate improves while the situation does not. Watch the participation rate alongside it, which is exactly why it is published.
โ Multiple Choice 2
The unemployment that rises during a recession is:
A. Frictional.
B. Structural.
C. Cyclical.
D. Natural.
โ C. Cyclical unemployment follows the business cycle and rises in recessions.
๐งฎ Numerical Exercise
A country has 4.5 million employed, 0.5 million unemployed and 3 million out of the labor force.
a) Compute the labor force and the unemployment rate.
b) Compute the participation rate.
c) 200,000 unemployed give up looking. Recompute both rates.
d) With a separation rate \(s = 2\%\) per quarter, what finding rate \(f\) sustains a 10 percent unemployment rate?
โ Solution
a) Labor force \(= 4.5 + 0.5 = 5\) million, so the rate is \(0.5/5 = 10\%\).
b) Adult population \(= 5 + 3 = 8\) million, so participation is \(5/8 = 62.5\%\).
c) Labor force \(= 4.8\) million and unemployed \(= 0.3\), so the rate falls to \(6.25\%\) while participation falls to \(4.8/8 = 60\%\). Unemployment improved and nothing got better. โ ๏ธ
d) \(u = \dfrac{s}{s+f} = 0.10\) gives \(f = 9s = 18\%\) per quarter: on average about five and a half quarters to find work. โ
Part 2 ยท Inflation
๐ถ What Inflation Is
Inflation: a general and sustained rise in the overall price level.
It is not one price going up: it is prices as a whole going up, year after year.
With inflation, each euro buys less. The purchasing power of money falls. ๐
๐ How It Is Measured: the Basket
We track the price of a basket of goods and services representative of a typical household.
Food, rent, transport, energy, leisure, each with a weight reflecting its importance in the budget.
The change in the cost of the basket over time gives the price index. ๐
๐ Source: OpenStax Macro 3e, ยง9.1 โTracking Inflationโ, โThe Price of a Basket of Goodsโ, which prices a college studentโs basket year by year and then turns it into index numbers.
๐ The HICP
In the euro area we use the Harmonised Index of Consumer Prices (HICP).
โHarmonisedโ (the official EU spelling) because it follows the same rules in every country, so as to be comparable.
It is the index the European Central Bank uses for its inflation target. ๐ฏ
๐ The US counterpart is the CPI: OpenStax Macro 3e, ยง9.2 โHow to Measure Changes in the Cost of Livingโ, including โThe Eight Major Categories in the Consumer Price Indexโ. The HICP is the euro areaโs harmonised version of the same idea.
๐งฎ Computing the Inflation Rate
The inflation rate is the percentage change in the index between two periods:
\[ \pi = \frac{\text{Index}_t - \text{Index}_{t-1}}{\text{Index}_{t-1}} \times 100. \]
If the basket cost 100 last year and 103 this year, inflation was 3%.
๐ Inflation Over Time
The red line marks the ECBโs 2% target. Note the 2022 spike. Source: Eurostat (HICP, Portugal). ๐ฅ
๐ Common Confusions
๐ Falling inflation is not falling prices: it is prices rising more slowly.
๐ธ Prices that actually fall are called deflation, and that brings its own problems.
๐ถ What matters is the real wage: the nominal wage adjusted for inflation.
๐๏ธ Headline and Core
Two numbers get published, and they answer different questions.
๐ฐ Headline: the whole basket. It is what households actually pay, so it is the right measure of the cost of living.
๐ฏ Core: the basket excluding food and energy, the two most volatile items and the two most driven by world prices.
Central banks watch core because it is a better signal of where inflation is heading, not because energy does not matter. Confusing the two is a standard mistake in commentary. ๐ง
๐ Source: OpenStax Macro 3e, ยง9.2, โThe CPI and Core Inflation Indexโ.
โ ๏ธ The Costs of Inflation
Split them, because the two halves behave very differently:
Expected inflation costs little: contracts, wages and rates are indexed to it. What is left is shoe-leather and menu costs, plus tax distortions where the tax code is written in nominal terms.
Unexpected inflation is the expensive one. It redistributes from creditors to debtors, arbitrarily, on every nominal contract already signed.
Every fixed-rate bond, mortgage and pension in Europe is such a contract. That transfer is not a side effect: it is the main event. ๐ถ
So the real objective is not zero inflation. It is predictable inflation, which is why the ECB targets a number and says it out loud. ๐ฏ
๐ Review ยท Part 2
Two multiple choice questions and one exercise. โ๏ธ
โ Multiple Choice 3
Inflation turns out much higher than everyone expected. On a fixed rate mortgage signed last year, this:
A. Hurts the borrower, since everything costs more.
B. Hurts nobody, since the contract is fixed.
C. Hurts the bank and the borrower equally.
D. Transfers value from the lender to the borrower.
โ D. The nominal payment is fixed, so its real value falls. The borrower repays in cheaper euros. This is the redistribution that makes unexpected inflation costly, and it runs on every nominal contract at once.
โ Multiple Choice 4
The HICP is โharmonisedโ because:
A. It is computed only in Portugal.
B. It follows common rules so as to be comparable across EU countries.
C. It ignores energy.
D. It measures GDP.
โ B. Harmonization guarantees comparability across euro area countries.
๐งฎ Numerical Exercise
The consumption basket cost 120 euros last year and costs 126 this year.
a) Compute the inflation rate.
b) Your nominal wage rose 3 percent. What happened to your real wage?
c) You hold a bond paying a fixed 4 percent. What is your real return?
d) Who gained from this, and would they still have gained if the 5 percent had been expected?
โ Solution
a) \((126 - 120)/120 = 5\%\).
b) Roughly \(3 - 5 = -2\%\). Exactly: \(1.03/1.05 - 1 \approx -1.9\%\). The real wage fell.
c) Roughly \(4 - 5 = -1\%\). You lent money and got back less purchasing power than you put in.
d) Whoever owed at a fixed nominal rate. And no: had the 5 percent been expected, the bond would have been issued at a higher nominal rate in the first place. It is the surprise that transfers value. โ
Part 3 ยท The Phillips Curve
๐ The Short-Run Phillips Curve
Less unemployment, more inflation. The economy appears able to pick a point.
๐ Source: OpenStax Macro 3e, ยง12.3 โThe Phillips Curveโ, โThe Discovery of the Phillips Curveโ. The next subsection, โThe Instability of the Phillips Curveโ, is the point of our next two slides.
๐ The Role of Expectations
But the trade-off is not stable. If people expect inflation, they demand higher wages right away.
The curve incorporates expectations: \[ \pi = \pi^e - \beta\,(u - u_n). \]
\(\pi^e\) is expected inflation and \(u_n\) the natural rate. The curve shifts when expectations change.
๐ The Long Run Is Vertical
In the long run, expectations adjust: \(\pi = \pi^e\).
From the equation, that forces \(u = u_n\): unemployment returns to the natural rate, whatever inflation is.
The long-run Phillips curve is vertical at \(u_n\). There is no permanent trade-off between inflation and unemployment. ๐
๐ฏ The Policy Lesson
Trying to keep unemployment below the natural rate produces only rising inflation, not lasting employment.
This is why the ECB focuses on price stability: in the long run, it is the best monetary policy can deliver. ๐ฆ
๐ธ What Disinflation Costs
Bringing inflation back down means running \(u > u_n\) for a while. How long is not a detail:
Sacrifice ratio: the cumulative percentage points of excess unemployment needed to cut inflation by one percentage point.
And it depends almost entirely on \(\pi^{e}\). If a credible announcement moves expectations directly, the curve shifts down without the recession.
Which is why a central bank spends so much effort on being believed. Credibility is not public relations here, it is the difference between a cheap disinflation and an expensive one. ๐ฃ๏ธ
And it is why independence matters: a central bank that can be leaned on by a government is one whose announcements nobody has to believe. ๐๏ธ
๐ Review ยท Part 3
Two multiple choice questions and one exercise. โ๏ธ
โ Multiple Choice 5
A central bank announces a disinflation and is fully believed. In \(\pi = \pi^{e} - \beta(u - u_n)\), this means:
A. \(\pi^{e}\) falls immediately, so inflation can come down with little excess unemployment.
B. \(\beta\) rises, making the trade-off steeper.
C. \(u_n\) falls, so the natural rate does the work.
D. Nothing changes, since only actual inflation matters.
โ A. Credibility moves the curve down directly instead of forcing the economy along it. That is the whole argument for central bank independence and for announcing a target out loud.
โ Multiple Choice 6
The long-run Phillips curve is vertical because:
A. Inflation does not exist in the long run.
B. Wages are perfectly rigid in the long run.
C. The central bank chooses the unemployment rate.
D. Expectations catch up, so \(\pi = \pi^{e}\) forces \(u = u_n\).
โ D. You cannot fool people forever. Once \(\pi^{e}\) has adjusted, the only unemployment rate consistent with the equation is the natural one, whatever inflation happens to be.
๐งฎ Numerical Exercise
Phillips curve \(\pi = \pi^{e} - 0.5\,(u - u_n)\), with \(u_n = 6\%\) and \(\pi^{e} = 2\%\).
a) Find inflation if unemployment is 4 percent.
b) Expectations catch up, so \(\pi^{e} = 3\%\). Find inflation at \(u = 4\%\) again.
c) What happens if the central bank keeps trying to hold \(u\) at 4 percent?
d) To cut inflation from 3 to 2 percent in one year, what unemployment is needed?
โ Solution
a) \(\pi = 2 - 0.5(4 - 6) = 3\%\).
b) \(\pi = 3 - 0.5(-2) = 4\%\). Same unemployment, higher inflation.
c) Inflation keeps ratcheting up, one point per round, and never settles. That is the accelerationist result: below \(u_n\) you do not buy low unemployment, you buy rising inflation.
d) Need \(\pi = 2\) with \(\pi^{e} = 3\): \(2 = 3 - 0.5(u - 6)\), so \(u = 8\%\). Two points of excess unemployment for one point of disinflation, unless expectations move on their own. โ
Wrap-Up
๐ฏ What to Take From This Session
๐ฅ The unemployment rate counts only those in the labor force who are looking for work.
๐ง Wage rigidity stops the wage from clearing the market: that is where involuntary unemployment comes from.
๐ถ Inflation is measured by the HICP, a consumption basket harmonized across the euro area.
๐ The Phillips curve is a short-run choice between inflation and unemployment, but in the long run it is vertical.
๐ Next Session
Money, Banking and Inflation.
If inflation is a monetary phenomenon, we need to understand what money is and who creates it. ๐ฆ
See you next week. ๐