First midterm territory~30 min with interactivestrains 3 of 16 mock-1 questions
In this lesson
Why even a healthy economy always has some unemployment (the natural rate)
The bathtub: jobs flow out through the drain, people flow in from the faucet, and one tiny formula gives the water level
Stuck wages and job queues: minimum wages, unions, and Henry Ford's $5 day
Searching for the right chair: frictional unemployment and what policy does to it
The three-Greek-letter model (s, f, μ) the mock actually tests
Before you start, three things you already own
from Macro-01 The unemployment rate is U / labor force, not U over population. You drilled the denominator traps. Today's model explains what that rate settles at when nothing dramatic is happening.
from Macro-02 Long-run output is Ȳ = F(K̄, L̄). The L̄ that goes into the recipe is employment at the natural rate. "Full employment" never meant zero unemployment; it means the bathtub at its steady level.
from Macro-00, pattern 1 "Given numbers, one formula." The mock's bathtub question hands you s and f and wants s/(s+f). One division, one point. You will do it in your sleep after this page.
The rate that never goes to zero
Marta hands in her notice in March. Her design studio was fine; she just wants work she likes better, and it takes her eleven weeks to find it. For those eleven weeks she is officially unemployed, and here is the point: nothing went wrong. An economy where nobody was ever between jobs would be an economy where nobody ever moved, closed, opened, or improved anything.
So every economy carries a baseline level of unemployment even in good times. The course calls it the natural rate of unemployment: the average rate around which the economy fluctuates. Recessions push the actual rate above it, booms pull it below, and this chapter asks what sets the baseline itself. (What pushes the actual rate around in the short run is the second half of the course.) In the Italian data on the slides, that baseline hovers stubbornly around 8 to 10 percent across four decades: the natural rate is not small, and it is not the same everywhere.
Two forces keep it above zero, and they structure the whole chapter: wages that cannot fall (structural unemployment) and search that takes time (frictional unemployment, Marta's kind).
The bathtub
Before the two forces, the accounting machine that turns them into a number. Picture the pool of unemployed people as water in a bathtub. Every month the faucet adds water: some share s of employed workers separate from their jobs (layoffs, closures, quits like Marta's). Every month the drain removes water: some share f of unemployed workers find jobs. That is the entire model.
Watch the level settle, with real numbers. A town of 1000 workers, s = 1%, f = 19%. Suppose today 100 people are unemployed. This month the faucet drips in 1% of the 900 employed: 9 people lose or leave a job. The drain pulls out 19% of the 100 unemployed: 19 people find one. More leave the tub than enter it, so the water falls. Try again at 50 unemployed: the faucet drips in 1% of 950, about 9.5 people, and the drain removes 19% of 50, again 9.5. In equals out, and the level stops exactly there: 50 out of 1000, five percent. Nobody planned that number; the two streams negotiated it. The formula is just this settling point written once and for all, inflow s·E equal to outflow f·U, rearranged:
u* = ss + f
Read it like a bathtub owner. A leakier labor market (higher s, faucet open wider) means a higher water level. A faster drain (higher f, people find jobs quickly) means a lower one. Everything policy does to unemployment in this chapter works through one of those two dials.
The bathtub, live
The bathtub of unemployment
Faucet = separation rate s · drain = job-finding rate f · water level = steady-state unemployment u*
1.0%
19%
The fuller model on the slides (worth reading once)
The slides dress the bathtub up with two more dials: μ (mu), the efficiency of matching (how well job seekers and vacancies find each other; employment agencies raise it, generous unemployment insurance lowers it by making search less urgent), and J, the number of jobs firms want to fill. Raising μ or J drains faster: u* falls. Raising s fills faster: u* rises. The one sneaky case: firing costs. They close the faucet a little (fewer layoffs, s↓) but also clog the drain (firms hire more cautiously, μ↓), so the net effect on u* is genuinely ambiguous, and the exam knows it.
Stuck wages: structural unemployment
The drain clogs badly when the price of labor cannot fall. If the real wage is stuck above the level where labor supply meets labor demand, firms want fewer workers than the number of people willing to work: there are simply not enough chairs, and someone must stand no matter how well everyone searches. That standing crowd is structural unemployment, and the queue is visible in the picture below.
The diagram reads by the same rules as Macro-02's: the quantity (people working) runs along the horizontal axis, the price (here the price of labor, the real wage) up the vertical, and the answer to "how many have jobs?" is read sideways, never as height. The blue line is the firms' wish list: at each wage, how many workers they would hire. Drag the wage floor:
A wage floor in the labor market
labor demand (W = 200 − L) · labor supply (vertical at L̄ = 100) · minimum wage · pink area = the queue
90
The trap that pays a full point
The mock gives exactly this market (labor demand 200 − L, supply fixed at 100) and a minimum wage of 90. Panic answer: "10 unemployed". Correct answer: the market-clearing wage is 200 − 100 = 100, which is above 90. A floor below the ceiling touches nothing. Zero unemployed. Always compute the equilibrium wage first and check whether the floor actually binds.
Three reasons real wages get stuck above equilibrium:
Minimum-wage laws. They can price the least experienced out of work (US evidence: a 10% rise cuts teen employment 1 to 3%), but most workers earn far above the minimum, so this explains only a sliver of the natural rate. A nugget the professor likes: Italy has no legal minimum wage at all.
Unions. Collective bargaining pushes wages above market clearing for members. The slides frame it as insiders (employed members who want wages high) versus outsiders (the unemployed who would happily work for less, if anyone would let the wage fall). Italy is an extreme case: about 80% of workers are covered by collective agreements, against 12% in the US.
Efficiency wages. Sometimes the firm itself refuses to cut wages, because a well-paid worker is a better worker: higher pay attracts stronger applicants, discourages slacking, cuts turnover, and (in poor countries) even improves health. The classic case is Henry Ford in 1914: assembly-line turnover was 370% a year, so he doubled pay to the famous $5 day. Turnover collapsed to 16%, absenteeism fell fourfold, productivity jumped by up to 70%, and profits rose. Paying above the market was the profitable move, and the queue outside Ford's gates was structural unemployment in the flesh.
Structural unemployment in one picture: four people, three chairs, and a wage that will not fall to make a fourth chair appear. Someone stands no matter how well everyone searches.
The search: frictional unemployment
Now suppose wages are perfectly flexible and there are enough chairs for everyone. Unemployment still is not zero, because the chairs are all different. Workers differ in skills and tastes, jobs differ in requirements and location, and information about who wants whom travels slowly. Matching Marta to the studio that actually suits her takes time, and that time is frictional unemployment.
Frictional unemployment: the chairs exist, but finding the one that fits takes time. Marta's eleven weeks live here.
It gets a steady refill from sectoral shifts: demand forever migrates between industries and regions (typewriter repair out, computer repair in; agriculture from 58% of the US workforce in 1850 to 2% now), and every migration strands workers who must search anew. A dynamic economy cannot avoid this kind; it can only make the search faster or slower:
Unemployment insurance pays part of the old wage for a while. It slows the drain (search feels less urgent, and the data confirms spells lengthen with benefit duration, with a spike in job-finding right when benefits run out). But the slides insist on the other side of the ledger: extra search time can mean better matches, and the cushion matters in deep recessions when the jobs are temporarily just not there. UI trades a higher natural rate for better matches and softer landings; where to set that dial is politics, not arithmetic.
Sort the causes
Structural (not enough chairs at the stuck wage) or frictional (finding the right chair takes time)? The exam expects the reflex.
Cheat sheet
Everything this lesson asks you to remember
Steady-state unemployment
u* = s / (s + f)
Faucet s ↑ (sectoral shifts)
u* rises
Drain f or μ ↑ (agencies, training)
u* falls
Generous UI
μ↓, search slows, u* rises (but matches improve)
Firing costs
s↓ and μ↓ together: effect on u* ambiguous
Wage floor questions
compute the clearing wage FIRST; a floor below it binds nothing
