Unemployment as a matching problem: vacancies, job-finding rates, and the Beveridge curve.
Warming up the engine…
The modern theory of unemployment: workers and vacancies search for each other, matches form according to a matching function, and the Beveridge curve traces the vacancy-unemployment trade-off.
Matches = m(U, V) ; Beveridge curve: V falls as U rises along the cycle
Hiring is not instant shopping: both sides search, screen, and settle, so vacancies and unemployment coexist. Booms slide the economy up the Beveridge curve (many vacancies, few unemployed); a structural mismatch (wrong skills, wrong cities) shifts the whole curve outward, meaning MORE unemployment at any vacancy level, the signature of a broken matching process.
Movement along the Beveridge curve = business cycle; outward shift = worse matching efficiency. Post-COVID data is the go-to modern example of an outward shift.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at u 4.9, v 2.4.
Equilibrium: u* = 4.9, v* = 2.4
Current equations
Vacancies and unemployment coexist, the puzzle a frictionless market can't explain. The Beveridge curve traces that tradeoff: when jobs are plentiful, unemployment is low, and vice versa. The economy sits where firms' hiring appetite crosses it.