A star singer's fee and land near a station split the same way — see why both are so high.
The payment for a factor splits into two parts. What it could earn in its next job is transfer earnings. The pure bonus above that is economic rent. The harder a factor is to replace, the more of its pay hardens into rent. The formula below ties that to a steep supply.
For example, a 🧑 singer nobody can replace gets a fee of 1,000,000 won. A karaoke singing job would pay only 100,000. The other 900,000 is pure rent. If that voice were common, the fee would sink toward 100,000.
A star singer's market has demand w=22−q and supply w=6+7q — there is only one of her, so supply is very steep.
What are the equilibrium payment and quantity, and how much of the payment is pure rent?
Supply slope 7, demand 22 — the top triangle (rent) is thick.Show proof
Equilibrium is where 22−q=6+7q: q=2 and the payment is w=20. The total bill is 20×2=40.
Of that, transfer earnings — what it takes to keep her in this job — are the area under the supply curve, 6×2+27×22=26.
The remaining 40−26=14, or 35%, is pure rent.
That is why she earns so much more than she ever could doing anything else.
For comparison, with the same demand but a flat supply (s=0.5) — an ordinary job — the rent share thins to about 23%. The more people could replace you, the closer the pay sticks to opportunity cost.
News of a new subway station pushes demand for the land in front of it from w=16−q to w=22−q.
Supply stays at w=6+3q.
How much does the land's rent jump?
After demand jumped to 22 — the land is unchanged, only the rent grew.Show proof
Before the news, equilibrium was 16−q=6+3q, giving q=2.5, w=13.5, and rent of 2(13.5−6)×2.5≈9.4.
After the news, q=4, w=18, and of the total 72, transfer earnings are 48 and rent is 24. The land did not improve by an inch, yet its rent jumped from 9.4 to 24 — two and a half times. When people rush in, the rent of what cannot expand jumps first.