The lighthouse beam is non-excludable โ every ship on the water sees it whether or not its owner paid for it โ and non-rivalrous โ one ship watching the beam doesn't dim it for anyone else. Each citizen below has a private willingness-to-pay (WTP) drawn independently. Under voluntary funding, a rational citizen weighs their own tiny effect on whether the lighthouse gets built at all against the certainty that they'll enjoy its light regardless โ so contributions fall well short of true WTP, and the gap widens as the population grows and each person's contribution feels less pivotal.
contribution_i = isFreeRider_i ? 0
: WTP_i ยท baseRate ยท dilution(N)
tax_i = (ฮฃWTP / N) ยท taxRate โ i
- Civic-mindedness โ raises the share of citizens willing to contribute something voluntarily, but never fully closes the gap to collective WTP.
- Compulsory tax โ everyone pays their assigned share regardless of personal free-riding incentive, so funding reliably reaches (or exceeds) the collectively desired level.
- The lighthouse's beam range/brightness and the surrounding haze respond live to whichever mechanism is active โ watch how many ships drift beyond the safe, lit radius when funding is short.