Principles of Microeconomics / Unit 12 MIC 1113 worked example, 60 to 90 seconds
The Free-Rider Matrix
The idea
Set the free-rider problem up as unit nine's prisoner's dilemma. Two neighbors can share the cost of a good each values. List each one's choices, contribute or not, and each cell's payoff as benefit minus contribution. Mark best replies. Show that not contributing is dominant for both, that the Nash equilibrium is that nobody pays and the good is not built, and that both would have done better contributing. Then show what a tax does: it removes the choice and leaves the cell both preferred.
In practice
Worked example: a streetlight costs one hundred dollars and is worth eighty to each of two neighbors. Both contribute fifty: each nets thirty. One pays the whole hundred alone: the payer nets minus twenty, the other eighty. Neither pays: zero each. For the first neighbor, not paying beats paying whether the other pays, eighty against thirty, or does not, zero against minus twenty; not paying is dominant for both. Nobody pays, no light, zero each, though thirty each was available. A tax of fifty on each builds the light and leaves both with thirty.
Where people slip
The tax is efficient only because the light was worth more than it cost; a tax can also build goods not worth building. And the matrix scales badly: with a thousand neighbors one contribution changes almost nothing, so the temptation to ride free grows with the group.
Your place on the trail
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