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Monday, September 04, 2006

On negative externalities c. 1906

From the September 4, 1906 NYT:
LONDON Sept. 3 - If any one throws a banana skin on a London pavement and is caught at it by the police, he will have to pay a fine of 40s.

This is according to a law just enacted by the London County Council, and public knowledge of it has come through the announcement to-day by the Coronoer at the inquest on a man who died from the effects of slipping on a banana skin.

2 Pounds in 1906 is worth approximately 143 pounds in 2005. At today's exchange rate, the 143 pounds is worth about $272.

Going with the naive Becker model of crime, criminal behavior is dissuaded when the Marginal Benefit of the crime equals the Expected Marginal Cost of being caught, tried, and convicted. The EMC is a weighted average of the fine paid when caught and the fine paid when not caught, typically assumed to be zero.

Therefore, assuming once caught, one is convicted, the net expected benefit of disposing of a banana peel on a London street was then:

Expected Net Benefit = Actual Benefit - Expected Costs = AB - (c*F - (1-c)*0),

where AB is the actual benefits that accrue from the crime (assumed to be positive), c is the odds of being caught (assumed to be less than one) and F is the fine paid when caught.

The optimal fine, given the actual benefits of the crime and the odds of being caught, sets the Expected Net Benefits equal to zero. This is the typical classroom approach to the model - determine the optimal fine for a given AB and c. However, there is also the rather counter-intuitive possibility that, for a given AB and F, enforcement (c) might adjust (possibly downwards) so that Expected Net benefits equal zero.*

Assume c = 0.10, or there was a ten percent chance that a banana-peel tosser would be caught and convicted (although this would seem a rather high enforcement rate). If the fine were chosen optimally, the fine would reflect an AB of banana-peel tossing of (0.10)x($272) = $27.2. This too sounds a bit high. Why? Ask yourself if is sounds reasonable for an individual to require $27 to not throw their banana peel on the sidewalk?

There is really no basis for one number of another (except for the groan and laugh test), but let's assume that an individual would be indifferent between tossing their banana peel and holding on to it for $1. If the $272 (in 2005 real dollars) fine were optimal, this would yield an implicit odds of being caught of:

c = AB/F = 1/272 = 0.0036,

i.e., the implicit odds of being caught would be considerably less than one percent. Believable? Who knows, but perhaps on a crowded London street it would be difficult to tell who exactly proffered a dangerous peel. One wonders if the ex ante odds were more or less than implied by the legislated fine. If they were higher, then the crackdown on peel-droppers might actually decline after the ordinance. Why? Because the fine was set too high.

Such simple analysis is often eye-opening to the economics student. When the unconditional odds of being caught and prosecuted for a crime are considerably low, the optimal fine might be considerably higher than many imagine (even if the anticipated benefits to the criminal are likewise low). On the other hand, for high damage crimes (high AB) with a high probability of being caught, (that is c is high), the optimal fine might not be so Draconian. This, perhaps, explains (but doesn't necessary justify) the disparate penalties associated with drug crimes versus, say, white collar crimes.

* This is a rather subtle, if rarely mentioned, aspect of the Becker crime model. The assumption is that the fine is the action variable, chosen with actual benefits and enforcement efforts parameteric to the problem. However, given that police enforcement is itself the outcome of optimal decision making, the legislated fine might just as easily be considered exogenous to the model and therefore the variable that adjusts, given the actual benefits and the legislated fine, is crime enforcement.

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