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# Von-Neumann-Morgenstern utility functions

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In a particular country there are three types of citizens: (1) people in jail who were caught commiting crimes; (2) people who are honest and therefore not in jail; (3) people who commited crimes but were not caught and therefore not in jail. Everyone derives utility only from income. The decision to commit a crime is based on non-ethical, rational criteria, and depends upon the individual utility that can be derived. All citizens have Von-Neumann-Morgenstern utility functions. In this country each honest person gets a guaranteed income of Â£10,000, but if in jail you get Â£1,000. Income when commiting a crime and not being caught is Â£13,000 (i.e. Â£10,000 from false honesty plus Â£3,000 from criminal activity). Given the relative inefficiency of the country's criminal justice system, the probability of being caught and convicted when commiting a crime is 0.75.

- Is it possible to deduce (without ambiguity) the shape of the criminals utility function? Explain what shape it will have

- Is it possible to deduce (without ambiguity) the shape of an honest persons utility function? Explain what shape it will have

- If a company sells insurance to criminals to pay them an income, in addition to the Â£1,000 if they are in jail will it have any business? Why or why not?

- Would your conclusions in the question above change also apply to honest people if there was a non-zero probability of incorrectly being found guilty of a crime?

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#### Solution Summary

Is it possible to deduce (without ambiguity) the shape of the criminals utility function? Explain what shape it will have

- Is it possible to deduce (without ambiguity) the shape of an honest persons utility function? Explain what shape it will have.

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