Purchase Solution

Von-Neumann-Morgenstern utility functions

Not what you're looking for?

Ask Custom Question

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 £10,000, but if in jail you get £1,000. Income when commiting a crime and not being caught is £13,000 (i.e. £10,000 from false honesty plus £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 £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?

Purchase this Solution
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.

Purchase this Solution
Free BrainMass Quizzes
Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

View More Free Quizzes
Related BrainMass Solutions

  • Choice Under Uncertainty

    (b) Explain what it means that the preference relation has a utility function representation, and define the notion of a von Neumann-Morgenstern utility function. Please refer to the attachment.

  • CARA: vNM utility with constant absolute risk aversion

    This solution shows how to find the von Neumann-Morgenstern utility functions that displays constant measure of absolute risk-aversion (Arrow-Pratt measure) - CARA.

  • Risk Aversion

    The individual might get w+h with probability p But might get w-h with probability (1-p) The von Neumann-Morgenstern utility is: EU = p U(w+h) + (1-p) U(w-h) If the utility exceeds the utility of w, i.e.

  • von Neumann-Morgenstern utility function - risk averse agent

    The agent has the von Neumann-Morgenstern utility function, u=lnx, where x is wealth. How much insurance should the agent buy? Suppose the risk cover is L. Then the agent will choose the risk cover such that his expected utility is maximized.

  • Uncertainty, insurance

    The von Neumann-Morgenstern Utility function with uncertainty is U = pr(good)*u(good Y) + pr(bad)*u(bad Y) where pr(good) = pr(bad) = 0.5, and u = lnY.

  • Calculating maximum insurance premium with uncertainty

    162507 Calculating maximum insurance premium given a von Neumann-Morgenstern utility function. 1. Consider a von Neumann-Morgenstern individual whose utility function is logarithmic, i.e. u(w)=ln(w), where w is wealth.

  • A risk adverse agent

    Prove that a risk-averse von Neumann-Morgenstern individual will over-insure, fully-insure, or under-insure according as the insurance is available at a price ∏ lower than, equal to, or higher than the actuarially fair price. ∏ - symbol

  • Risky Assets

    The risk averse von Neumann-Morgenstern investor chooses x to maximize . Prove that if the investor's measure of absolute risk aversion is a decreasing function of w, the wealthier investor will hold more of the risky asset.

  • Market for Lemon - Decisions under risk and uncertainty

    The von Neumann Morgenstern utility functions of the sellers and buyer are, respectively: Us=x+q Ub=x+1.2q Where x is a numeraire good with price 1.

View More Related Solutions