Q2: Consider a person who is thinking about whether to engage in a life of crime. He knows that, if he gets caught, he will be in jail and his consumption will be low, xo, but if he does not get caught, he will be able to consume an amount x₁ that is considerably above xo. (a) Suppose that xo 20; x₁ = 80 (where both are expressed in thousands of pounds) and suppose the probability of getting caught is 8 = 0.5. What is the expected consumption level if the life of crime is chosen? = (b) Suppose the potential criminal's tastes over gambles can be expressed using the following utility function u(x) = ln (x). Calculate the person's expected utility from a life of crime. How does it compare with the utility of the expected value of consumption? Based on your answer, explain this individual's attitude towards risk and draw the consumption/utility relationship. (c) Consider the level of consumption this person could attain by not engaging in a life of crime. What level of consumption from an honest living would make the person indifferent between a life of crime and an honest living? Denote this consumption level and show it on your diagram. The Minister for Crime proposes an increased deterrence policy, but no extra spending on law enforcement. This policy increases the penalties for committing crimes, which thus reduces xo, the consumption level of an individual who gets caught. (d) Suppose, therefore, that the expected consumption level (found in part (a)) for a person gaged in a life of crime remains unchanged under this policy. Using a diagram, illustrate what will happen and with reference to the certainty equivalent,
Q2: Consider a person who is thinking about whether to engage in a life of crime. He knows that, if he gets caught, he will be in jail and his consumption will be low, xo, but if he does not get caught, he will be able to consume an amount x₁ that is considerably above xo. (a) Suppose that xo 20; x₁ = 80 (where both are expressed in thousands of pounds) and suppose the probability of getting caught is 8 = 0.5. What is the expected consumption level if the life of crime is chosen? = (b) Suppose the potential criminal's tastes over gambles can be expressed using the following utility function u(x) = ln (x). Calculate the person's expected utility from a life of crime. How does it compare with the utility of the expected value of consumption? Based on your answer, explain this individual's attitude towards risk and draw the consumption/utility relationship. (c) Consider the level of consumption this person could attain by not engaging in a life of crime. What level of consumption from an honest living would make the person indifferent between a life of crime and an honest living? Denote this consumption level and show it on your diagram. The Minister for Crime proposes an increased deterrence policy, but no extra spending on law enforcement. This policy increases the penalties for committing crimes, which thus reduces xo, the consumption level of an individual who gets caught. (d) Suppose, therefore, that the expected consumption level (found in part (a)) for a person gaged in a life of crime remains unchanged under this policy. Using a diagram, illustrate what will happen and with reference to the certainty equivalent,
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.3P
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Transcribed Image Text:Q2: Consider a person who is thinking about whether to engage in a life of crime. He
knows that, if he gets caught, he will be in jail and his consumption will be low, xº, but if he
does not get caught, he will be able to consume an amount x₁ that is considerably above
Χρ·
(a) Suppose that x₁ = 20; x₁ = 80 (where both are expressed in thousands of pounds)
and suppose the probability of getting caught is 8 = 0.5. What is the expected
consumption level if the life of crime is chosen?
(b) Suppose the potential criminal's tastes over gambles can be expressed using the
following utility function u(x) = In (x). Calculate the person's expected utility from
a life of crime. How does it compare with the utility of the expected value of
consumption? Based on your answer, explain this individual's attitude towards risk
and draw the consumption/utility relationship.
(c) Consider the level of consumption this person could attain by not engaging in a life
of crime. What level of consumption from an honest living would make the person
indifferent between a life of crime and an honest living? Denote this consumption
level and show it on your diagram.
The Minister for Crime proposes an increased deterrence policy, but no extra spending
on law enforcement. This policy increases the penalties for committing crimes, which
thus reduces x, the consumption level of an individual who gets caught.
(d) Suppose, therefore, that the expected consumption level (found in part (a)) for a
person engaged in a life of crime remains unchanged under this policy. Using a
diagram, illustrate what will happen and with reference to the certainty equivalent,
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