Economic Decision-Making Concepts

Expected Utility Theory

• Expected utility theory is a framework for decision-making under uncertainty.
• Individuals are assumed to be expected utility maximisers, meaning they choose the action that maximises their expected utility.
• The expected utility of an action is calculated by weighting the utility of each possible outcome by its probability.

Labour Supply and Corner Solutions

• Corner solutions in labour supply occur when the marginal rate of substitution (MRS) between leisure and consumption is greater than the real wage.
• This means individuals are willing to sacrifice more consumption to have an extra hour of leisure than the real wage would compensate them for.
• The MRS is equal to the real wage in optimum decisions.

Reservation Wage

• The reservation wage is the minimum wage an individual is willing to accept for a job.
• It represents the wage at which an individual is indifferent between working and not working.
• The reservation wage is determined by the condition MRS = W_res.

Risk vs. Uncertainty

• Risk involves known probabilities of outcomes, while uncertainty involves unknown probabilities.
• The classic example of a risk situation is a roulette wheel, where the probabilities of the outcomes are known and agreed upon.
• Horse races, in contrast, represent a situation of uncertainty, because the probabilities of different horses winning are subjective and vary between individuals.

Attitudes to Risk

• A fair bet involves an equal probability of winning or losing an amount. The expected value of a fair bet is zero.
• Individuals can exhibit risk aversion, risk neutrality, or risk-seeking behaviours.
• Risk averse individuals prefer the certainty of a smaller expected payout to a lottery with a larger but uncertain expected payout.
• Risk-neutral individuals are indifferent to risk and base their decisions solely on expected value.
• Risk-seeking individuals prefer a lottery with a larger but uncertain expected payout to a smaller certain payout.

Expected Value vs. Expected Utility

• The expected value of a risky prospect is the weighted sum of the possible outcomes, weighted by their probabilities.
• The expected utility of a risky prospect is the weighted sum of the utilities associated with the possible outcomes, weighted by their probabilities.

Decreasing Marginal Utility

• Marginal utility is the added utility one derives from an additional unit of consumption.
• Decreasing marginal utility means that the additional utility derived from each additional unit of consumption decreases as consumption increases.

Different Possible Risk Attitudes

• Attitudes to risk can be characterised by marginal utility decreasing, constant or increasing. - Decreasing marginal utility leads to risk aversion - Constant marginal utility leads to risk neutrality - Increasing marginal utility leads to risk seeking behaviour

A Fair Bet (Utility Function)

• The utility derived from a lottery can be greater than the expected utility if risky prospects are not fair bets.

Certainty Equivalent and Risk Premium

• The certainty equivalent is the amount of guaranteed income that an individual values equally to a risky income stream.
• The risk premium is the difference between the expected value of a risky outcome and its certainty equivalent.

Attitudes to Risk (Again)

• Risk-averse individuals require a risk premium to accept a risky investment.
• Risk-neutral individuals have no risk premium required.
• Risk-seeking individuals have risk premium reduced or negative.

Arrow-Pratt Measure of Risk Aversion

• Risk aversion is determined by the curvature of the utility function. A risk averse individual receives less expected utility compared to a risk neutral individual or a risk-seeking individual..

Modelling Economic Decisions

• Using expected utility theory facilitates the modelling of economic decisions in the presence of uncertainty.
• Applying expected utility maximisation necessitates solving for the most optimal choices and considering first-order conditions.

Testing the Model -- Data

• Testing economic models in the presence of uncertainty generally employs macroeconomic or microeconomic datasets.
• Life cycle data can be used in the estimation process, for example, data on individuals at different ages, including crime aspects.
• Macrodata is a commonly used approach and some research has supported the Becker Crime Model.

Extending the Model

• The basic expected utility model can be expanded and applied to various types of crime and decisions beyond monetary gains and losses.
• Some decisions might not involve ex ante/ex post consistency given the non-materialistic items that drive the outcome.

What About Wealth?

• Wealth has no effect on probability, but it has an impact on the marginal utility of income which can be used to inform decision making.

Marginal Utility and Risk Aversion

• Risk aversion is correlated with diminishing marginal utility.
• A decision maker’s risk perception is influenced by their marginal utility, probability of success and other variables.

Basic Takeaways of Rational Choice Model

• Reducing crime is usually about increasing punishments and/or increasing probability of being caught.
• Reducing inequality can also impact crime rates, or have an equivalent effect to modifying the expected payoff for crime.