Explain why diminishing marginal utility implies that a decision maker will be risk averse.

Name: Problem 4, Chapter 15: Microeconomics
Uploaded: 2024-03-16T03:06:20-08:00
Duration: 2 min 10 s
Channel: Jennifer Stoner
Description: Explain why diminishing marginal utility implies that a decision maker will be risk averse.

step 1 Diminishing marginal utility is an economic concept that describes a situation where the satisfa

Explain why diminishing marginal utility implies that a...

Key Concepts

Concave Utility Function

A concave utility function mathematically represents diminishing marginal utility. It curves downward, indicating that the increase in utility from an additional unit of wealth is less when starting from a higher wealth level. This curvature ensures that the expected utility of a risky prospect is lower than the utility of its expected outcome, motivating risk-averse behavior.

Jensen's Inequality

Jensen's Inequality provides the mathematical basis for why a concave utility function leads to risk aversion. It shows that for a concave function, the utility of the expected value of an uncertain outcome is greater than the expected value of the utility of that outcome, thus explaining why decision makers favor a sure outcome over a risky one.

Diminishing Marginal Utility

This concept states that as a person consumes more of a good or increases their wealth, the additional satisfaction (or utility) gained from each extra unit decreases. In decision-making, this diminishing benefit from additional outcomes is key in understanding behavior under uncertainty.

Risk Aversion

Risk aversion is the preference for a certain outcome over a gamble with the same expected value. Individuals who are risk averse weigh potential losses more heavily than equivalent gains, often preferring the security of a known result.

Expected Utility Theory

This theory models how individuals evaluate risky prospects by considering the weighted average of utilities across different outcomes, with their respective probabilities. It integrates diminishing marginal utility and the concavity of the utility function to explain why a decision maker might choose a certain outcome over a riskier alternative with identical expected monetary value.

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