Book cover for Intermediate Microeconomics: A Modern Approach

Intermediate Microeconomics: A Modern Approach

Hal R. Varian

ISBN #9780393927023

7th Edition

224 Questions

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7,544 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

The chapter on Uncertainty outlines how uncertain outcomes affect economic decision-making through the concepts of contingent consumption, utility functions, and expected utility. It emphasizes the importance of rational risk aversion in guiding choices and market behavior, with practical applications demonstrated in areas such as insurance, diversification, and taxation. Understanding these principles is critical for evaluating risk and making informed decisions in uncertain economic environments.

Learning Objectives

1

Explain the role of uncertainty in economic decision-making and how it affects market behaviors.

2

Understand and apply the concept of expected utility in evaluating economic risks and outcomes.

3

Analyze how contingent consumption and utility functions integrate uncertainty and risk preferences.

4

Assess the implications of rational risk aversion through examples such as insurance demand, catastrophe bonds, and diversification.

Key Concepts

CONCEPT

DEFINITION

Uncertainty

The state of having limited knowledge about the outcome of future events, which influences economic decision-making.

Expected Utility

A concept that integrates both the probabilities of outcomes and the corresponding utility values, allowing for the evaluation of risky prospects.

Utility Function

A mathematical representation of an individual’s preference ranking over a set of goods or outcomes, often used to assess choices under risk.

Contingent Consumption

Consumption patterns that depend on the realization of uncertain events or states of the world.

Rational Risk Aversion

The tendency of individuals to prefer outcomes with less uncertainty, even if this means a lower expected return, as captured by their utility function.

Example Problems

Example 1

How can one reach the consumption points to the left of the endowment in Figure $12.1 ?$

Example 2

Which of the following utility functions have the expected utility property? (a) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=a\left(\pi_{1} c_{1}+\pi_{2} c_{2}\right)$ (b) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} c_{1}+$ $\pi_{2} c_{2}^{2}$ (c) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} \ln c_{1}+\pi_{2} \ln c_{2}+17$.

Example 3

A risk-averse individual is offered a choice between a gamble that pays $\$ 1000$ with a probability of $25 \%$ and $\$ 100$ with a probability of $75 \%,$ or a payment of $\$ 325 .$ Which would he choose?

Example 4

What if the payment was $\$ 320 ?$

Example 5

Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles.
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Step-by-Step Explanations

QUESTION

How is expected utility used to evaluate a risky investment decision?

STEP-BY-STEP ANSWER:

Step 1: Identify all possible outcomes of the investment along with their corresponding probabilities.
Step 2: Assign a utility value to each outcome based on the investor's utility function.
Step 3: Multiply each outcome's utility by its probability.
Step 4: Sum all the weighted utilities to obtain the expected utility of the investment.
Final Answer: The expected utility represents the overall value of the investment under uncertainty, guiding the investor to compare risky opportunities.

Expected Utility Calculation

QUESTION

How does diversification reduce individual investment risk?

STEP-BY-STEP ANSWER:

Step 1: Recognize that diversification involves investing in various assets whose returns are not perfectly correlated.
Step 2: Understand that spreading investments across different sectors or instruments helps reduce the impact of adverse outcomes in any one asset.
Step 3: Calculate the combined risk profile and compare it to the individual risk levels of each asset.
Final Answer: By diversifying investments, the overall risk is reduced while maintaining a similar level of expected return, mitigating the effects of uncertainty on the portfolio.

Risk Diversification

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Common Mistakes

  • Confusing uncertainty with randomness, rather than understanding it as a lack of complete knowledge about future events.
  • Assuming that risk-averse individuals always avoid risk, when in fact they make calculated choices based on expected utility.
  • Overlooking the role of probabilities in the expected utility calculation, leading to an inaccurate assessment of risky prospects.
  • Ignoring the impact of external factors such as taxation and market conditions on risk preferences and decision-making.