In a situation of decision under uncertainty, if a consumer faces equal expected income from two alternatives, then s/he will take decision on the basis of
Variation of risk attached with each alternative
Understanding Decision Making Under Uncertainty
When individuals make decisions where the outcomes are not certain, they are operating under a condition of uncertainty. This is common in many economic choices, such as investing, choosing a career path, or even selecting between different consumption bundles when future prices or income are unknown.
In such situations, the decision maker needs a way to evaluate the potential outcomes and choose the option that best suits their preferences and attitudes towards risk.
Comparing Alternatives with Equal Expected Income
The question describes a specific scenario where a consumer faces two alternatives, and both offer the same expected income. Expected income is the average outcome if the decision were repeated many times. Mathematically, for an alternative with possible incomes \(I_1, I_2, \dots, I_n\) occurring with probabilities \(p_1, p_2, \dots, p_n\), the expected income (\(E[I]\)) is calculated as:
\( E[I] = p_1 I_1 + p_2 I_2 + \dots + p_n I_n = \sum_{i=1}^{n} p_i I_i \)
If two alternatives have the same expected income, the consumer cannot make a decision based solely on this average value. They must consider other aspects of the alternatives.
The Role of Risk in Decision Making
Risk is the uncertainty associated with the possible outcomes. Even if two alternatives have the same expected income, the spread or variation of the actual outcomes around that expected value can be different. An alternative with high risk might have a chance of a very high income and a chance of a very low income, while an alternative with low risk might have outcomes that are clustered closely around the expected income.
In the context of decision under uncertainty, especially when expected incomes are equal, the consumer's attitude towards risk becomes crucial. Most people are risk-averse, meaning they prefer a certain outcome to an uncertain outcome with the same expected value.
Evaluating the Options
Let's analyze the given options in the context of a consumer facing two alternatives with equal expected income:
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Option 1: Expected utility of both the alternatives
Decision under uncertainty is fundamentally based on expected utility theory. A rational consumer aims to maximize their expected utility. Expected utility considers both the possible outcomes and the consumer's preferences for those outcomes, weighted by their probabilities. A risk-averse consumer's utility function is concave, meaning they get diminishing marginal utility from income. For such a consumer, an alternative with higher risk (more variation in outcomes) will yield lower expected utility compared to an alternative with the same expected income but lower risk. So, while the decision is *based on* expected utility maximization, the *factor* that differentiates the options when expected income is equal is the risk.
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Option 2: Probability of risk attached with each alternative
This option is vague. Risk isn't typically quantified by a single "probability of risk." Risk is about the entire distribution of possible outcomes and their probabilities. While probabilities are involved in calculating expected income and assessing risk, just knowing a single "probability of risk" (whatever that might mean) is insufficient to compare the overall riskiness of two alternatives.
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Option 3: Variation of risk attached with each alternative
This option refers to measures of risk like variance or standard deviation. Variance (\(\sigma^2\)) measures the average squared deviation of possible outcomes from the expected income. For an alternative with incomes \(I_i\) and probabilities \(p_i\), the variance is:
\( \sigma^2 = \sum_{i=1}^{n} p_i (I_i - E[I])^2 \)
The standard deviation (\(\sigma\)) is the square root of the variance. These measures quantify the spread or variation of outcomes. When two alternatives have the same expected income, a risk-averse consumer will prefer the one with lower variation because it offers outcomes that are less spread out, meaning less chance of a very low outcome, even though there is also less chance of a very high outcome. This lower variation is associated with higher expected utility for a risk-averse person when expected incomes are equal.
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Option 4: Mean of risk of each alternative
This option uses the term "mean of risk," which is not standard terminology in economics or statistics when discussing risk measures. Risk is typically measured by dispersion (like variance or standard deviation), not by a mean value. The mean is usually applied to the outcomes themselves (expected income), which in this scenario is stated to be equal for both alternatives.
Given that the expected incomes are equal, the consumer, assuming they are risk-averse, will differentiate between the alternatives based on their riskiness. Risk is most appropriately measured by the variation or spread of the possible outcomes. The alternative with lower variation is less risky.
| Factor | Relevance when E[Income] is Equal |
|---|---|
| Expected Income | Cannot be the basis, as it's equal for both options. |
| Risk (measured by Variation) | Crucial factor. Lower variation indicates lower risk, preferred by risk-averse consumers. |
| Expected Utility | The ultimate decision criterion, but when E[Income] is equal, the difference in expected utility stems from the difference in risk variation. |
Therefore, when expected income is equal, the consumer will decide based on the variation of risk attached with each alternative, choosing the one with lower variation if they are risk-averse.
Revision Table: Key Concepts
| Concept | Definition/Significance |
|---|---|
| Decision under Uncertainty | Choices where outcomes are not known for sure. |
| Expected Income | Weighted average of possible incomes, using probabilities as weights. |
| Risk | Uncertainty regarding outcomes, often measured by dispersion. |
| Risk Aversion | Preference for a certain outcome over an uncertain one with the same expected value. |
| Variation of Risk | Measures like variance or standard deviation that quantify the spread of possible outcomes around the expected value. |
Additional Information: Risk Attitudes
Understanding risk attitudes is key to decision making under uncertainty:
- Risk-Averse: Prefers a certain outcome to an uncertain one with the same expected value. Marginal utility of income is diminishing (utility function is concave). Most people are risk-averse for significant amounts of money.
- Risk-Neutral: Indifferent between a certain outcome and an uncertain one with the same expected value. Marginal utility of income is constant (utility function is linear). Decision is based solely on expected value.
- Risk-Loving: Prefers an uncertain outcome to a certain one with the same expected value. Marginal utility of income is increasing (utility function is convex). Rare for large outcomes, but might explain gambling behavior.
In typical economic analysis, risk aversion is assumed. If the consumer were risk-neutral, they would be indifferent between the two alternatives if their expected incomes are equal, regardless of risk variation. However, the question implies a basis for decision, suggesting a non-risk-neutral (likely risk-averse) consumer who looks beyond just the expected value.
Important Questions from Consumer behaviour
In relation to theory of consumers behaviour, which of the following statements is INCORRECT?
The concept of consumer surplus was propounded by __________.
Goods whose demand varies inversely with income are called ____ goods.
_____ have an income elasticity of demand of between 0 and +1.
According to ____ theory, a consumer will continue to buy such products that will deliver him the most utility or maximum satisfaction at relative prices.
