Microeconomics - Theory of Consumer Behaviour

Welcome to the study of consumer behavior, a cornerstone of microeconomics. Understanding how consumers make choices is fundamental to understanding how markets function. This section will explore various theories that explain consumer decision-making, from early approaches to more modern and nuanced perspectives. We will cover the cardinal and ordinal approaches to utility, the revealed preference hypothesis, Hicks' revision of demand theory, and how consumers make choices when faced with risk and uncertainty.

Cardinal Approach to Utility

The cardinal approach to utility treats utility, the satisfaction a consumer derives from consuming a good or service, as a measurable quantity. It assumes that consumers can assign a numerical value to the satisfaction they receive. This approach was pioneered by economists like Jeremy Bentham and William Stanley Jevons, and later refined by Alfred Marshall.

Assumptions of the Cardinal Approach

• Measurability of Utility: Utility is quantifiable and can be expressed in cardinal numbers (e.g., 10 utils, 20 utils). A consumer can say that good A gives them twice as much satisfaction as good B.
• Additivity of Utility: The total utility derived from consuming multiple goods can be calculated by summing the individual utilities of each good.
• Diminishing Marginal Utility: As a consumer consumes more units of a particular good, the additional satisfaction (marginal utility) gained from each extra unit tends to decrease. This is a crucial concept for understanding demand.
• Consistency of Preferences: Consumers are rational and make consistent choices.
• Interdependence of Utilities: In its simplest form, it assumes the utility derived from one good is independent of the utility derived from another. However, this was later relaxed to consider complementary and substitute goods.

Law of Diminishing Marginal Utility

This law states that as an individual consumes more and more units of a commodity, the extra utility (Marginal Utility or MU) derived from each successive unit of that commodity will eventually decrease, assuming other factors remain constant.

For example, imagine you are very thirsty and drink a glass of water. The satisfaction you get from that first glass is very high. If you drink a second glass, the satisfaction will likely be less than the first. By the time you drink a fourth or fifth glass, you might get very little additional satisfaction, or even feel discomfort.

Mathematically, if T is Total Utility and X is the quantity of a good consumed:

Marginal Utility (MU) = Change in Total Utility / Change in Quantity = ΔTU / ΔQ

Alternatively, MU is the derivative of the Total Utility function with respect to quantity: MU = dTU/dQ.

Consumer Equilibrium under Cardinal Approach

A rational consumer aims to maximize their total utility given their limited income and the prices of goods.

For a single commodity: A consumer will continue to buy a commodity as long as its marginal utility is greater than or equal to its price (expressed in money terms). The equilibrium is reached when the marginal utility of the commodity is equal to its price (MU = P). If MU > P, the consumer buys more, increasing consumption and decreasing MU until MU=P. If MU < P, the consumer buys less, decreasing consumption and increasing MU until MU=P.

For two commodities (say, Good X and Good Y): Let Px be the price of Good X, Py be the price of Good Y, and MUX and MUY be their respective marginal utilities. The consumer is in equilibrium when the marginal utility per dollar spent on each good is equal. This is expressed as:

MUx / Px = MUy / Py = MUm

Where MUm is the marginal utility of money. This condition ensures that the consumer cannot increase their total utility by shifting expenditure from one good to another. If MUx/Px > MUy/Py, the consumer gets more satisfaction per dollar from X, so they will buy more X and less Y, moving towards equilibrium.

Limitations of the Cardinal Approach

• The assumption that utility is measurable in cardinal terms is unrealistic. It is difficult, if not impossible, to assign precise numerical values to satisfaction.
• The additivity assumption is also questionable, as the satisfaction from one good can influence the satisfaction from another (e.g., coffee and sugar).
• It fails to adequately explain certain phenomena like the paradox of value (why water, essential for life, is cheaper than diamonds, a luxury).

Ordinal Approach to Utility

The ordinal approach, developed by economists like John Hicks and R.G.D. Allen, offers a more realistic alternative. It posits that consumers cannot measure utility in cardinal units but can rank their preferences. Consumers can state that they prefer bundle A to bundle B, or bundle B to bundle A, or are indifferent between them.

Assumptions of the Ordinal Approach

• Comparability: Consumers can compare any two bundles of goods and decide which they prefer or if they are indifferent.
• Transitivity: If a consumer prefers bundle A to bundle B, and bundle B to bundle C, then they must prefer bundle A to bundle C. (A > B and B > C implies A > C).
• Non-Satiation (More is Better): Consumers generally prefer more of a good to less.
• Diminishing Marginal Rate of Substitution: As a consumer consumes more of one good, they are willing to give up progressively less of another good to obtain an additional unit of the first good.

Indifference Curves

An indifference curve represents all the combinations of two goods that provide a consumer with the same level of satisfaction or utility.

• Properties of Indifference Curves:
  • Downward sloping: Reflects the trade-off between two goods; to get more of one, you must give up some of the other.
  • Convex to the origin: Reflects the diminishing marginal rate of substitution. The curve is steeper at the top left and flatter at the bottom right.
  • Indifference curves do not intersect: If they did, it would violate the transitivity assumption.
  • Higher indifference curves represent higher levels of utility.

Marginal Rate of Substitution (MRS)

The MRS is the rate at which a consumer is willing to give up one good (say, Y) to get one more unit of another good (say, X) while maintaining the same level of satisfaction. It is represented by the slope of the indifference curve.

MRSxy = - ΔY / ΔX

As consumption of X increases and consumption of Y decreases along an indifference curve, the MRSxy diminishes. This means the consumer is willing to give up less and less of Y for each additional unit of X.

Budget Line (Budget Constraint)

The budget line shows all the combinations of two goods that a consumer can afford to buy given their income and the prices of the goods.

Let I be income, Px be the price of Good X, and Py be the price of Good Y. The equation for the budget line is:

Px * X + Py * Y = I

The slope of the budget line is -Px / Py, representing the market trade-off between the two goods.

Consumer Equilibrium under Ordinal Approach

The consumer reaches equilibrium at the point where the highest possible indifference curve is tangent to the budget line. At this point:

• The slope of the indifference curve (MRSxy) is equal to the slope of the budget line (Px/Py).
• MRSxy = Px / Py
• This means the rate at which the consumer is willing to substitute X for Y is equal to the rate at which the market allows them to substitute X for Y.

If MRSxy > Px/Py, the consumer is willing to give up more Y for an extra unit of X than the market requires. They will buy more X and less Y, moving towards equilibrium.

If MRSxy < Px/Py, the consumer is willing to give up less Y for an extra unit of X than the market requires. They will buy less X and more Y, moving towards equilibrium.

Revealed Preference Hypothesis

The Revealed Preference Hypothesis was proposed by Paul Samuelson as a way to derive the laws of demand without relying on the subjective and difficult-to-measure concept of utility. It focuses on observing actual consumer choices.

Core Idea

If a consumer chooses a bundle of goods A over bundle B when both were affordable, then bundle A is "revealed" to be preferred to bundle B. The hypothesis attempts to establish a set of axioms about consumer behavior that are consistent with observed choices and from which demand curves can be derived.

Axioms of Revealed Preference

Samuelson proposed several axioms. The most fundamental is the Axiom of Revealed Preference (Strong Axiom):

• If bundle A is chosen over bundle B, then bundle B cannot be revealed to be preferred to bundle A. In simpler terms, if a consumer chooses bundle X when bundle Y was also available, they cannot, under any circumstances, choose bundle Y when bundle X is available. This ensures consistency.

A weaker version, the Weak Axiom of Revealed Preference (WARP): states that if a consumer chooses bundle A over bundle B when both are affordable, then bundle A must not be strictly more expensive than bundle B. If the prices change and bundle B is chosen, it implies bundle A is now more expensive than bundle B.

Deriving the Demand Curve

The revealed preference approach allows economists to derive the law of demand (that demand curves slope downwards) by observing how a consumer's choices change when prices change. By holding income and other prices constant and observing choices at different prices for a specific good, one can infer the consumer's preferences and construct a demand curve.

For example, if a consumer buys more of good X when its price falls (while income and other prices remain constant), this observed behavior is consistent with the downward-sloping demand curve predicted by utility theory.

Significance

This approach is considered more scientific because it is based on observable behavior rather than introspection about utility. It provides a foundation for demand theory that does not require the strong, often unrealistic, assumptions of cardinal or ordinal utility.

Hicks' Revision of Demand Theory

John Hicks, building upon the ordinal utility framework and incorporating insights from revealed preference, significantly revised the theory of demand. His work, particularly in "A Revision of Demand Theory" (1956), aimed to provide a more robust explanation of consumer choice and the effects of price changes.

Slutsky Equation and Income/Substitution Effects

Hicks refined the analysis of how a price change affects the quantity demanded. A price change has two effects:

1. Substitution Effect: As the price of a good falls, it becomes relatively cheaper compared to other goods. Consumers tend to substitute the cheaper good for the relatively more expensive ones, increasing the demand for the cheaper good. This effect always leads to an increase in demand when price falls (or decrease when price rises).
2. Income Effect: When the price of a good falls, the consumer's real income (purchasing power) increases. This increase in real income can lead to an increase or decrease in the demand for the good, depending on whether it is a normal or inferior good.

Hicks developed a method to decompose the total price effect into these two components. He used the concept of a hypothetical "compensating variation" in income to isolate the substitution effect. This involves adjusting the consumer's income after the price change so that they remain on their original indifference curve. The change in consumption due to this adjustment represents the pure substitution effect. The remaining change in consumption (from the original point to the final point after the price change) is the income effect.

Normal, Inferior, and Giffen Goods

Hicks' analysis clarifies the nature of different types of goods:

• Normal Goods: For normal goods, both the substitution effect and the income effect are positive when price falls. Thus, demand increases as price falls.
• Inferior Goods: For inferior goods, the substitution effect is positive, but the income effect is negative (as real income rises, demand for inferior goods falls). If the substitution effect is stronger than the income effect, demand still increases as price falls.
• Giffen Goods: A Giffen good is a rare exception where the negative income effect is so strong that it outweighs the positive substitution effect. As the price falls, demand for a Giffen good actually decreases, and as the price rises, demand increases. This results in an upward-sloping demand curve. Giffen goods must be inferior and constitute a significant portion of the consumer's budget.

Hicksian vs. Marshallian Demand

Hicks distinguished between two types of demand curves:

• Marshallian Demand: This is the standard demand curve showing the relationship between price and quantity demanded, holding money income constant. It combines both substitution and income effects.
• Hicksian Demand (or Compensated Demand): This demand curve shows the relationship between price and quantity demanded, holding real income (utility) constant. It isolates the substitution effect.

Hicks argued that the compensated demand curve is a more fundamental representation of consumer behavior because it captures the pure substitution response to price changes, independent of the changes in purchasing power.

Modern Utility Theory

Modern utility theory largely builds upon the ordinal approach and incorporates insights from behavioral economics. It seeks to provide a comprehensive framework for understanding consumer preferences and choices.

Expected Utility Theory

Developed by John von Neumann and Oskar Morgenstern, Expected Utility Theory (EUT) provides a framework for understanding how rational individuals make choices among alternatives where the outcomes are uncertain. It extends the ordinal approach to situations involving risk.

Key Concepts:

• Lottery: A choice between different outcomes, each with a certain probability.
• Expected Utility: The weighted average of the utilities of all possible outcomes, where the weights are the probabilities of those outcomes.

If a lottery L has outcomes x₁, x₂, ..., x_n with probabilities p₁, p₂, ..., p_n, then the expected utility of lottery L is:

E(U(L)) = p₁U(x₁) + p₂U(x₂) + ... + p_nU(x_n)

Where U(x_i) is the utility of outcome x_i.

Von Neumann-Morgenstern Axioms: EUT is based on a set of axioms that define rational behavior under uncertainty, including completeness, transitivity, continuity, and independence. The independence axiom is particularly important: if a consumer prefers lottery L1 to L2, then adding an identical outcome with the same probability to both lotteries should not change the preference.

Risk Aversion, Risk Neutrality, Risk Loving: The shape of the utility function determines an individual's attitude towards risk:

• Risk Averse: Concave utility function (U''(x) < 0). They prefer a certain outcome to a lottery with the same expected monetary value. They are willing to pay a premium to avoid risk.
• Risk Neutral: Linear utility function (U''(x) = 0). They are indifferent between a certain outcome and a lottery with the same expected monetary value.
• Risk Loving: Convex utility function (U''(x) > 0). They prefer a lottery to a certain outcome with the same expected monetary value.

Behavioral Economics and Anomalies

While EUT provides a benchmark for rational decision-making, behavioral economics highlights systematic deviations from these predictions. These deviations often arise from cognitive biases and psychological factors.

• Prospect Theory: Developed by Kahneman and Tversky, Prospect Theory offers a more descriptive model of decision-making under risk. It suggests that people evaluate potential losses and gains relative to a reference point (status quo) rather than absolute wealth levels. It also posits that people are generally risk-averse in the domain of gains but risk-seeking in the domain of losses, and that probabilities are often distorted (overweighting small probabilities, underweighting moderate to high probabilities).
• Framing Effects: The way choices are presented (framed) can significantly influence decisions, even if the underlying options are identical.
• Endowment Effect: People tend to value something they own more highly than something they do not own.
• Loss Aversion: The psychological impact of a loss is generally greater than the psychological impact of an equivalent gain.

Choice Under Risk and Uncertainty

This area deals with how consumers make decisions when the outcomes of their choices are not known with certainty.

Distinction between Risk and Uncertainty

While often used interchangeably, economists sometimes distinguish between:

• Risk: Situations where the probabilities of different outcomes are known. For example, gambling with known odds.
• Uncertainty: Situations where the probabilities of different outcomes are unknown or cannot be objectively determined. For example, investing in a new, unproven technology.

Decision Making Under Risk

As discussed with Expected Utility Theory, individuals facing risk can make decisions by comparing the expected utility of different choices. A rational, risk-averse individual will choose the option with the highest expected utility, which may not necessarily be the option with the highest expected monetary value. They might choose a slightly lower expected payout if it significantly reduces the risk.

Example: Consider two job offers:

• Job A: A certain salary of $50,000.
• Job B: A 50% chance of $80,000 and a 50% chance of $30,000 (Expected Monetary Value = 0.5 * $80,000 + 0.5 * $30,000 = $55,000).

A risk-neutral person would choose Job B because its expected monetary value ($55,000) is higher than Job A's ($50,000). However, a risk-averse person might choose Job A because the certainty of $50,000 provides higher utility than the gamble, even though the expected value of Job B is higher. The degree of risk aversion determines this choice.

Decision Making Under Uncertainty

Making decisions under uncertainty is more challenging because probabilities are unknown. Several heuristics or rules of thumb have been proposed to describe how people might decide:

• Maximin Criterion (Pessimist's Rule): Choose the option that maximizes the minimum possible outcome. This is a very conservative strategy, focusing on the worst-case scenario.
• Maximax Criterion (Optimist's Rule): Choose the option that maximizes the maximum possible outcome. This is a highly optimistic strategy, focusing on the best-case scenario.
• Minimax Regret Criterion: Choose the option that minimizes the maximum potential regret. Regret is the difference between the payoff you received and the payoff you could have received had you made the optimal choice for that outcome.
• Hurwicz Criterion: A compromise between maximin and maximax, using a coefficient of optimism (α) between 0 and 1. The decision-maker calculates a weighted average of the best and worst outcomes for each option and chooses the option with the highest weighted average.

These criteria highlight different approaches to dealing with the unknown, reflecting varying degrees of risk preference or caution.

Insurance and Diversification

Consumers use strategies like insurance and diversification to manage risk.

• Insurance: A risk-averse individual is willing to pay a premium (which is often higher than the expected loss) to transfer risk to an insurance company. This is because the utility loss from a large, unexpected loss is much greater than the utility gain from avoiding the premium payment.
• Diversification: "Don't put all your eggs in one basket." By spreading investments or consumption across various assets or goods, the impact of any single negative outcome is reduced. This is a key strategy for managing risk in financial markets and other areas.