Consumer Choice: Utility Theory and Optimization in Microeconomics chapter 7

Chapter 7: Consumer Choice

Learning Objectives

• Distinguish between total utility and marginal utility, and explain why marginal utility ultimately falls as a person consumes more of an item.

• Explain why an optimal choice of how much to consume entails equalizing the marginal utility per dollar spent across all items.

• Describe the substitution effect and real-income effect of a price change.

• Discuss why bounded rationality may prevent reaching a true consumer optimum.

7.1 Utility Theory

Introduction to Utility Theory

Utility theory is a foundational concept in microeconomics that explains how consumers make choices to maximize their satisfaction given limited resources. Utility analysis helps economists understand and predict consumer behavior.

• Utility: The want-satisfying power of a good or service; a measure of the satisfaction or happiness derived from consumption.

• Utility analysis: The study of consumer decision-making based on the goal of utility maximization.

Measuring Utility

• Util: A representative unit by which utility is measured. The concept was developed by philosopher Jeremy Bentham and is central to utilitarianism.

Total and Marginal Utility

Consumers derive satisfaction from consuming goods and services. The concepts of total and marginal utility help explain how satisfaction changes with consumption.

• Total utility: The overall satisfaction received from consuming a certain quantity of a good or service.

• Marginal utility: The additional satisfaction gained from consuming one more unit of a good or service.

Formula:

$\text{Marginal utility} = \frac{\text{Change in total utility}}{\text{Change in number of units consumed}}$

Table: Total and Marginal Utility of Downloading and Using Digital Apps

Number of Digital Apps Downloaded and Used per Week	Total Utility (utils per week)	Marginal Utility (utils per week)
0	0	-
1	10	10
2	18	8
3	24	6
4	28	4
5	28	0

Additional info: Table values inferred from standard utility schedules and the description in the notes.

Law of Diminishing Marginal Utility

The law of diminishing marginal utility states that as a person consumes more units of a good or service, the additional satisfaction (marginal utility) from each extra unit decreases.

• Marginal utility falls as more is consumed.

• Marginal utility equals zero when total utility is at its maximum.

• If marginal utility becomes negative, further consumption reduces overall satisfaction.

Example: The first slice of pizza provides high satisfaction, but each additional slice offers less, and eventually may even cause discomfort.

7.2 Optimizing Consumption Choices

Consumer Optimum

Consumers aim to maximize their satisfaction (utility) given their limited income. The consumer optimum is the combination of goods and services that yields the highest possible utility within a budget constraint.

• Occurs when the marginal utility per dollar spent is equalized across all goods.

• All available income is spent.

Rule of Equal Marginal Utility per Dollar Spent

To maximize utility, consumers allocate their budget so that the last dollar spent on each good provides the same amount of marginal utility.

Formula:

$\frac{MU_A}{P_A} = \frac{MU_B}{P_B} = \frac{MU_C}{P_C} = \ldots$

Where $MU$ is marginal utility and $P$ is price for goods A, B, C, etc.

Example: If a consumer spends $100 on a designer T-shirt, the marginal utility per dollar spent on the T-shirt must equal that of other goods purchased.

7.3 How a Price Change Affects Consumer Optimum

Substitution and Real-Income Effects

When the price of a good changes, two main effects influence consumer choices:

• Substitution effect: Consumers substitute cheaper goods for more expensive ones.

• Real-income effect: A change in price affects the consumer's purchasing power. If the price falls, real income increases; if the price rises, real income decreases.

Example: If the price of digital apps drops, consumers buy more apps, and the marginal utility per app falls as consumption increases.

Deriving the Demand Curve

The demand curve is derived by observing how changes in the price of a good affect the quantity demanded, holding other factors constant (income, tastes, prices of related goods).

• As price decreases, the budget line rotates outward, allowing for higher consumption and a new consumer optimum.

• The demand curve slopes downward, reflecting the inverse relationship between price and quantity demanded.

Diamond-Water Paradox

This paradox illustrates the difference between total utility and marginal utility:

• Water is essential and provides high total utility but is cheap due to low marginal utility.

• Diamonds are non-essential but have high marginal utility and are expensive.

Behavioural Economics and Consumer Choice Theory

Bounded Rationality

Traditional consumer choice theory assumes rational behavior aimed at utility maximization. However, bounded rationality recognizes that consumers have limited information, time, and cognitive ability to make optimal choices.

• Behavioural economics questions the rationality assumption and suggests that real-world choices may deviate from utility maximization.

• Despite these limitations, utility theory remains useful for predicting consumer behavior.

Appendix 7A: More Advanced Consumer Choice Theory

Indifference Curves

Indifference curves represent combinations of goods that yield the same level of satisfaction to the consumer.

• Downward (negative) slope; convex to the origin.

• 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 substitute one good for another while maintaining the same level of satisfaction.

Formula:

$MRS = -\frac{\Delta Q_A}{\Delta Q_B}$

Where $\Delta Q_A$ is the change in quantity of good A and $\Delta Q_B$ is the change in quantity of good B.

Budget Constraint and Consumer Optimum

The budget constraint shows all possible combinations of goods that can be purchased with a fixed income at given prices.

• Consumer optimum is achieved at the tangency point between the highest indifference curve and the budget constraint.

Table: Budget Constraint Example

Wireless Earbuds (per year)	Stylus Pens (per year)	Total Cost ($)
5	0	25
4	3	25
2	7	25

Additional info: Table values inferred from standard budget constraint examples.

Deriving the Demand Curve from Indifference Analysis

• When the price of one good changes (holding income and other prices constant), the budget line rotates, leading to a new consumer optimum and a change in quantity demanded.

• This process generates the downward-sloping demand curve.

Summary of Key Concepts

• Total utility is the overall satisfaction from consumption; marginal utility is the additional satisfaction from one more unit.

• Marginal utility declines as more is consumed (law of diminishing marginal utility).

• Consumer optimum is achieved when marginal utility per dollar spent is equalized across all goods and all income is spent.

• Price changes lead to substitution and real-income effects, influencing consumer choices and demand.

• Bounded rationality recognizes limits to consumer decision-making.

• Indifference curves and budget constraints provide a graphical approach to consumer choice and demand derivation.