Utility and Demand: Marginal Utility Theory and Consumer Choice

Utility and Demand

Introduction

This chapter explores how consumers make choices about what to buy, given their limited resources. It introduces the concept of utility, the marginal utility theory of consumer choice, and uses these ideas to predict how changes in prices and income affect demand.

Consumption Choices

Consumption Possibilities

Consumers face constraints in their choices due to limited income and the prices of goods and services. Economists summarize these constraints as:

• Consumption possibilities: All the combinations of goods and services a consumer can afford.

• Preferences: The consumer's likes and dislikes, which determine the benefit or satisfaction (utility) derived from consumption.

A Consumer's Budget Line

The budget line represents the boundary of consumption possibilities, given income and prices. For example, if Lisa has $40, movies cost $8 each, and cola costs $4 per case, her budget line shows all combinations of movies and cola she can purchase by spending her entire budget.

• Lisa can afford any combination on or inside her budget line.

• Combinations outside the budget line are unaffordable.

The budget constraint equation is:

$p_m Q_m + p_c Q_c = Y$

where $p_m$ and $p_c$ are the prices of movies and cola, $Q_m$ and $Q_c$ are the quantities, and $Y$ is income.

Divisible and Indivisible Goods

• Indivisible goods: Must be purchased in whole units (e.g., tickets).

• Divisible goods: Can be purchased in any quantity (e.g., gasoline).

Preferences and Utility

Utility

Utility is the satisfaction or benefit a consumer receives from consuming goods and services.

• Total utility: The total benefit from consuming a given quantity of goods.

• Utility function: The relationship between utility values and every possible bundle of goods. For example:

$U(Z, B) = \\sqrt{ZB}$

If bundle x has 16 pizzas and 9 burritos, $U(x) = \\sqrt{16 \\times 9} = 12$ utils. If bundle y has 13 of each, $U(y) = \\sqrt{13 \\times 13} = 13$ utils. Lisa prefers y to x.

Ordinal vs. Cardinal Preferences

• Ordinal measure: Ranks bundles by preference but does not indicate how much more one is preferred over another (like letter grades).

• Cardinal measure: Allows absolute comparisons between ranks (e.g., money).

Maximizing Utility

Total and Marginal Utility

As the quantity of a good consumed increases, total utility increases, but the extra utility from each additional unit (marginal utility) decreases.

• Marginal utility (MU): The extra utility from consuming one more unit of a good.

$MU_z = \\frac{\\Delta U}{\\Delta Z}$

Law of Diminishing Marginal Utility

The law of diminishing marginal utility states that as a person consumes more of a good, the marginal utility from each additional unit declines.

Example Table: Marginal Utility

Quantity (Q)	Total Utility (U)	Marginal Utility (MU)
0	0	-
1	4	4
2	7	3
3	9	2
4	10	1
5	10	0

Utility-Maximizing Choice

Consumer Equilibrium

Consumers aim to maximize total utility given their budget constraint. The utility-maximizing combination is the one that yields the highest total utility among all affordable options.

Example Table: Lisa's Utility from Movies and Cola

Movies (per month)	Total Utility	Marginal Utility	Cola (cases per month)	Total Utility	Marginal Utility
0	0	-	0	0	-
1	50	50	2	75	75
2	90	40	4	123	48
3	125	35	6	225	102
4	150	25	8	248	23
5	170	20	10	265	17

Choosing at the Margin

• Marginal utility per dollar: The marginal utility from a good divided by its price.

For movies: $\\frac{MU_M}{P_M}$ For cola: $\\frac{MU_C}{P_C}$

To maximize utility, consumers should allocate their budget so that the marginal utility per dollar is equal for all goods:

$\\frac{MU_M}{P_M} = \\frac{MU_C}{P_C}$

Utility-Maximizing Rule

• Spend all available income.

• Equalize the marginal utility per dollar for all goods.

Example Table: Equalizing Marginal Utilities per Dollar

Movies (Quantity)	Marginal Utility	Marginal Utility per Dollar	Cola (Cases)	Marginal Utility	Marginal Utility per Dollar
1	50	6.25	8	23	2.88
2	40	5.00	6	102	12.75
3	35	4.38	4	48	6.00

Predictions of Marginal Utility Theory

A Fall in the Price of a Movie

When the price of a good falls, the quantity demanded increases. For example, if the price of a movie falls, $MU_M/P_M$ rises, so the consumer increases the number of movies seen to restore equilibrium ($MU_M/P_M = MU_C/P_C$).

Table: How a Change in the Price of Movies Affects Choices

Movies ($4 each)	Marginal Utility per Dollar	Cola (Cases)	Marginal Utility per Dollar
1	12.50	7	1.25
2	10.00	6	2.50
3	8.75	5	5.00
4	7.00	4	6.00
5	6.00	3	8.00

A Rise in the Price of Cola

If the price of cola rises, $MU_C/P_C$ falls. The consumer decreases cola consumption and increases movie consumption to restore equilibrium.

Table: How a Change in the Price of Cola Affects Choices

Movies ($4 each)	Marginal Utility per Dollar	Cola ($8 per case)	Marginal Utility per Dollar
2	10.00	4	3.00
4	7.00	2	6.00
6	6.00	0	0.00

A Rise in Income

When income increases, the demand for normal goods increases. For example, if Lisa's income rises from $40 to $56, she buys more movies and more cola.

Table: Lisa's Choices with Increased Income

Movies (per month)	Cola (cases per month)
6	4
8	6

Summary

• Consumers face limits to consumption due to income and prices.

• Utility and marginal utility explain how consumers make choices to maximize satisfaction.

• The law of diminishing marginal utility means each additional unit of a good provides less extra satisfaction.

• Consumers maximize utility by equalizing the marginal utility per dollar across all goods.

• Changes in prices and income affect consumption choices and demand.

Additional info: Tables and calculations have been inferred and expanded for clarity and completeness.