chapter 9

Possibilities, Preferences, and Choices

Introduction

This chapter explores how consumers make choices given their limited resources. It introduces the concepts of the budget line, indifference curves, and the effects of changes in prices and income on consumption decisions. The analysis provides the foundation for understanding consumer behavior in microeconomics.

Consumption Possibilities

Budget Constraints

• Budget Line: The budget line represents all combinations of two goods that a consumer can afford given their income and the prices of the goods.

• Constraint: Consumers can choose any combination on or inside the budget line, but not outside it.

• Example: Lisa has $40 to spend. The price of a movie is $8, and the price of cola is $4 per case. The budget line shows all combinations of movies and cola she can purchase.

Table: Possible Combinations of Movies and Cola

Possibility	Movies (Quantity)	Expenditure on Movies	Cola (Cases)	Expenditure on Cola
A	0	$0	10	$40
B	1	$8	8	$32
C	2	$16	6	$24
D	3	$24	4	$16
E	4	$32	2	$8
F	5	$40	0	$0

Additional info: Table inferred from context and typical textbook examples.

The Budget Equation

• The budget line can be described by the equation:

$P_C Q_C + P_M Q_M = Y$

• Where $P_C$ is the price of cola, $Q_C$ is the quantity of cola, $P_M$ is the price of movies, $Q_M$ is the quantity of movies, and $Y$ is income.

• Dividing both sides by $P_C$ gives:

$Q_C + \left(\frac{P_M}{P_C}\right) Q_M = \frac{Y}{P_C}$

• Solving for $Q_C$:

$Q_C = \frac{Y}{P_C} - \left(\frac{P_M}{P_C}\right) Q_M$

• Real Income: $\frac{Y}{P_C}$ is the consumer's real income in terms of cola.

• Relative Price: $\frac{P_M}{P_C}$ is the relative price of a movie in terms of cola.

Changes in Budget Line

• Change in Price: A rise in the price of a good (e.g., movies) rotates the budget line inward, reducing the affordable quantity of that good and increasing the slope.

• Change in Income: An increase or decrease in income shifts the budget line outward or inward, respectively, without changing its slope (relative prices remain constant).

Preferences and Indifference Curves

Indifference Curves

• Indifference Curve: A line showing all combinations of two goods among which a consumer is indifferent (derives the same satisfaction).

• All points above an indifference curve are preferred; all points below are less preferred.

• Preference Map: A set of indifference curves representing different levels of utility.

Marginal Rate of Substitution (MRS)

• Definition: The MRS measures the rate at which a consumer is willing to give up one good (y) to get an additional unit of another good (x), while remaining on the same indifference curve.

• The MRS is the (absolute value of the) slope of the indifference curve at any point.

• Steep Curve: High MRS (willing to give up a lot of y for x).

• Flat Curve: Low MRS (willing to give up little y for x).

Diminishing Marginal Rate of Substitution

• As a consumer has more of good x and less of good y, the willingness to substitute y for x diminishes.

• This is reflected in the convex shape of typical indifference curves.

• Example: At point C, Lisa is willing to give up 2 cases of cola for one more movie (MRS = 2). At point G, she is willing to give up only 0.5 case of cola for one more movie (MRS = 0.5).

Degree of Substitutability

• The shape of indifference curves indicates how easily two goods can be substituted for each other.

• Ordinary Goods: Convex indifference curves.

• Perfect Substitutes: Straight-line indifference curves.

• Perfect Complements: Right-angle indifference curves.

Predicting Consumer Choices

Best Affordable Choice

• The consumer's optimal choice is where the highest attainable indifference curve is tangent to the budget line.

• At this point, the MRS equals the relative price of the two goods:

$MRS = \frac{P_M}{P_C}$

• Any other point on the budget line is less preferred or not affordable.

Effects of Changes in Price and Income

Price Effect

• The price effect is the change in the quantity of a good consumed resulting from a change in its price.

• A decrease in the price of a good rotates the budget line outward, increasing the quantity consumed of that good.

Income Effect

• The income effect is the change in consumption resulting from a change in real income (purchasing power), holding prices constant.

• An increase in income shifts the budget line outward, allowing the consumer to reach a higher indifference curve.

Substitution Effect and Income Effect

• The total effect of a price change can be separated into:

  • Substitution Effect: The change in consumption when the consumer stays on the same indifference curve but faces new relative prices.

  • Income Effect: The change in consumption due to the change in real income, moving to a new indifference curve.

• For a normal good, both effects increase quantity demanded when price falls.

• For an inferior good, the income effect is negative, but as long as the substitution effect dominates, the demand curve still slopes downward.

Summary Table: Effects of Price and Income Changes

Effect	Definition	Direction for Normal Good	Direction for Inferior Good
Substitution Effect	Change in quantity due to change in relative price, same indifference curve	Increases quantity demanded when price falls	Increases quantity demanded when price falls
Income Effect	Change in quantity due to change in real income	Increases quantity demanded when price falls	Decreases quantity demanded when price falls

Key Terms and Concepts

• Budget Line: Shows all affordable combinations of two goods given income and prices.

• Indifference Curve: Shows all combinations of goods yielding the same satisfaction.

• Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility.

• Substitution Effect: The effect of a change in relative prices on consumption, holding utility constant.

• Income Effect: The effect of a change in purchasing power on consumption.

• Normal Good: A good for which demand increases as income increases.

• Inferior Good: A good for which demand decreases as income increases.