Possibilities, Preferences, and Choices: Consumer Theory in Microeconomics

Consumption Possibilities

Budget Constraints and the Budget Line

Household consumption choices are limited by income and the prices of goods and services. The budget line represents the combinations of goods and services a household can afford given its income and the prices of those goods.

• Budget Line: The graphical representation of all possible combinations of two goods that can be purchased with a given income at given prices.

• Affordable Region: All combinations on or below the budget line are affordable; combinations above the line are unaffordable.

Example: Budget Line Calculation

Suppose Lisa has $40 to spend. The price of a movie is $8, and the price of a case of cola is $4. The table below shows possible combinations Lisa can purchase:

Consumption Possibility	Movies (per month)	Cola (cases per month)
A	0	10
B	1	8
C	2	6
D	3	4
E	4	2
F	5	0

Key Point: The line through points A to F is Lisa's budget line.

Budget Equation

The budget line can be described mathematically using the budget equation:

• Budget Equation:

$P_C Q_C + P_M Q_M = Y$

• $P_C$ = Price of cola

• $Q_C$ = Quantity of cola

• $P_M$ = Price of movies

• $Q_M$ = Quantity of movies

• $Y$ = Income

This equation shows all combinations of cola and movies that exhaust Lisa's income.

Divisibility of Goods

• Indivisible Goods: Must be bought in whole units (e.g., cars, appliances).

• Divisible Goods: Can be bought in any quantity (e.g., gasoline, electricity).

Graphical Interpretation

• Points on the budget line: All income is spent.

• Points below the budget line: Not all income is spent (affordable, but not maximizing consumption).

• Points above the budget line: Unaffordable given current income and prices.

Effects of Changes in Prices and Income

• Change in Price: A rise in the price of one good rotates the budget line inward (reducing affordable quantity of that good), while a fall rotates it outward.

• Change in Income: An increase in income shifts the budget line outward (parallel shift), while a decrease shifts it inward. The slope remains unchanged because relative prices are constant.

Formulas and Definitions

• Real Income: Income expressed as the quantity of goods a household can afford to buy.

• Relative Price: The price of one good divided by the price of another. It is the magnitude of the slope of the budget line.

$\text{Relative Price of Movies in terms of Cola} = \frac{P_M}{P_C}$

$\text{Real Income in terms of Cola} = \frac{Y}{P_C}$

Example Application

• If Lisa spends all her income on cola: $Q_C = \frac{Y}{P_C}$, $Q_M = 0$

• If Lisa spends all her income on movies: $Q_M = \frac{Y}{P_M}$, $Q_C = 0$

Additional info: The budget line is a foundational concept in consumer theory, illustrating the trade-offs and opportunity costs faced by consumers in allocating their limited resources.