Consumer Theory in Microeconomics

Consumer theory is one of the core components of microeconomics. Its central research focus is to explain how rational consumers choose combinations of goods and services to maximize their utility (satisfaction level) under the constraint of limited income. This theory provides a systematic analytical framework for understanding consumer purchasing decisions, and it is mainly divided into two branches: Cardinal Utility Theory and Ordinal Utility Theory.

I. Core Premise Assumptions

The derivation of consumer theory is based on the following fundamental assumptions:

1. Rationality Assumption
   Consumers are rational economic agents who pursue utility maximization. When making consumption decisions, they will weigh the benefits and costs of different commodity combinations.
2. Three Axioms of Preferences
   • Completeness
     Consumers can rank any two commodity combinations (e.g., Combination A: 2 apples + 1 bread; Combination B: 1 apple + 2 breads). That is, they can clearly judge that "A is better than B", "B is better than A", or "A is indifferent to B".
   • Transitivity
     If a consumer thinks A is better than B and B is better than C, then he or she must think A is better than C. This ensures the consistency of consumer preferences.
   • Non-satiation (More is Better)
     Assuming the quality of goods is the same, consumers always prefer more goods to fewer. In other words, a commodity combination with a larger quantity will bring a higher level of utility.
3. Income Constraint Assumption
   Consumers' income is limited, and their purchasing behavior is restricted by the given income level and commodity prices.

II. Core Concept: Utility

Utility refers to the satisfaction that consumers obtain from consuming a certain good or service. It is a quantitative expression of consumers' subjective psychological feelings and the core concept of consumer theory.

• Total Utility (TU)
  It is the total satisfaction obtained by consumers after consuming a certain quantity of goods or services. The total utility tends to rise first and then fall as the consumption quantity increases.
• Marginal Utility (MU)
  It is the increment of total utility brought by each additional unit of commodity consumption. The formula is:
  $$MU=\frac{\Delta TU}{\Delta Q}$$
  Marginal utility is the key variable determining consumer consumption decisions, and it follows the Law of Diminishing Marginal Utility.

III. Branch 1: Cardinal Utility Theory

1. Core View

Cardinal Utility Theory assumes that utility can be measured and aggregated by specific numerical values (such as 1, 2, 3). For example, the utility of consuming 1 bread is 5, and the utility of consuming 1 bottle of milk is 3, so the total utility of this combination is 8.

2. Core Law: Law of Diminishing Marginal Utility

Within a certain period, when consumers continuously consume a certain commodity, the marginal utility of the commodity will gradually decrease and even become negative as the consumption quantity increases.

• Example: When a person is hungry, the marginal utility of the first bread is very high (say 10); when eating the second bread, the satisfaction decreases, and the marginal utility becomes 5; when eating the third bread, the person may already be full, and the marginal utility becomes 0; continuing to eat the fourth bread will cause discomfort, and the marginal utility becomes -2.

3. Consumer Equilibrium Condition

Consumer equilibrium refers to the state of commodity purchase combination where consumers maximize their utility under given income and commodity prices. At this time, consumers are unwilling to adjust the purchase quantity any more.

For the case of two commodities (X and Y), the equilibrium condition is:
$$\frac{MU_X}{P_X}=\frac{MU_Y}{P_Y}=\lambda$$
Where:

• $MU_X$ and $MU_Y$ are the marginal utilities of commodity X and Y respectively;
• $P_X$ and $P_Y$ are the prices of commodity X and Y respectively;
• $\lambda$ is the marginal utility of money (assumed to be a constant).

The meaning of this formula is: the marginal utility obtained by the last unit of money spent on each commodity by consumers is equal, and the total utility reaches the maximum at this time. If $\frac{MU_X}{P_X}>\frac{MU_Y}{P_Y}$, consumers will increase the purchase of X and reduce the purchase of Y until the two are equal.

IV. Branch 2: Ordinal Utility Theory

1. Core View

Ordinal Utility Theory holds that utility is a kind of subjective preference, which cannot be measured by specific numerical values, but only expressed by ranking (such as first, second, third). For example, consumers can judge that "combination A is better than combination B", but cannot determine how much higher the utility of A is than that of B.

This theory analyzes consumer equilibrium from a geometric perspective by using two tools: Indifference Curve and Budget Line.

2. Key Tool 1: Indifference Curve

An indifference curve is the locus of all combinations of two commodities that can bring the same level of utility to consumers.

• Basic Characteristics
  1. It slopes downward to the right: To maintain the same utility level, increasing the consumption of one commodity must be accompanied by reducing the consumption of the other commodity.
  2. It is convex to the origin: This is determined by the Law of Diminishing Marginal Rate of Substitution.
  3. There are countless indifference curves in the same coordinate plane, and the farther the curve is from the origin, the higher the utility level it represents.
  4. Any two indifference curves will not intersect.
• Core Concept: Marginal Rate of Substitution (MRS)
  The marginal rate of substitution refers to the quantity of another commodity that consumers need to give up when increasing one unit of consumption of a certain commodity under the premise of maintaining the utility level unchanged. The formula is:
  $$MRS_{XY}=-\frac{\Delta Y}{\Delta X}$$
  Its absolute value is equal to the slope of the indifference curve at that point, and it follows the Law of Diminishing Marginal Rate of Substitution (as the consumption of commodity X increases, the quantity of commodity Y that consumers are willing to give up becomes less and less).

3. Key Tool 2: Budget Line

The budget line (also called the consumption possibility line) is the locus of all maximum combination points of two commodities that consumers can buy under given income and commodity prices.

For two commodities (X and Y), the equation of the budget line is:
$$I=P_X \cdot X+P_Y \cdot Y$$
Where $I$ is the consumer's given income.

• Slope of the Budget Line: $-\frac{P_X}{P_Y}$, reflecting the price ratio of the two commodities.
• Movement of the Budget Line: Changes in income will lead to the parallel movement of the budget line (shifting to the right when income increases, shifting to the left when income decreases); changes in commodity prices will lead to the rotation of the budget line (if the price of a certain commodity decreases, the intercept of the budget line on the axis of that commodity extends).

4. Consumer Equilibrium Condition

The consumer equilibrium point is the tangent point of the indifference curve and the budget line. At this point, the slope of the budget line is equal to the slope of the indifference curve, and the formula is expressed as:
$$MRS_{XY}=\frac{P_X}{P_Y}$$
The commodity combination corresponding to this tangent point is the combination that can bring the highest utility level to consumers under income constraints.

V. Application of Consumer Theory: Impact of Price Changes

When commodity prices change, consumers' equilibrium points will shift, which in turn affects consumption quantity. This change can be decomposed into Substitution Effect and Income Effect:

1. Substitution Effect
   When the price of a commodity decreases, the commodity becomes cheaper relative to other commodities, and consumers will increase the purchase of this commodity and reduce the purchase of substitute commodities (the utility level remains unchanged).
2. Income Effect
   When the price of a commodity decreases, the consumer's real income (purchasing power) increases, which in turn increases or decreases the purchase of this commodity (the utility level changes).

• Normal Goods: Both substitution effect and income effect are positive. When the price decreases, the consumption quantity increases.
• Inferior Goods: The substitution effect is positive, while the income effect is negative, and the substitution effect is greater than the income effect. The consumption quantity still increases when the price decreases.
• Giffen Goods: A special type of inferior goods. The substitution effect is positive, the income effect is negative and exceeds the substitution effect, so the consumption quantity decreases when the price decreases (such as potatoes during the famine period).