Individual and Market Demand: Microeconomics Study Notes

Individual and Market Demand

Introduction

This chapter explores the foundations of demand in microeconomics, focusing on how individual and market demand curves are derived, the effects of price and income changes, and the empirical estimation of demand. Key concepts include the substitution and income effects, consumer surplus, network externalities, and mathematical approaches to demand theory.

Individual Demand

Effect of Price Changes

• Price-Consumption Curve: Traces the utility-maximizing combinations of two goods as the price of one changes, holding income and the price of the other good constant.

• Individual Demand Curve: Relates the quantity of a good that a single consumer will buy to its price.

• Key Properties:

  • The attainable utility level changes as we move along the demand curve.

  • At every point, the consumer maximizes utility, satisfying the condition that the marginal rate of substitution (MRS) equals the ratio of the prices of the two goods.

• Example: If the price of food decreases (with income and the price of clothing fixed), the consumer chooses a new market basket, tracing out the demand curve for food.

Effect of Income Changes

• Income-Consumption Curve: Traces the utility-maximizing combinations of two goods as the consumer’s income changes, holding prices constant.

• As income increases, the consumer alters their choice of goods, shifting the demand curve to the right.

• Example: If income rises from $10 to $30, the consumer’s optimal basket changes, and the income-consumption curve is traced out.

Normal versus Inferior Goods

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

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

• Example: Hamburger may be a normal good at low incomes but becomes an inferior good at higher incomes, as shown by a backward-bending income-consumption curve.

Engel Curves

• Engel Curve: Relates the quantity of a good consumed to income.

• For normal goods, the Engel curve is upward sloping; for inferior goods, it may bend backward at higher incomes.

• Example: Health care and entertainment are normal goods, while rental housing may become inferior at higher incomes.

Substitutes and Complements

• Substitutes: An increase in the price of one good leads to an increase in the quantity demanded of another good.

• Complements: An increase in the price of one good leads to a decrease in the quantity demanded of another good.

• Independent Goods: A change in the price of one good has no effect on the quantity demanded of another.

Income and Substitution Effects

Definitions and Decomposition

• Substitution Effect: The change in consumption of a good associated with a change in its price, holding utility constant.

• Income Effect: The change in consumption resulting from a change in purchasing power, holding relative prices constant.

• Total Effect: The sum of the substitution and income effects.

• Formula:

  • $\text{Total Effect} = \text{Substitution Effect} + \text{Income Effect}$

Normal and Inferior Goods

• For normal goods, both effects reinforce each other: a price decrease increases quantity demanded.

• For inferior goods, the income effect is negative but usually smaller than the substitution effect, so a price decrease still increases quantity demanded.

• Giffen Good: An inferior good where the negative income effect outweighs the substitution effect, causing the demand curve to slope upward.

Market Demand

From Individual to Market Demand

• Market Demand Curve: Relates the total quantity of a good demanded by all consumers in the market to its price.

• Obtained by horizontally summing individual demand curves at each price.

• Market demand shifts right as more consumers enter the market or as individual demands increase.

Elasticity of Demand

• Price Elasticity of Demand: Measures the responsiveness of quantity demanded to a change in price.

• Formula:

  • $E_d = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q}$

• Elastic Demand: $|E_d| > 1$; quantity demanded is responsive to price changes.

• Inelastic Demand: $|E_d| < 1$; quantity demanded is less responsive to price changes.

• Unit Elastic: $|E_d| = 1$; total expenditure remains constant as price changes.

Examples of Market Demand

• Aggregate Demand for Wheat:

  • Domestic demand: $Q_d = 1430 - 55P$

  • Foreign demand: $Q_f = 1470 - 70P$

  • Total world demand: $Q = Q_d + Q_f = 2900 - 125P$

• Speculative Demand: Demand driven by expectations of future price increases, not just current utility.

Consumer Surplus

Definition and Measurement

• Consumer Surplus: The difference between what a consumer is willing to pay for a good and what they actually pay.

• Graphically, it is the area under the demand curve and above the price line, up to the quantity purchased.

• Formula for a linear demand curve:

  • $\text{Consumer Surplus} = \frac{1}{2} (\text{Maximum Price} - \text{Market Price}) \times \text{Quantity}$

• Application: Used to evaluate the benefits of market structures and public policies.

Network Externalities

Types and Effects

• Network Externality: When an individual's demand depends on the purchases of others.

• Positive Network Externality (Bandwagon Effect): Demand increases as more people buy the good.

• Negative Network Externality (Snob Effect): Demand decreases as more people buy the good, due to a desire for exclusivity.

• Example: Social media platforms benefit from positive network externalities, while luxury goods may exhibit snob effects.

Empirical Estimation of Demand

Statistical and Experimental Approaches

• Statistical Estimation: Uses observed data and regression analysis to estimate demand functions.

• General Linear Demand Function:

  • $Q = a - bP + cI$

• Isoelastic Demand Curve: Elasticity is constant; written as:

  • $\log(Q) = a - b\log(P) + c\log(I)$

• Cross-Price Elasticity: Measures the responsiveness of demand for one good to the price change of another.

  • If positive, goods are substitutes; if negative, they are complements.

• Experimental Estimation: Uses controlled experiments or surveys to estimate demand, though costly and limited in scope.

Appendix: Demand Theory—A Mathematical Treatment

Utility Maximization

• Utility Function: Represents consumer preferences. Example: $U(X, Y) = \log X + \log Y$

• Budget Constraint: $P_X X + P_Y Y = I$

• Optimization Problem: Maximize $U(X, Y)$ subject to the budget constraint.

Method of Lagrange Multipliers

• Lagrangian Function: $\mathcal{L} = U(X, Y) - \lambda (P_X X + P_Y Y - I)$

• First-Order Conditions:

  • $\frac{\partial \mathcal{L}}{\partial X} = 0$

  • $\frac{\partial \mathcal{L}}{\partial Y} = 0$

  • $\frac{\partial \mathcal{L}}{\partial \lambda} = 0$

• Equal Marginal Principle: $\frac{MU_X}{P_X} = \frac{MU_Y}{P_Y}$

• Marginal Rate of Substitution (MRS): $MRS_{XY} = \frac{MU_X}{MU_Y} = \frac{P_X}{P_Y}$

Cobb-Douglas Utility Function

• Form: $U(X, Y) = X^a Y^{1-a}$

• Demand Functions:

  • $X = \frac{aI}{P_X}$

  • $Y = \frac{(1-a)I}{P_Y}$

• Lagrange Multiplier: Represents the marginal utility of income.

Expenditure Minimization (Duality)

• Minimize $P_X X + P_Y Y$ subject to $U(X, Y) = U^*$

• Yields the same demand functions as utility maximization.

Income and Substitution Effects: The Slutsky Equation

• Slutsky Equation: Decomposes the total effect of a price change into substitution and income effects.

• Formula:

  • $\Delta X = \left( \frac{\partial X}{\partial P_X} \right)_{U} + \left( \frac{\partial X}{\partial I} \right) \Delta I$

• Hicksian Substitution Effect: Alternative decomposition using compensated demand curves.

Summary Table: Types of Goods and Effects

Type of Good	Income Effect	Substitution Effect	Total Effect of Price Decrease
Normal Good	Positive	Positive	Increase in quantity demanded
Inferior Good	Negative	Positive	Usually increase in quantity demanded
Giffen Good	Negative (large)	Positive	Decrease in quantity demanded

Additional info: Some mathematical derivations and empirical examples have been expanded for clarity and completeness.