Microeconomics Study Notes: Demand, Utility, and Marginal Analysis

Demand and Quantity Demanded

Definitions and Key Concepts

Understanding the distinction between demand and quantity demanded is fundamental in microeconomics. These concepts describe consumer behavior in response to price changes and other factors.

• Demand: The relationship between the price of a good and the quantity consumers are willing and able to purchase at each price, holding other factors constant.

• Quantity Demanded: The specific amount of a good that consumers are willing to buy at a particular price.

• Individual vs. Market Demand: Individual demand refers to a single consumer, while market demand aggregates all consumers in the market.

Example: If the price of apples decreases, the quantity demanded by each consumer may increase, leading to a higher market demand.

Determinants of Demand

Several factors influence demand beyond price.

• Income

• Prices of related goods (substitutes and complements)

• Tastes and preferences

• Expectations about future prices

• Number of buyers

Demand Function and Equation

The demand function mathematically expresses the relationship between quantity demanded and its determinants.

• General form: $Q_d = f(P, I, P_r, T, E, N)$ Where: $Q_d$ = quantity demanded $P$ = price of the good $I$ = income $P_r$ = price of related goods $T$ = tastes $E$ = expectations $N$ = number of buyers

Law of Demand

The law of demand states that, ceteris paribus, as the price of a good increases, the quantity demanded decreases, and vice versa.

• Downward-sloping demand curve: Graphically represents the inverse relationship between price and quantity demanded.

Market Demand

Market demand is the sum of all individual demands for a good or service.

• Market demand curve: Obtained by horizontally summing individual demand curves.

Utility and Consumer Choice

Utility Function

Utility measures the satisfaction or happiness a consumer derives from consuming goods and services.

• Utility Function: Assigns a numerical value to each possible bundle of goods, representing the consumer's level of satisfaction. $U = U(x, y)$ Where $x$ and $y$ are quantities of two goods.

• Indifference Curve: A curve showing all combinations of goods that provide the consumer with the same level of utility.

Example: If a consumer is equally satisfied with 2 apples and 3 oranges or 4 apples and 1 orange, both bundles lie on the same indifference curve.

Properties of Indifference Curves

• Downward sloping: More of one good requires less of the other to maintain the same utility.

• Cannot intersect: Each curve represents a unique level of utility.

• Convex to the origin: Reflects diminishing marginal rate of substitution.

Marginal Utility

Marginal utility is the additional satisfaction gained from consuming one more unit of a good.

• Marginal Utility of X: $MU_x = \frac{\partial U(x, y)}{\partial x}$

• Marginal Utility of Y: $MU_y = \frac{\partial U(x, y)}{\partial y}$

Example: If consuming an extra apple increases utility by 5 units, $MU_x = 5$.

Marginal Rate of Substitution (MRS)

The marginal rate of substitution is the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility.

• Formula: $MRS_{xy} = -\frac{MU_x}{MU_y}$

• Represents the slope of the indifference curve at any point.

Demand Curve Shifts and Elasticity

Shifts in Demand Curve

Factors other than price can shift the demand curve.

• Increase in demand: Rightward shift (e.g., higher income for normal goods).

• Decrease in demand: Leftward shift (e.g., lower income for normal goods).

Elasticity of Demand

Elasticity measures the responsiveness of quantity demanded to changes in price.

• Price Elasticity of Demand: $E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$

• Elastic demand: $|E_d| > 1$ (quantity demanded changes more than price)

• Inelastic demand: $|E_d| < 1$ (quantity demanded changes less than price)

Example: If a 10% increase in price leads to a 20% decrease in quantity demanded, $E_d = -2$ (elastic demand).

Tables

Comparison of Individual and Market Demand

Type	Definition	Graphical Representation
Individual Demand	Quantity demanded by a single consumer at each price	Single demand curve
Market Demand	Sum of all individual demands at each price	Horizontal sum of individual curves

Properties of Indifference Curves

Property	Description
Downward Sloping	More of one good requires less of the other to maintain utility
Convexity	Reflects diminishing marginal rate of substitution
No Intersection	Each curve represents a unique utility level

Additional info:

• Some content inferred from context and standard microeconomics curriculum, such as the mathematical form of utility functions and elasticity formulas.

• Graphical examples referenced in the notes (e.g., indifference curves, demand curves) are described in text, as images cannot be rendered in HTML tables.