Demand

Definition and Determinants

Demand refers to the quantity of a good or service that consumers are willing and able to purchase at various prices over a given period of time. The determinants of demand include:

• Price of the good (P)

• Income of consumers (I)

• Prices of related goods (substitutes and complements)

• Tastes and preferences

• Expectations about future prices and income

• Number of buyers

Demand Equation and Example

The demand for used cars can be represented as a function of several variables:

• QD = f(P, INCOME, PNEW CAR, PINSURANCE)

For example:

\$ QD = 100 + 0.3I + 0.4P_{nc} - 0.008P_{ins} - 2P \$

• P: Price of used car (in thousands of dollars)

• I: Income (in thousands of dollars)

• Pnc: Price of new car (in thousands of dollars)

• Pins: Price of insurance (in dollars/year)

Interpreting coefficients: Positive coefficients indicate a direct relationship; negative coefficients indicate an inverse relationship.

Example Calculation: If I = 85, Pnc = 40, Pins = 600, P = 25:

\$ QD = 100 + 0.3(85) + 0.4(40) - 0.008(600) - 2(25) = 100 + 25.5 + 16 - 4.8 - 50 = 86.7 \$

Normal vs. Inferior Goods: If the coefficient on income is positive, the good is normal; if negative, it is inferior.

Substitutes vs. Complements: If the coefficient on the price of another good is positive, the goods are substitutes; if negative, they are complements.

Supply

Definition and Determinants

Supply is the quantity of a good or service that producers are willing and able to sell at various prices over a given period. The determinants of supply include:

• Price of the good (P)

• Input prices (e.g., wages)

• Technology

• Expectations about future prices

• Number of sellers

Supply Equation and Example

For used cars:

\$ QS = 25 + 3P - 0.1W \$

• P: Price of used car (in thousands of dollars)

• W: Wage of workers (in dollars/hour)

Interpreting coefficients: A positive coefficient on price means higher prices increase quantity supplied; a negative coefficient on wage means higher wages decrease supply.

Example Calculation: If W = 50, P = 25:

\$ QS = 25 + 3(25) - 0.1(50) = 25 + 75 - 5 = 95 \$

Equilibrium

Definition and Analysis

Equilibrium occurs where quantity demanded equals quantity supplied. The corresponding price and quantity are the equilibrium price (P*) and equilibrium quantity (Q*).

• Change in demand shifts the demand curve, affecting equilibrium P and Q.

• Change in supply shifts the supply curve, affecting equilibrium P and Q.

• Simultaneous changes in demand and supply require analyzing both shifts together.

Example: If income rises to $100,000, only demand shifts. Recalculate QD using the new income and solve for equilibrium with the supply equation.

Elasticity

Price Elasticity of Demand

Own Price Elasticity of Demand (OPE) measures the responsiveness of quantity demanded to a change in the good's own price:

\$ OPE = \frac{dQD}{dP} \times \frac{P}{QD} \$

• If |OPE| > 1: Demand is elastic

• If |OPE| < 1: Demand is inelastic

• If |OPE| = 1: Demand is unit elastic

Interpretation: Elastic demand means consumers are sensitive to price changes; inelastic means they are not.

Example Calculation: Calculate OPE at equilibrium P and Q, and at P = $25.

Elasticity and Total Revenue

• If demand is elastic, a price increase decreases total revenue (TR); a price decrease increases TR.

• If demand is inelastic, a price increase increases TR; a price decrease decreases TR.

Income Elasticity of Demand

Income Elasticity (IE) measures the responsiveness of quantity demanded to changes in income:

\$ IE = \frac{dQD}{dI} \times \frac{I}{QD} \$

• If IE > 0: Normal good

• If IE < 0: Inferior good

• If |IE| > 1: Luxury

• If |IE| < 1: Necessity

Example Calculation: Calculate IE for I = 85, Pnc = 40, Pins = 600, P = 25.

Cross Price Elasticity of Demand

Cross Price Elasticity (CPE) measures the responsiveness of demand for one good to the price change of another good:

\$ CPE = \frac{dQ_{dx}}{dP_{y}} \times \frac{P_{y}}{Q_{dx}} \$

• If CPE > 0: Goods are substitutes

• If CPE < 0: Goods are complements

• If |CPE| > 1: Strong relationship

• If |CPE| < 1: Weak relationship

Example: For Qdgas = 0.02 – 1.8Pgas + 0.69Poil, calculate CPE when Poil = $50 and Pgas = $3.

Supply Elasticity

Supply Elasticity (SE) measures the responsiveness of quantity supplied to a change in price:

\$ SE = \frac{dQS}{dP} \times \frac{P}{QS} \$

• If SE < 1: Inelastic supply

• If SE > 1: Elastic supply

• If SE = 1: Unit elastic supply

Example Calculation: Calculate SE at P = $10, W = $10.

Elasticity and Tax Incidence

Tax Incidence and Elasticity

Tax incidence refers to who ultimately bears the burden of a tax, not necessarily who pays it to the government. The division of the tax burden depends on the relative elasticities of supply and demand:

• If supply is more elastic than demand, consumers bear more of the tax burden.

• If demand is more elastic than supply, producers bear more of the tax burden.

Examples: Taxes on gasoline (inelastic demand) vs. luxury boats (elastic demand).

Consumer and Producer Surplus

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. It is the area above the price and below the demand curve.

• Individual consumer surplus: Maximum willingness to pay minus actual price paid.

• Total consumer surplus: Sum of all individual consumer surpluses in the market.

Example: Willing to pay $100, buy for $60; consumer surplus = $40.

Graphical Calculation: If P = 35, Q = 400, maximum price = 100:

\$ \text{Consumer Surplus} = \frac{400 \times (100 - 35)}{2} = 13,000 \$

Producer Surplus

Producer surplus is the difference between the price producers receive and the minimum they are willing to accept. It is the area above the supply curve and below the price.

• Individual producer surplus: Actual price received minus minimum acceptable price.

• Total producer surplus: Aggregate for the market.

Example: Willing to sell for $40, sell for $60; producer surplus = $20.

Graphical Calculation: If P = 60, Q = 270:

\$ \text{Producer Surplus} = 6,750 \$

Changes in Surplus

• If price increases, consumer surplus decreases; if price falls, producer surplus decreases.

Overall Economic Welfare and Deadweight Loss

Definition and Application

Overall Economic Welfare (OEW) is the sum of consumer and producer surplus. It is used to evaluate the impact of price controls, taxes, and market structures on economic efficiency.

• Deadweight loss (DWL): The loss in total surplus due to market distortions such as price floors, price ceilings, or taxes.

Examples:

1. Imposition of a price floor

2. Imposition of a tax