Supply, Demand, and Elasticity Review

Demand

Demand refers to the quantity of a good or service that consumers are willing and able to purchase at various prices during a given period. Understanding demand is fundamental to analyzing market behavior.

• Definition: The relationship between the price of a good and the quantity demanded, holding other factors constant (ceteris paribus).

• Determinants of Demand: Income, prices of related goods (substitutes and complements), tastes and preferences, expectations, and number of buyers.

• Demand Equation: A mathematical representation of how quantity demanded (QD) depends on its determinants.

Example: For used cars: Where: I = income (in thousands of dollars), = price of new car (in thousands), = insurance price (in dollars/year), P = price of used car (in thousands).

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

• Application: Predict demand by substituting values for the variables. For example, if I = 85, = 40, = 600, P = 25, plug these into the equation to find QD.

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, they are substitutes; if negative, they are complements.

Supply

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

• Definition: The relationship between the price of a good and the quantity supplied, holding other factors constant.

• Determinants of Supply: Input prices (e.g., wages), technology, expectations, number of sellers, and prices of related goods.

• Supply Equation: For used cars: Where P = price (in thousands), W = wage (in dollars/hour).

• Interpreting Coefficients: Positive coefficient on P means higher prices increase supply; negative coefficient on W means higher wages decrease supply.

• Application: Predict supply by substituting values. For example, if W = 50 and P = 25, plug into the equation to find QS.

Market Equilibrium

Market equilibrium occurs where quantity demanded equals quantity supplied. At this point, the market-clearing price and quantity are established.

• Definition: The price (P*) and quantity (Q*) where QD = QS.

• Impact of Changes:

  • Change in Demand: Shifts the demand curve, affecting equilibrium price and quantity.

  • Change in Supply: Shifts the supply curve, affecting equilibrium price and quantity.

  • Simultaneous Changes: Both curves shift; the net effect depends on the magnitude and direction of each shift.

• Application: Use demand and supply equations to solve for equilibrium values. For example, set QD = QS and solve for P and Q.

Example: If income rises to $100,000, only demand shifts. Substitute the new value into the demand equation and solve for the new equilibrium.

Elasticity

Elasticity measures the responsiveness of one variable to changes in another, commonly used to analyze demand and supply sensitivity to price and income changes.

• Own Price Elasticity of Demand (OPE): Measures how much quantity demanded changes in response to a change in the good's own price.

• Interpretation: If |OPE| > 1, demand is elastic; if |OPE| < 1, demand is inelastic; if |OPE| = 1, demand is unit elastic.

• Application: Calculate at equilibrium or at a specific price. For example, calculate OPE when P = $25.

• Relationship to Total Revenue (TR):

  • If demand is elastic, a price increase decreases 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 measures how quantity demanded responds to changes in consumer income.

• Formula:

• Interpretation:

  • If IE > 0, the good is normal; if IE < 0, the good is inferior.

  • If IE > 1, the good is a luxury; if 0 < IE < 1, the good is a necessity.

• Application: Calculate using the demand equation and interpret the result (e.g., normal/inferior, luxury/necessity, responsiveness).

Cross Price Elasticity of Demand

Cross price elasticity measures how the quantity demanded of one good responds to a change in the price of another good.

• Formula:

• Interpretation:

  • If CPE > 0, goods are substitutes; if CPE < 0, goods are complements.

  • Absolute value > 1: highly responsive; < 1: not very responsive.

• Example: For , calculate CPE when and .

Supply Elasticity

Supply elasticity measures how quantity supplied responds to changes in price.

• Formula:

• Interpretation:

  • SE < 1: inelastic supply; SE > 1: elastic supply; SE = 1: unit elastic supply.

• Application: Calculate at a specific price and wage, e.g., P = $10, W = $10.

Elasticity and Tax Incidence

Tax incidence refers to how the burden of a tax is distributed between buyers and sellers, which depends on the relative elasticities of supply and demand.

• Key Points:

  • 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 and producer surplus are measures of economic welfare, representing the net benefits to buyers and sellers in a market.

• Consumer Surplus: The difference between what consumers are willing to pay and what they actually pay. Formula: Area above the price and below the demand curve. Example: Willing to pay $100, pay $60; surplus = $40. Total Consumer Surplus: Sum for all buyers; for a linear demand curve, area of triangle:

• Producer Surplus: The difference between the price received and the minimum price at which producers are willing to sell. Formula: Area above the supply curve and below the price. Example: Willing to sell for $40, receive $60; surplus = $20. Total Producer Surplus: Aggregate for all sellers; for a linear supply curve, area of triangle:

Overall Economic Welfare and Deadweight Loss

Overall economic welfare (OEW) is the sum of consumer and producer surplus. Changes in market conditions or government policies (e.g., taxes, price floors) can affect OEW and may create deadweight loss (DWL), which is the loss of total surplus due to market inefficiency.

• Examples of DWL:

  1. Imposition of a price floor (e.g., minimum wage).

  2. Imposition of a tax.