Supply, Demand, and Elasticity: Core Concepts and Applications

Supply, Demand, and Elasticity

Changes in Supply

Changes in supply occur when factors affecting production costs change, regardless of the output level. Common causes include technological advancements, input price changes, or regulatory shifts. When supply increases, the entire supply curve shifts to the right; when supply decreases, it shifts to the left.

• Supply Curve Shift: A rightward shift indicates increased supply at every price; a leftward shift indicates decreased supply.

• Example: Introduction of new technology reduces production costs, shifting the supply curve right.

Changes in Demand

Demand changes when factors affecting consumer benefits or preferences shift. These include changes in tastes, income, network effects, or the prices of related goods. An increase in demand shifts the demand curve right; a decrease shifts it left.

• Demand Curve Shift: Rightward shift means higher quantity demanded at every price; leftward shift means lower quantity demanded.

• Example: A new health trend increases demand for a product, shifting the demand curve right.

Market Equilibrium

Market equilibrium is the price at which quantity supplied equals quantity demanded. At this point, there is no shortage or surplus in the market. If the price is set below equilibrium, a shortage occurs; if above, a surplus results.

• Equilibrium Price (P0): The price where supply and demand intersect.

• Shortage: Occurs when price is below equilibrium; quantity demanded exceeds quantity supplied.

• Surplus: Occurs when price is above equilibrium; quantity supplied exceeds quantity demanded.

Changing Equilibrium: Supply Shifts

When the supply curve shifts, the equilibrium price and quantity change. An increase in supply (rightward shift) lowers equilibrium price and raises equilibrium quantity. A decrease in supply (leftward shift) raises equilibrium price and lowers equilibrium quantity.

• Rightward Supply Shift: Price decreases, quantity increases.

• Leftward Supply Shift: Price increases, quantity decreases.

Changing Equilibrium: Demand Shifts

When the demand curve shifts, equilibrium price and quantity also change. An increase in demand (rightward shift) raises both equilibrium price and quantity. A decrease in demand (leftward shift) lowers both equilibrium price and quantity.

• Rightward Demand Shift: Price increases, quantity increases.

• Leftward Demand Shift: Price decreases, quantity decreases.

Simultaneous Shifts in Supply and Demand

When both supply and demand shift, the effect on equilibrium price and quantity depends on the relative magnitude and direction of each shift. Predictions become less clear and require analysis of the size of each shift.

• Both Curves Shift: The final equilibrium depends on which shift is larger.

• Example: If supply increases more than demand, price may fall even if demand also increases.

Algebraic Perspective: Solving for Equilibrium

Supply and demand can be represented as linear equations involving price and quantity. The equilibrium is found by solving these equations simultaneously.

• General Form: Demand: $Q = a - bP$ Supply: $Q = c + dP$

• Steps to Solve:

  1. Isolate quantity in both equations.

  2. Set quantity supplied equal to quantity demanded.

  3. Solve for price ($P$).

  4. Substitute $P$ back to find equilibrium quantity ($Q$).

Elasticities of Supply and Demand

Elasticity measures the responsiveness of quantity demanded or supplied to changes in price, income, or the price of other goods.

• Arc Elasticity of Demand: Measures elasticity over a range of prices. Formula: $E_P = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q}$

• Point Elasticity: Measures elasticity at a specific price and quantity. Formula: $E_p = \frac{\partial Q}{\partial P} \cdot \frac{P}{Q}$

• Linear Demand Curve: $Q = a - bP$; elasticity varies along the curve, being higher at high prices and low quantities.

• Infinitely Elastic Demand: Any price increase drops quantity demanded to zero; elasticity is infinite.

• Completely Inelastic Demand: Quantity demanded does not change with price; elasticity is zero.

• Income Elasticity of Demand: Percentage change in quantity demanded from a 1% increase in income. Formula: $E_I = \frac{\Delta Q}{\Delta I} \cdot \frac{I}{Q}$

• Cross-Price Elasticity of Demand: Percentage change in quantity demanded of one good from a 1% increase in the price of another.

• Price Elasticity of Supply: Percentage change in quantity supplied from a 1% increase in price. Formula: $E_S = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q}$

Short-Run vs. Long-Run Elasticities

Elasticity can differ in the short run and long run due to the time needed for consumers and producers to adjust. Generally, demand and supply are more elastic in the long run.

• Gasoline: Short-run demand is less elastic; long-run demand is more elastic as consumers can change vehicles.

• Automobiles: Short-run demand is more elastic; long-run demand is less elastic as old cars must eventually be replaced.

• Copper Supply: Primary copper supply is more elastic in the long run; secondary copper supply is less elastic in the long run due to limited scrap availability.

Fitting Linear Supply and Demand Curves to Data

Given equilibrium price and quantity, and estimates of elasticities, we can calculate the parameters of supply and demand curves. This allows for quantitative market analysis.

• Goal: Find constants $a$, $b$, $c$, and $d$ in $Q = a - bP$ and $Q = c + dP$ using known values for equilibrium price, quantity, and elasticities.

Effects of Government Intervention—Price Controls

Price controls, such as price ceilings, prevent prices from rising above a set maximum. This leads to increased quantity demanded and decreased quantity supplied, resulting in shortages.

• Without Controls: Market clears at equilibrium price and quantity.

• With Price Ceiling: Quantity supplied falls, quantity demanded rises, and a shortage develops.