Source: Pindyck & Rubinfeld, Ch. 2 | Microeconomic Theory, Texas A&M University
Tags: equilibrium shift, supply increase, demand increase, simultaneous shifts, price elasticity of demand, income elasticity of demand, price elasticity of supply, elastic, inelastic, unit elastic, infinitely elastic, infinitely inelastic
When supply or demand shifts, the equilibrium price and quantity both change in predictable directions. Elasticity measures how sensitive one variable is to a percentage change in another, and it is the workhorse concept for predicting the size of those changes. The three elasticities covered here are price elasticity of demand, income elasticity of demand, and price elasticity of supply.
Equilibrium price (P*)
The price at which quantity demanded equals quantity supplied. It is the price the market settles on when there is no external interference.
Equilibrium quantity (Q*)
The quantity bought and sold at the equilibrium price.
Elasticity
The percentage change in one variable resulting from a 1% increase in another variable.
Price elasticity of demand (E_P)
The percentage change in quantity demanded resulting from a 1% increase in the good's price. Normally negative because demand curves slope downward.
Elastic demand
|E_P| > 1. Quantity demanded is highly responsive to price changes. A 1% price increase causes more than a 1% drop in quantity demanded.
Inelastic demand
|E_P| < 1. Quantity demanded is relatively unresponsive to price changes.
Unit elastic demand
|E_P| = 1. The percentage change in quantity demanded exactly matches the percentage change in price.
Infinitely inelastic demand (perfectly inelastic)
E_P = 0. The demand curve is vertical. Quantity demanded does not change at all when price changes.
Infinitely elastic demand (perfectly elastic)
E_P = −∞. The demand curve is horizontal. Consumers will buy any quantity at price P*, but nothing at even a slightly higher price.
Income elasticity of demand (E_I)
The percentage change in quantity demanded resulting from a 1% increase in income.
Price elasticity of supply (E_S)
The percentage change in quantity supplied resulting from a 1% increase in the good's price.
Increase in supply (supply shifts right):
Equilibrium price falls.
Equilibrium quantity rises.
Intuition: more goods flood the market at every price, pushing the price down and the quantity traded up.
Increase in demand (demand shifts right):
Equilibrium price rises.
Equilibrium quantity rises.
Intuition: consumers want more at every price, bidding the price up and drawing out more supply.
The reverse applies for decreases in supply or demand. Decrease in supply raises price and lowers quantity. Decrease in demand lowers both price and quantity.
When supply and demand both shift at the same time, the direction of one variable becomes ambiguous unless you know the relative magnitudes.
Both increase: quantity definitely rises, but price depends on which shift is larger.
If demand increases more than supply, price rises.
If supply increases more than demand, price falls.
The chapter example: supply and demand both increase, but the supply increase is smaller in magnitude. Result: equilibrium quantity rises, and equilibrium price rises mildly.
Formula:
E_P = (% change in Q) / (% change in P) = (ΔQ/Q) / (ΔP/P) = (ΔQ · P) / (ΔP · Q)
For continuous functions, ΔQ/ΔP is replaced by the derivative Q'(P), giving:
E_P = Q'(P) · (P / Q)
Worked example 1: linear demand
Suppose Q = 8 − 2P.
Q'(P) = −2
E_P = (−2) · (P / Q)
This means elasticity varies along the curve. At high prices (low Q), demand is elastic. At low prices (high Q), demand is inelastic.
At the midpoint (P = 2, Q = 4): E_P = (−2)(2/4) = −1 (unit elastic).
At the vertical intercept (P = 4, Q = 0): E_P → −∞.
At the horizontal intercept (P = 0, Q = 8): E_P = 0.
Worked example 2: constant-elasticity demand
Suppose Q(P) = 100/P. When P = 4:
Q(4) = 100/4 = 25
Q'(P) = −100/P²
E_P = (−100/P²) · (P/Q) = (−100/16) · (4/25) = −1
Because E_P = −1 everywhere on Q = 100/P, a 0.5% price increase leads to exactly a 0.5% decrease in quantity demanded.
E_P = −1.5 means a 1% price increase causes a 1.5% decrease in quantity demanded. Equivalently, a 2% price increase causes a 3% decrease.
The sign is negative because price and quantity demanded move in opposite directions.
Infinitely inelastic (perfectly inelastic): the demand curve is a vertical line at some quantity Q*. No matter how much price changes, quantity stays the same. Example: a life-saving medication with no substitutes.
Infinitely elastic (perfectly elastic): the demand curve is a horizontal line at some price P*. Consumers buy unlimited quantities at P* but zero above it. Example: a perfectly competitive firm selling a commodity.
Formula:
E_I = (% change in Q) / (% change in I) = (ΔQ · I) / (ΔI · Q)
E_I > 0: the good is a normal good (demand rises with income).
E_I < 0: the good is an inferior good (demand falls as income rises).
Formula:
E_S = (% change in Q_S) / (% change in P)
Measures how responsive producers are to a price change. A higher E_S means supply adjusts more readily.
Price elasticity of demand: E_P = Q'(P) · (P / Q)
Income elasticity of demand: E_I = (ΔQ · I) / (ΔI · Q)
Price elasticity of supply: E_S = (ΔQ_S / ΔP) · (P / Q_S)
Diagrams to review from the chapter:
Linear demand curve with E_P = −∞ at the price intercept, E_P = −1 at the midpoint, and E_P = 0 at the quantity intercept.
Vertical line for infinitely inelastic demand.
Horizontal line for infinitely elastic demand.
Supply-and-demand diagrams showing the effect of a rightward shift in supply alone, demand alone, and both simultaneously.
⚠️ Elasticity varies along a linear demand curve. At the top (high P, low Q) demand is elastic; at the bottom (low P, high Q) demand is inelastic; at the midpoint, demand is unit elastic. A common exam question gives you a linear demand function and asks for E_P at a specific price.
⚠️ Know how to use the derivative form: E_P = Q'(P) · (P/Q). You will be given a demand function, asked to differentiate, plug in the price, and interpret the result.
⚠️ When both supply and demand shift, one of the two equilibrium changes (price or quantity) becomes ambiguous without knowing the relative magnitudes. Exam questions often test whether you recognise which variable is ambiguous.
⚠️ Distinguish clearly between infinitely inelastic (vertical, E_P = 0) and infinitely elastic (horizontal, E_P = −∞). Students sometimes swap these.
⚠️ The sign of income elasticity tells you whether the good is normal (positive) or inferior (negative). This is a straightforward but frequently tested classification.
Q: If the demand function is Q = 8 − 2P, what is the price elasticity of demand when P = 1?
A: Q(1) = 8 − 2(1) = 6. Q'(P) = −2. E_P = (−2)(1/6) = −1/3. Demand is inelastic at this price.
Q: A demand curve is given by Q(P) = 100/P. What is E_P at any price?
A: E_P = −1 at every point on this curve. It is a constant unit-elastic demand function.
Q: Both supply and demand increase simultaneously. What can you say with certainty about equilibrium quantity and price?
A: Equilibrium quantity definitely increases. The direction of the price change is ambiguous and depends on which shift is larger.
Q: A demand curve is perfectly vertical. What is its price elasticity, and what does that mean?
A: E_P = 0 (infinitely inelastic). Quantity demanded does not respond to price changes at all.
Q: If income elasticity of demand for a good is −0.4, what type of good is it, and what happens to demand when income rises by 10%?
A: It is an inferior good. Demand falls by 4% (10% × 0.4).
Q: Supply increases while demand stays the same. What happens to equilibrium price and quantity?
A: Equilibrium price falls and equilibrium quantity rises.
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