Elasticity and Its Application

1. 5 Elasticity and Its Application

2. The Elasticity of Demand • Elasticity • Measure of the responsiveness of quantity demanded or quantity supplied • Percentage change in quantity demanded (∆Qd/Qd) • Percentage change in quantity supplied (∆Qs/Qs) • To a change in one of its determinants (driver variables) • Demand-side • (own) price <-> demand elasticity (∆Qx/Qx)/ (∆Px/Px ) • Price of substitute/complement <-> cross-price (∆Qx/Qx)/(∆Py/Py ) • Income <-> income elasticity ((∆Qx/Qx)/ (∆I/I )

3. The Elasticity of Demand • (Own) Price elasticity of demand • Elastic demand (e.g. price elasticity) • Quantity demanded responds substantially to changes in the price • elasticity of demand > 1 • ∆Qd/Qd > ∆P/P %change in Qd > % change in P • Inelastic demand • Quantity demanded responds only slightly to changes in the price • elasticity < 1 (closer to zero) • ∆Qd/Qd < ∆P/P

4. 1 The price elasticity of demand (d, e) (d) Elastic demand: Elasticity > 1 (e) Perfectly elastic demand: Elasticity equals infinity Price Price 1. an 1. an 1. At any price above $4, quantity demanded is zero • A 22% • increase • in price… 3. At any price below $4, quantity demanded is infinite $5 Demand $4 Demand 4 2. … leads to a 67% decrease in quantity demanded 2. At exactly $4, consumers will buy any quantity 50 100 0 0 Quantity Quantity The price elasticity of demand determines whether the demand curve is steep or flat. Note that all percentage changes are calculated using the midpoint method.

5. The Elasticity of Demand • Determinants of (own) price elasticity of demand • (∆Qx/Qx)/ (∆Px/Px ) • Availability of close substitutes • Goods with close substitutes • More elastic demand • Necessities (0->1) vs. luxuries (>1) (defined by Income elasticity) • Necessities – inelastic demand • Luxuries – elastic demand • Definition of the market • Narrowly defined markets – more elastic demand • Time horizon • More elastic over longer time horizons

6. The Elasticity of Demand (own) • Computing the price elasticity of demand • Percentage change in quantity demanded • Divided by percentage change in price • Use absolute value (drop the minus sign) • It’s always negative (own-price) • Midpoint method • Two points: (Q1, P1) and (Q2, P2)

7. The Elasticity of Demand • Variety of demand curves • Demand is elastic • Elasticity > 1 • Demand is inelastic • Elasticity < 1 • Demand has unit elasticity • Elasticity = 1

8. The Elasticity of Demand • Cigarettes (US)[41] • -0.3 to -0.6 (General) • -0.6 to -0.7 (Youth) – proportion of income? • Soft drinks • -0.8 to -1.0 (general)[51] (broadly defined) • -3.8 (Coca-Cola)[52] (narrow) • -4.4 (Mountain Dew)[52] (narrow) • Car fuel[45] • -0.25 (Short run) (same car – reduce trips) • -0.64 (Long run) (new car?)

9. The Elasticity of Demand • Total revenue • Amount paid by buyers • Received by sellers of a good • Computed as: price of the good times the quantity sold (P ˣ Q)

10. 2 Total revenue 1. an Price P ˣ Q=$400 (revenue) $4 P Demand 100 0 Quantity Q The total amount paid by buyers, and received as revenue by sellers, equals the area of the box under the demand curve, P × Q. Here, at a price of $4, the quantity demanded is 100, and total revenue is $400.

11. 4 Elasticity of a linear demand curve (graph) 1. an Price Elasticity is larger than 1 $7 6 5 4 Elasticity is smaller than 1 3 2 1 0 2 4 6 8 10 12 14 Quantity Demand The slope of a linear demand curve is constant, but its elasticity is not. The demand schedule in the table was used to calculate the price elasticity of demand by the midpoint method. At points with a low price and high quantity, the demand curve is inelastic. At points with a high price and low quantity, the demand curve is elastic.

12. 4 Elasticity of a linear demand curve (schedule) The slope of a linear demand curve is constant, but its elasticity is not. The demand schedule in the table was used to calculate the price elasticity of demand by the midpoint method. At points with a low price and high quantity, the demand curve is inelastic. At points with a high price and low quantity, the demand curve is elastic.

13. Elasticity and Total Revenue The following equation holds: whereR' is the marginal revenue (MR)P is the priceProof:TR = Total Revenue

14. The Elasticity of Demand • When demand is inelastic • Price and total revenue move in the same direction • When demand is elastic • Price and total revenue move in opposite directions • If demand is unit elastic • Total revenue remains constant when the price changes

15. The Elasticity of Demand • Income elasticity of demand • Measure of how much the quantity demanded of a good responds • To a change in consumers’ income • Percentage change in quantity demanded • Divided by the percentage change in income • Normal goods: positive income elasticity • Necessities: smaller income elasticities (~0, <1) • Luxuries: large income elasticities ( > 1) • Inferior goods: negative income elasticities (<0)

16. The Elasticity of Demand • Cross-price elasticity of demand • Measure of how much the quantity demanded of one good responds • To a change in the price of another/different good • [∆Qx/Qx] / [∆Py/Py ] • Sign matters -> tells whether substitute or complement • Magnitude (<1 or >1) -> how “good” a substitute/essential a complement • Substitutes: Positive cross-price elasticity • >1 -> “close” or good substitute as big shift with small price change • Complements: Negative cross-price elasticity • >1 -> “essential” to be used/consumed together (cars and gas)

17. The Elasticity of Supply • Price elasticity of supply • Measure of how much the quantity supplied of a good responds • To a change in the price of that good • Percentage change in quantity supplied • Divided by the percentage change in price • Depends on the flexibility of sellers to change the amount of the good they produce

18. The Elasticity of Supply • Price elasticity of supply • Elastic supply • Quantity supplied responds substantially to changes in the price • Inelastic supply • Quantity supplied responds only slightly to changes in the price • Determinant of price elasticity of supply • Time period • Supply is more elastic in long run

19. The Elasticity of Supply • Computing price elasticity of supply • Percentage change in quantity supplied • Divided by percentage change in price • Variety of supply curves • Supply is perfectly inelastic • Elasticity =0 • Supply curve – vertical • Supply is perfectly elastic • Elasticity = infinity • Supply curve – horizontal

20. The Elasticity of Supply • Variety of supply curves • Unit elastic supply • Elasticity =1 • Elastic supply • Elasticity >1 • Inelastic supply • Elasticity < 1

21. 5 The price elasticity of supply (a, b) • Perfectly inelastic supply: • Elasticity = 0 (b) Inelastic supply: Elasticity < 1 Price Price Supply 1. an 1. an Supply • A 22% • increase • in price… • An • increase • in price… 2. … leads to a 10% increase in quantity supplied $5 $5 2. …leaves the quantity supplied unchanged 4 4 100 110 0 0 100 Quantity Quantity The price elasticity of supply determines whether the supply curve is steep or flat. Note that all percentage changes are calculated using the midpoint method.

22. 5 The price elasticity of supply (c) (c) Unit elastic supply: Elasticity =1 Price Supply 1. an • A 22% • increase • in price… $5 2. … leads to a 22% increase in quantity supplied 4 100 125 0 Quantity The price elasticity of supply determines whether the supply curve is steep or flat. Note that all percentage changes are calculated using the midpoint method.

23. 5 The price elasticity of supply (d, e) (d) Elastic supply: Elasticity > 1 (e) Perfectly elastic supply: Elasticity equals infinity Price Price 1. At any price above $4, quantity supplied is infinite 1. an 1. an • A 22% • increase • in price… 3. At any price below $4, quantity supplied is zero Supply $5 $4 Supply 4 2. … leads to a 67% increase in quantity supplied 2. At exactly $4, producers will supply any quantity 50 100 0 0 Quantity Quantity The price elasticity of supply determines whether the supply curve is steep or flat. Note that all percentage changes are calculated using the midpoint method.

24. 6 How the price elasticity of supply can vary Elasticity is small (less than 1). Supply Price 1. an Elasticity is large (greater than 1). $15 4 12 3 Because firms often have a maximum capacity for production, the elasticity of supply may be very high at low levels of quantity supplied and very low at high levels of quantity supplied. Here an increase in price from $3 to $4 increases the quantity supplied from 100 to 200. Because the 67 percent increase in quantity supplied (computed using the midpoint method) is larger than the 29 percent increase in price, the supply curve is elastic in this range. By contrast, when the price rises from $12 to $15, the quantity supplied rises only from 500 to 525. Because the 5 percent increase in quantity supplied is smaller than the 22 percent increase in price, the supply curve is inelastic in this range. 525 500 200 100 0 Quantity

25. Applications of Supply, Demand, & Elasticity • Why did OPEC fail to keep the price of oil high? • 1970s: OPEC reduced supply of oil • Increase in prices 1973-1974 and 1971-1981 • Short-run: supply is inelastic • Decrease in supply: large increase in price • 1982-1990 – price of oil decreased • Long-run: supply is elastic • Decrease in supply: small increase in price

26. 8 A reduction in supply in the world market for oil (a) The Oil Market in the Short Run (b) The Oil Market in the Long Run 2. … leads to a large increase in price 1. In the long run, when supply and demand are elastic, a shift in supply. . . 1. In the short run, when supply and demand are inelastic, a shift in supply. . . 1. an 1. an Price Price 2. … leads to a small increase in price S1 S2 S2 S1 P1 P2 P2 P1 Demand Demand Quantity Quantity 0 0 When the supply of oil falls, the response depends on the time horizon. In the short run, supply and demand are relatively inelastic, as in panel (a). Thus, when the supply curve shifts from S1 to S2, the price rises substantially. By contrast, in the long run, supply and demand are relatively elastic, as in panel (b). In this case, the same size shift in the supply curve (S1 to S2) causes a smaller increase in the price.