The Concept of Elasticity

Prof. John M. Abowd

Themes of Today's Lecture

• What is an Elasticity?
• Why Economists Use Elasticity
• Definitions of Elasticity
• How to Compute the Elasticity of Demand and Supply
• Examples of Elasticity of Demand and Supply

What is an Elasticity?

• Measurement of the percentage change in one variable that results from a 1% change in another variable.
• When the price rises by 1%, quantity demanded might fall by 5%.
• The price elasticity of demand is -5 in this example.

Different Types of Elasticities

• Price elasticity of demand: how sensitive is the quantity demanded to a change in the price of the good.
• Price elasticity of supply: how sensitive is the quantity supplied to a change in the price of the good.

Examples of Demand Elasticities

• When the price of gasoline rises by 1% the quantity demanded falls by 0.2%, so gasoline demand is not very price sensitive.
  • Price elasticity of demand is -0.2 .
• When the price of gold jewelry rises by 1% the quantity demanded falls by 2.6%, so jewelry demand is very price sensitive.
  • Price elasticity of demand is -2.6 .

Examples of Supply Elasticities

• When the price of DaVinci paintings increases by 1% the quantity supplied doesn't change at all, so the quantity supplied of DaVinci paintings is completely insensitive to the price.
  • Price elasticity of supply is 0.
• When the price of beef increases by 1% the quantity supplied increases by 5%, so beef supply is very price sensitive.
  • Price elasticity of supply is 5.

Why Economists Use Elasticity

• Economists want to compare apples and oranges all the time.
• Is oil market demand more price sensitive than wheat demand? (no)
• Is the labor supply of women more wage sensitive than the labor supply of men? (yes)
• An elasticity is a unit-free measure.
• By comparing markets using elasticities it does not matter how we measure the price or the quantity in the two markets.
• Elasticities allow economists to quantify the differences among markets without standardizing the units of measurement.

Examples of Unit-free Comparisons

• Gasoline and jewelry
  • It doesn't matter that gas is sold by the gallon for about $1.09 and gold is sold by the ounce for about $290.
  • We compare the demand elasticities of -0.2 (gas) and -2.6 (gold jewelry).
  • Gold jewelry demand is more price sensitive.

• Paintings and meat
  • It doesn't matter that classical paintings are sold by the canvas for millions of dollars each while beef is sold by the pound for about $1.50.
  • We compare the supply elasticities of 0 (classical paintings) and 5 (beef).
  • Beef supply is more price sensitive.

Inelastic Economic Relations

• When an elasticity is small (between 0 and 1 in absolute value), we call the relation that it describes inelastic.
• Inelastic demand means that the quantity demanded is not very sensitive to the price.
• Inelastic supply means that the quantity supplied is not very sensitive to the price.

Elastic Economic Relations

• When an elasticity is large (greater than 1 in absolute value), we call the relation that it describes elastic.
• Elastic demand means that the quantity demanded is sensitive to the price.
• Elastic supply means that the quantity supplied is sensitive to the price.

Size of Price Elasticities

• Inelastic: price elasticity less than 1
• Unit elastic: price elasticity equal to 1
• Elastic: price elasticity greater than 1

General Formula for a Price Elasticity

• P = the current price of a good
• Q = the quantity demanded at that price
• DP = small change in the current price
• DQ = small change in the quantity demanded
• Elasticity = (Percentage Change in Quantity) / (Percentage Change in Price)
• Elasticity = ((DQ/Q)/(DP/P)) = dlnQ/dlnP (from the calculus).

Slope of the Demand Curve DP = small change in the current price (DP < 0). DQ = small change in the quantity demanded slope = DP/DQ

Elasticity: Mathematical Definition

• slope = DP/DQ
• 1/slope = DQ/DP
• elasticity = (P/Q) x (1/slope)

Slope Compared to Elasticity

• The slope measures the rate of change of one variable (Q, say) in terms of another (P, say).
• The elasticity measures the percentage change of one variable (Q, say) in terms of another (P, say).

Example Elasticity Calculation Slope = (40-32)/(10-14)=-2 1/slope = -1/2 P/Q = 36/12 = 3 at point A P/Q x 1/slope = -1.5 Elasticity of demand = -1.5 Absolute value of the elasticity = 1.5

Exercise -- Linear Demand Compute the elasticity of demand at the point indicated in red on the table at the right (Q=18,P=24). Slope = -2 1/Slope = -1/2 P/Q = 24/18 = 4/3 Elasticity = -2/3

Demand Elasticities

• The price elasticity of demand is always negative.
• Economists usually refer to the price elasticity of demand by its absolute value (ignore the negative sign).
• So, even though the formula says that the price elasticity of demand is negative, we would say the elasticity of demand is 1.5 in the first example and 0.67 in the second.

Symmetric Midpoint Formula for Elasticity

• Although the exact formula for calculating an elasticity is useful for theory, in practice economists usually calculate an approximation called the symmetric midpoint formula elasticity.
• Elasticity =
  (Average Percentage Change in Quantity)
    (Average Percentage Change in Price)

Example of Midpoint Formula from Linear Demand Curve Suppose we wanted to evaluate the elasticity of demand for the linear demand curve illustrated  to the right at the point P=36, Q=12 Choose the point B above and C below the point A with a symmetric distance along the quantity axis (P=38, Q=11) and (P=34, Q=13). Midpoint percentage change in Q is (11-13)/((11+13)/2) = -16.67% Midpoint percentage change in P is (38-34)/((38+34)/2) = 11.11% Symmetric midpoint elasticity = -0.1667/0.1111= -1.5

Constant Elasticity Demand Curves A constant elasticity demand curve is an arc. The demand curve shown in the graph has a constant price elasticity of -0.5.

Constant Elasticity Demand Curve (Table Form) Notice that the price and quantity vary nonlinearly. The slope is not a constant. The exact elasticity is a constant. The symmetric midpoint formula gives a good approximation.

Example of Midpoint Formula for Nonlinear Demand

• Suppose we wanted to evaluate the elasticity of demand for the nonlinear demand curve illustrated above at the point P=2.80, Q=12
• Choose the point above and below this one with a symmetric distance along the quantity axis (P=3.33, Q=11) and (P=2.39, Q=13).
• Midpoint percentage change in Q is (11-13)/((11+13)/2) = -16.7%
• Midpoint percentage change in P is (3.33-2.39)/((3.33 + 2.39)/2) = 33.1%
• Symmetric midpoint elasticity = -0.167/0.331 = -0.5035

Review of Today's Lecture

• Elasticity measures the magnitude of an economic effect in percentages.
• Price "inelastic" demand (supply) means the quantity demanded (supplied) is not very price sensitive.
• Price "elastic" means the opposite: the relation is price sensitive.
• Standard formula elasticity = (P/Q) x (1/slope)
• Symmetric midpoint formula elasticity =
  (Change in Quantity/Average Quantity)
  (Change in Price/Average Price)

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