Elasticity Measures Part 1 Dr. Jennifer P. Wissink ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

Elasticity Measures u What are they? –Responsiveness measures u Why introduce them? –Demand and supply responsiveness clearly matters for lots of market analyses. »EPI of taxes on demanders and suppliers »Division of NSS between CS and PS »And much more…. u Why not just look at slope? –Want to compare across markets: inter market –Want to compare within markets: intra market –slope can be misleading –want a unit free measure

What Is An Elasticity? u A unit free measure. u Measurement of the percentage change in one variable that results from a 1% change in another variable. u Lots of them! u Example: –Suppose: when P X rises by 1%, quantity demanded falls by 5%. –The own price elasticity of demand is -5 in this example.

2 Very Important Elasticities u Own Price Elasticity of Demand: –Captures how sensitive the quantity demanded is to a change in the own price of the good. u Own Price Elasticity of Supply: –Captures how sensitive the quantity supplied is to a change in the own price of the good.

Examples: Own Price Demand Elasticities u When the price of gasoline rises by 1% the quantity demanded falls by 0.2%, so gasoline demand is not very price sensitive. –Own price elasticity of demand is u When the price of gold jewelry rises by 1% the quantity demanded falls by 2.6%, so jewelry demand is very price sensitive. –Own price elasticity of demand is -2.6.

Examples: Own Price Supply Elasticities u 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. –Own price elasticity of supply is 0. u When the price of beef increases by 1% the quantity supplied increases by 5%, so beef supply is very price sensitive. –Own price elasticity of supply is 5.

Beauty Of Unit-free Comparisons u Gasoline and jewelry –It doesn’t matter that gas is sold by the gallon for about $3.50 per gallon and gold is sold by the ounce for about $1000 per ounce. –We compare the demand elasticities of -0.2 (gas) and -2.6 (gold jewelry). –Gold jewelry demand is more price sensitive. u 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 $4.99. –We compare the supply elasticities of 0 (classical paintings) and 5 (beef). –Beef supply is more price sensitive.

Size Of Own Price Elasticities And Terminology u If we “report” them as positive numbers… u Not a problem with supply (owing to law of supply) u Take absolute values with demand (owing to law of demand) u Terms work the same way for demand and supply elasticities price elasticprice inelastic unit elastic

Estimation Of Elasticity u LET’S STICK TO DEMAND ONLY FOR NOW! u How does one calculate the own price elasticity of demand? u Depends on the accuracy you want and information you’ve got. –Arc Formula: an approximation using sets of data points & discrete differences. –Point Formula: an exact measure, used when we have the demand function and its slope.

Definition: Own Price Elasticity of Demand u P = Current price of the good X. u Q D = Quantity demanded of X at that price.   P = Small change in the current price.   Q D = Resulting change in quantity demanded.

Example: Own Price Demand Elasticity Calculation Via “Bigger Delta” Arc Method u Goal: Approximate the elasticity at point A using B and C u Choose point B and get (P=38, Q=11) u Choose point C and get (P=34, Q=13).

u Goal: Approximation for elasticity at A via points B and C u Percent change in Q is (11-13)/((11+13)/2) = -2/12 = % u Percent change in P is (38-34)/((38+34)/2) = 4/36 = 11.11% u Elasticity is approx /11.11= -1.5 Example: Own Price Demand Elasticity Calculation Via “Bigger Delta” Arc Method u NOTE: Slight modification of standard %change formula. –Standard: %change=[(new-old)/old]*100 –Modification: %change= [(change)/(average of the two points)] * 100

u Goal: get elasticity between A and B (ignore C) u Percent change in Q is (11-12)/((11+12)/2) = -1/11.5 = -8.69% u Percent change in P is (38-36)/((38+36)/2) = 2/37 = 5.40% u Elasticity is approx /5.40= -1.6 u WHICH ONE????? –Bigger Delta? –Smaller Delta? Alternate Example: Own Price Demand Elasticity Calculation Via Textbook “Smaller Delta” Arc Method

Elasticity: The Exact Measurement Via The Point Formula u Let’s make B&C get closer and closer to A. In the limit we would get the exact elasticity at point A. u So, taking the limit as points B and C converge on A, note the following: –(average of the two Qs) = Q D evaluated at point A. –(average of the two Ps) = P at point A. u Rearranging, you now get: η = (ΔQ D / ΔP) (P /Q D ). u Note that: (ΔQ D / ΔP) is actually the slope of the demand curve equation when you have the equation, Q D = f(P), evaluated at point A. u Note: When you GRAPH demand, the slope you see is actually (ΔP/ΔQ D ), since it’s rise over run and the “rise” variable is price and the “run” variable is quantity. Books tend to call this the slope.

Slope Compared To Elasticity u The slope measures the rate of change of one variable (P, for example) in terms of another (Q, for example). –Slope of demand = ΔQ D /ΔP u An elasticity measures the percentage change of one variable (Q) in terms of percentage change in another (P). –Own Price Elasticity of demand = %ΔQ D / %ΔP!

Example Point Elasticity Calculation At P=$36 u Q D = 30 – 1/2P OR u P D = 60 – 2Q u (dQ D /dP) = -1/2 OR u (dP D /dQ) = -2 = “slope” u Note: (1/“slope” ) = -1/2 u At point A, P=36  Q D =12 u SO...own-price elasticity of demand = (-1/2)(3) = -1.5 u Absolute value of the elasticity = 1.5 $ Q Demand A 36

Point Elasticity As We Move Down A Linear Demand Curve u Q D = 30 – 1/2P OR u P D = 60 – 2Q $ Q Demand A 36 Midpoint (P=30, Q=15) u GIVEN A LINEAR DEMAND CURVE… u For prices above the midpoint, demand will be price elastic. u For prices below the midpoint, demand will be price inelastic. u At the midpoint, demand will be unitary elastic.

Exercise – “Large Delta” Arc Formula With Nonlinear Demand u Compute the elasticity of demand at P=$1.25 (the point indicated in red) on the table at the right using the large delta arc formula. –That is, use the row before and the row after the row in red where P=$1.25 u Percentage change in Q = (17-19)/((17+19)/2) = -1/9 = % u Percentage change in P = ( )/(( )/2) = 22% u Elasticity = -0.50