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Elasticity Measures Part 2 Dr. Jennifer P. Wissink ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved. Recall: Own Price 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. – Own 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. – Own price elasticity of supply is 5. Supply Elasticity Extremely similar formulas are used to calculate the own price elasticity of supply – Arc midpoint formula » Large delta style or small delta style – Point formula Just need to substitute in – Quantity supplied and change in quantity supplied where appropriate Supply Elasticity Definition: S X ,P X Arc Percentage Change in Quantity Supplied Percentage Change in Price Formula: Arc formula for Point S S X , PX QS /(average of the two Qs) x100 P/(average of the two Ps) formula: X , PX (dQ S X / dPX )( PX / Q S X ) Example: Arc Calculation of Own Price Elasticity of Supply Want supply elasticity at A Use B: QS=9 and P=5 Use C: QS=16 and P=7 Nonlinear Supply Curve 12 10 QS % change in = (16-9)/((16+9)/2)*100 = 56% % change in P = (7-5)/((7+5)/2)*100 = 33.33% C 8 Price 6 B A 4 2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Supply elasticity at A = 56/33.33 = 1.68 Quantity Example: Point Calculation of Own Price Elasticity of Supply S X , PX (dQ S X / dPX )( PX / Q S X ) Suppose you are given: QS = -10 + 4P – Note, that’s the same as: PS = 2.50 +.25Q Suppose you want the exact own price elasticity of supply at P = $12 At P = $12, QS = -10 + 48 = 38 Note: (dQS/dP) = 4 – (Slope of drawn supply curve = .25, so.... 1/slope = 4) So supply elasticity at P=$12 is... (4)•(12/38) = 48/38 = 1.26 Some Technical Definitions For Extreme Elasticity Values Perfectly elastic means the quantity demanded or supplied is as price sensitive as possible. – a.k.a. completely elastic – a.k.a. infinitely elastic Perfectly inelastic means that the quantity demanded or supplied has no price sensitivity at all. – a.k.a. completely inelastic Perfectly Elastic Demand Demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded. Example: Price Perfectly Elastic Demand (elasticity = -) Quantity Perfectly Inelastic Demand Demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded. Example: Price Perfectly Inelastic Demand (elasticity = 0) Quantity Perfectly Inelastic Supply Supply is perfectly inelastic when a 1% change in the price would result in no change in quantity supplied. Example: wheat? – At harvest? Price Perfectly Inelastic Supply (elasticity = 0) » Yes. – Across planting seasons? » No. Quantity Perfectly Elastic Supply Supply is perfectly elastic when a 1% change in the price would result in an infinite change in quantity supplied. Example: wheat? Price Perfectly Elastic Supply (elasticity = ) – Across planting seasons? » Yes. Quantity Determinants of Elasticity What is a major determinant of the own price elasticity of demand? – Availability of substitutes in consumption. What is a major determinant of the own price elasticity of supply? – Availability of alternatives in production. Real World Example – Getting It Wrong Gas taxes in Washington DC, 1980 – Extra 6% tax imposed Aug 16, 1980 to raise much needed revenue for D.C. – Increased price at pump by 8¢ (a nearly 6% increase). – By end of first month, QD down by 27.5%. – elasticity = 27.5÷6 = 4.5 pretty darn elastic! – Way off on expected revenue, too. – By October, sales had dropped by 40% and 242 gas station workers were laid off. – Tax lifted by Mayor Marion Barry on November 24, 1980. – What went wrong? What didn’t they account for? Real World Example – Getting It Wrong Own Price Elasticity of Demand & Total Expenditures Question: What happens to total expenditures made by buyers (TE) in a market when market price increases? Note: TE = P•QD P↑ tends to increase TE, but it also decreases QD. QD↓ tends to decreases TE. So what happens to TE? Knowing own price elasticity will help! – If demand is price ELASTIC, then TE ↓ » Why? – If demand is price INELASTIC, then TE ↑ » Why? On you own: reverse this argument to determine the relationship between total expenditure and elasticity when you consider a price decrease! Bridge Toll Example Suppose: Current toll for the George Washington Bridge is $6.00/trip. Suppose: The quantity demanded at $6.00/trip is 100,000 trips/hour. So: TE on trips per hour = $600,000 If the own price elasticity of demand for bridge trips is known to be 2.0, then what is the effect of a 10% toll increase? – Note: since demand is price ELASTIC TE↓ A 10% toll increase means the price is now $6.60 per trip. If η=-2, a toll increase of 10% implies a 20% decline in the quantity demanded. If there is a 20% decline in trip, number of trips falls to 80,000/hour. Total expenditure falls to $528,000/hour (= 80,000 x $6.60). $528,000 < $600,000 Own Price Elasticity of Demand & Total Expenditure with Linear Demand $TE Price Price elastic Demand Price inelastic Quantity Quantity Starting at the “top” of the demand curve, where demand is price elastic, as price falls, and quantity demanded rises, total expenditures rise, but increase at a decreasing rate. At the midpoint, where demand is unit elastic, total expenditures will be at their maximum value. As you continue down the demand curve, where demand is now price inelastic, as price falls, and quantity demanded rises, total expenditures fall. Cross-Price Elasticity of Demand Elasticity of demand with respect to the price of a complementary good (cross-price elasticity) – This elasticity is negative because as the price of a complementary good rises, the quantity demanded of the good itself falls. – Example: software is complementary with computers. When the price of software rises the quantity demanded of computers falls. Elasticity of demand with respect to the price of a substitute good (also a cross-price elasticity) – This elasticity is positive because as the price of a substitute good rises, the quantity demanded of the good itself rises. – Example: hockey is substitute for basketball. When the price of hockey tickets rises the quantity demanded of basketball tickets rises. Cross-price elasticities quantify effects like these. Cross-Price Elasticity of Demand Definition: Arc Formula: Point Formula: D X , PY Percentage Change in Quantity Demanded of X Percentage Change in Price of Y D X ,P ( Q D X / Q D ) /( PY / PY ) Y D X , P Y (dQ D X / dPY )( PY / Q D X ) Income Elasticity of Demand The elasticity of demand with respect to a consumer’s income is called the income elasticity. – When the income elasticity of demand is positive (normal good), consumers increase their purchases of the good as their incomes rise (e.g. automobiles, food). » When the income elasticity of demand is greater than 1 (luxury good), consumers increase their purchases of the good more than proportionate to the income increase (e.g. ski vacations, haute cuisine). » When the income elasticity of demand is positive but less than 1 (a necessity), consumers increase their purchases of the good less than proportionate to the income increase (e.g. socks, bread). – When the income elasticity of demand is negative (inferior good), consumers reduce their purchases of the good as their incomes rise (e.g. spam, potatoes). Income Elasticity of Demand Definition: Arc Formula: Point Formula: D X ,I Percentage Change in Quantity Demanded Percentage Change in Income D X ,I (Q D X / Q D ) /( I / I ) D X ,I (dQ D X / dI )( I / Q D X ) All Four Elasticities You Need to Know Own Price Elasticity of Demand D X ,P (Q D X / Q D ) /( PX / PX ) X Cross D X , PY ( Q D X ,P (dQ D X / dPX )( PX / Q D X ) X Price Elasticity of Demand D X / Q ) /( PY / PY ) D D X ,PY (dQ D X / dPY )( PY / Q D X ) Income Elasticity of Demand D D D D D ( dQ / dI )( I / Q X , I X X) ( Q X / Q ) /( I / I ) D X ,I Own S X ,P X Price Elasticity of Supply S S S S S ( dQ / dP )( P / Q X ,P X X) ( Q X / Q ) /( PX / PX ) X X X