Measurement and Interpretation of Elasticities

Transcription

1 Measurement and Interpretation of lasticities hapter 2 + What Are lasticities? Measure of the relationship between two variables lasticity Percentage change in y Percentage change in x lastic vs. inelastic Arc vs. point Alfred Marshall Popularized concepts hanged the name and face of economics Quirks lasticities 1

2 lasticities of emand Own-price elasticity of demand responsiveness of changes in quantity associated with a change in the goods own price Income elasticity of demand responsiveness of changes in quantity associated with a change in income ross-price elasticity of demand responsiveness of changes in quantity associated with a change in price of another good Own- lasticity of emand Own-price lasticity Own-price elasticity ΔQ Q ΔQ P ΔP ΔP Q P Percentage change in quantity Percentage change in own price (Q A - Q B )/[(Q A + Q B )/2] (P A - P B )/[(P A + P B )/2] Interpretation -- 1% increase in price leads to a x% change in quantity purchased over this arc Own- lasticity A B onsumer bundle B to A hange in quantity 2 to 1 hange in price 9 to 1 What is the own-price elasticity of demand at this arc?

3 Math etails Recall change in quantity 2 to 1 and price 9 to 1 % change in quantity (1-2)/[(1+2)/2] % change in own price (1-9)/[(1+9)/2].15 or ΔQ ΔP P Q (1-2) (1-9) (1+9)/ (1+2)/ Interpretation -- 1% increase in price leads to a 6.33% decrease in quantity purchased over this arc Own- lasticity Bundles to % change in quantity (5-6)/[5+6)/2] % change in own price (6-5)/[(6+5)/2] Unitary lasticity -- 1% increase in price leads to a 1% decrease in quantity purchased over this arc Own- lasticity Interpretation -- 1% increase in price leads to a.29% decrease in quantity purchased F Bundles to F % change in quantity % change in price (8-9)/[8 9)/2] (3-2)/[(3 2)/2]

4 Own- lasticity ont. Generally elasticities vary over the curve Negative law of demand Linear demand curve - specific ΔQ ΔP P Q lastic where % Q > % P Unitary lastic where % Q % P Inelastic where % Q < % P Own- lasticity If value of the elasticity coefficient is emand is said to be % in quantity is Less than -1. lastic Greater than % in price qual to -1. Unitary elastic Same as % in price Greater than -1. Inelastic Less than % in price Use - example What is arc elasticity for corn between the prices of $15 (6 corn) and $2 (5 corn) / dozen? emand urve for orn dollar per dozen ears` dozen ears of corn 4

5 Use ont. alculation of arc elasticity % change in (2-15)/[(2+15)/2].28 % change in Q (5-6)/[(5+6)/2] -.18 Own-price elasticity -.18/(.28) -.63 lastic or inelastic Why? Goal is to increase s. The current price is $17.5 / dozen, should you increase or decrease price? Revenue Implications - Know Own-price elasticity is lastic Unitary elastic Inelastic utting the price will Increase No change in ecrease Increasing the price will ecrease No change in Increase Use ont. Necessary information from earlier calculations increase from 15 to 2 decreases from 6 to 5 Own-price elasticity -.18/(.28) -.63 urrent price $17.5 with Q 5.5 Goal is to increase s urrent TR 17.5 x Increase price TR 2 x 5 1 ecrease price TR 15 x 6 9 5

6 Revenue Implications Why? Unit lasticity emand urve Revenue price x quantity consumer expenditures Before change area Q b ut in price Brings about the same % increase in the quantity demanded definition of unit elasticity After Revenue area Q a O Q b Q a Revenue Implications Why? Unit lasticity emand urve What about a price increase? Loss in due to price change Gain in due to quantity change O Q b Q a Revenue Implications Why? Inelastic emand urve Revenue price x quantity consumer expenditures Before change area Q b ut in price Brings about a smaller increase in the % quantity demanded definition of inelastic After hange area Q a O Q b Q a 6

7 Revenue Implications Why? Inelastic emand urve Producer falls since % P is greater than % Q. Revenue before the change was Q b. Revenue after the change was Q a. O Q b Q a Revenue Implications Why? Inelastic emand urve Producer falls since the loss is greater than the gain O Q b Q a Revenue Implications lastic emand urve ut in price Brings about a larger % increase in the quantity demanded Q b Q a 7

8 Revenue Implications lastic emand urve Q b Q a Producer increases since % P is less that % Q. Revenue before the change was Q b. Revenue after the change was Q a. Revenue Implications Producer increases since the gain is Greater than the loss lastic emand urve Q b Q a Revenue Implications - Know Own-price elasticity is lastic Unitary elastic Inelastic utting the price will Increase No change in ecrease Increasing the price will ecrease No change in Increase 8

9 Relative lasticities Perfectly inelastic Perfectly elastic Relative lasticities Relatively more inelastic Relatively more elastic Long vs. Short-Run emand curves tend to be more elastic (flatter) over time as consumers adjust to changing prices Why? 9

10 onsumer Surplus lastic emand urve Inelastic emand urve c Gain in consumer surplus after the price cut is area onsumer surplus increased by area Q b Q a Q b Q a Income lasticity of emand Income lasticity of emand Income elasticity ΔQ Q ΔI I ΔQ ΔI Percentage change in quantity Percentage change in income I Q (Q A - Q B )/[(Q A + Q B )/2] (I A - I B )/[(I A + I B )/2] Interpretation -- 1% increase in income leads to a x% change in quantity purchased over this arc Income lasticity xample Income and orn Income change 2 to 4 orn quantity change 5 to 9 What is arc income elasticity of demand? % change in quantity % change in income (9-5)/[9 5)/2] (4-2)/[(4 2)/2] Interpretation? 1

11 Interpreting the Income lasticity of emand - Know If the income elasticity is Greater than 1. Less than 1. but greater than. Less than. The good is classified as A luxury and a normal good A necessity and a normal good An inferior good! ross- lasticity of emand ross-price lasticity of emand ross -price elasticity ΔQ Q ΔP P ΔQ P ΔP Q Percentage change in quantity of good Percentage change in price (Q A - Q B )/[(Q A +Q B )/2] (P A - P B )/[(P A + P B )/2] Interpretation -- 1% increase in price of good leads to a x% change in quantity purchased of good over this arc ross- lasticity xample Steak quantity and corn price orn price change from $2 to $15 / dozen Steak quantity changes from 2.5 to 2.75 pounds What is arc cross-price elasticity of demand for steak? % change in quantity steak Interpretation? % change in corn price ( )/[( )/2] (15-2)/[(15+2)/2]

12 Interpreting the ross lasticity of emand - Know If the cross price elasticity is Positive Negative Zero The goods are classified as Substitutes omplements Independent Stimulus Bill xample 29 Stimulus Bill Included a up to a $15 tax credit for insulation and energy efficient windows, doors, HVA units What is a tax credit? Why pass the bill and potential economic effects? - nonpolitical Stimulus Bill Insulation Assume you have calculated the following elasticities for insulation Income elasticity of demand 1.2 Own-price elasticity -.4 ross price elasticity with lumber -.2 ross price elasticity with energy.9 Assume tax credit decreases insulation price by 3% What is the effect of the stimulus bill given these elasticities? Recession has decreased incomes by 1% 12

13 Stimulus Bill Insulation ecrease in insulation sales recession -1% x % - decrease in insulation sales Increase in insulation sales stimulus bill -3% x % - increase in insulation sales hange in lumber sales stimulus bill -3% x -.2.6% - increase in lumber sales hange in energy use stimulus bill -3% x.9-2.7% - decrease in energy use osts of the Bill ecrease in tax s insulation tax credit Increase in tax s increase in insulation sales Increase in tax s increase in lumber sales ecrease in tax s decrease in energy use nvironmental / other Overall? Flexibility of emand flexibility is the reciprocal of own price elasticity flexibility 1/(own price elasticity) Flexibility of emand Percentage change in price Percentage change in quantity Rearrange % Δ price price flexibility x % Δ quantity 13

14 Flexibility Use xample If the calculated elasticity is -.25, then the price flexibility 1/(-.25) - 4. Useful concept to producers to help form price expectations xample USA projects an additional 2% of supply will come on the market, what happens to price. % price flexibility x % - 4. x (+2%) - 8% If supply increases by 2%, price would fall by 8%! Revenue Implications emand lasticity and hanges in Supply Own-price elasticity is lastic Unitary elastic Inelastic Increase in supply will Increase No change in ecrease ecrease in supply will ecrease No change in Increase haracteristic of agriculture Summary - Know Know how to interpret all three elasticities Know how to interpret a price flexibility Understand implications for producers if prices are cut (raised) Understand the welfare implications for consumers if prices are cut (raised) 14