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Quantitative Demand Analysis (Elasticity) Finance 514 Baye Chapter 3 Elasticity • General concept that measures the responsiveness of two variables to one another • Mechanism to characterize demand and supply • Measure of how markets react to changing conditions • Allows for a more detailed understanding and analysis of supply and demand Price Elasticity • ED = % change in Q / % change in P • Shortcut notation: ED = %Q / %P • A percentage change from 100 to 150 is 50% • A percentage change from 150 to 100 is -33% • For arc elasticities, we use the average as the base, as in 100 to 150 is +50/125 = 40%, and 150 to 100 is -40% • Arc Price Elasticity -- averages over the two points Average quantity arc price • elasticity ED = Q/ [(Q1 + Q2)/2] P/ [(P1 + P2)/2] • D Average price Arc Price Elasticity Example • Q = 1000 when the price is $10 • Q= 1200 when the price is reduced to $6 • Find the arc price elasticity • Solution: ED = %Q/ %P = +200/1100 -4/8 or -0.3636. – A 1% increase in price reduces quantity by .36 percent. Point Price Elasticity Example • Need a demand curve or demand function to find the price elasticity at a point. ED = %Q/ %P =(Q / P)(P/Q) If Q = 500 - 5•P, find the point price elasticity at P = 30; P = 50; and P = 80 1. ED = (Q / P)(P/Q) = - 5(30/350) = - .43 2. ED = (Q / P)(P/Q) = - 5(50/250) = - 1.0 3. ED = (Q / P)(P/Q) = - 5(80/100) = - 4.0 Price Elasticity (Both point price and arc elasticity ) • If ED = -1, unit elastic • If ED > -1, inelastic, e.g., - 0.43 • If ED < -1, elastic, e.g., -4.0 Straight line price demand curve elastic region example unit elastic inelastic region quantity Two Extreme Examples D D D’ D’ Perfectly Elastic | ED| = and Perfectly Inelastic |ED | = 0 Use For Elasticity • Elasticity is related to revenues • Suppose demand is elastic, and you raise price. • TR = P•Q, so, %TR = %P + % Q • If elastic, P increases but Q falls a lot • Hence TR FALLS • Suppose demand is inelastic, and we decide to raise price. What happens to TR? and profit? Another Way to Elastic P Remember Unit Elastic Inelastic • Linear demand curve • TR on the other TR Q curve • Look at arrows to TR see movement in TR Q 1979 Deregulation of Airfares • Prices declined after deregulation • And passengers increased • Also total revenue increased • What does this imply about the price elasticity of air travel? Determinants of the Price Elasticity • The availability and the closeness of substitutes – more substitutes, more elastic • The more durable is the product – Durable goods are more elastic than non-durables • The percentage of the budget – larger proportion of the budget, more elastic • The longer the time period permitted – more time, generally, more elastic – consider examples of business travel versus vacation travel for all three above. Time and Adjustment to an Reduction in Supply • Consider the market for gasoline of the late 1970s and early 1980s (and Price S2 now). ($ per gallon) • The price of a gallon of gasoline in S1 1978 was $.70 (point A). 1.20 B • When supply declined unexpectedly 1.10 in the late 1970s, prices increased 1.00 C to $1.20 and consumption fell to 7.0 .90 million barrels per day (from 7.4) as .80 consumers moved along their short A .70 run demand curve (to point B). .60 • Note how little quantity demanded .50 fell due to this shock. In the long .40 run, the demand for gasoline is more .30 responsive to price changes .20 DLR .10 DSR • By 1982, the market equilibrated at Quantity point C, with consumption of 6.6 6.6 7.0 7.4 (million million barrels a day and a market barrels of gas per day) price of $1.00 a gallon). Elasticity of Demand Inelastic Approximately Unitary Elasticity Salt 0.1 Movies owner occupied (long run) 0.9 Homes, Matches 0.1 Shellfish (consumed at home) 1.2 Toothpicks (short run) Airline travel 0.1 Oysters (consumed at home) 0.9 Gasoline (short run) 0.1 1.1 Gasoline (long run) 0.2 Private education Tires (short run 1.1 Natural gas, home (short run) 0.7 Tires (long run) 0.9 Natural gas, home (long run) 0.1 Radio and television receivers 1.2 0.5 1.2 Coffee Fish (cod), at home 0.3 Elastic Tobacco products (short run) 0.5 Restaurant meals run) 2.3 0.5 Foreign travel (long Legal services (short run) 4.0 0.4 Airline travel (long run) 2.4 Physician services Taxi (short run) 0.6 Fresh green peas run) Automobiles (short 2.8 Automobiles (long run) 0.6 1.4 0.2 Chevrolet automobiles 4.0 Fresh tomatoes 4.6 • Can you explain why the demand for some goods is highly inelastic while that for others is elastic. Income Elasticity EY = %Q/ %Y = ( Q/ Y)( Y/Q) point income EY = Q/ [(Q1 + Q2)/2] arc income Y/ [(Y1 + Y2)/2] elasticity • Arc income elasticity: – suppose dollar quantity of food expenditures for families earning $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000. – Find the income elasticity of food – %Q/ %Y = (1560/5980)•(10,000/25,000) = .652 – With a 1% increase in income, food purchases rise .652% Income Elasticity Definitions • If EY >0, then it is a normal good – some goods are Luxuries: EY > 1 with a high income elasticity – some goods are Necessities: EY < 1 with a low income elasticity • If EY is negative, then it’s an inferior good • Consider these examples: 1. Expenditures on new automobiles 2. Expenditures on new Chevrolets 3. Expenditures on 1996 Chevy Cavaliers with 150,000 miles Which of the above is likely to have the largest income elasticity? Which of the above might have a negative income elasticity? Point Income Elasticity Problem • Suppose the demand function is: Q = 10 - 2•P + 3•Y • find the income and price elasticities at a price of P = 2, and income Y = 10 • So: Q = 10 -2(2) + 3(10) = 36 • EY = (Q/Y)( Y/Q) = 3( 10/ 36) = .833 • ED = (Q/P)(P/Q) = -2(2/ 36) = -.111 • Characterize this demand curve, which means describe them using elasticity terms. Cross Price Elasticities EAB = %QA / %PB = (QA/ PB)(PB /QA) • Substitutes have positive cross price elasticities: Butter & Margarine • Complements have negative cross price elasticities: DVD machines and the rental price of DVDs at Blockbuster • When the cross price elasticity is zero or insignificant, the products are not related Problem Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, Y=20, and PS=9, if the demand function were estimated to be: QD = 90 - 8·P + 2·Y + 2·Ps Is the demand for this product elastic or inelastic? Is it a luxury or a necessity? Does this product have a close substitute or complement? Combined Effect of Demand Elasticities • Most managers find that prices and income change every year. The combined effect of several changes are additive. %Q = ED(% P) + EY(% Y) + EX(% PR) – where P is price, Y is income, and PR is the price of a related good. • If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity. Example: Combined Effects of Elasticities • Toro has a price elasticity of -2 for snow-throwers • Toro snow throwers have an income elasticity of 1.5 • The cross price elasticity with professional snow removal for residential properties is +.50 • What will happen to the quantity sold if you raise price 3%, income rises 2%, and professional snow removal companies raises its price 1%? Q: Will Total Revenue for your product rise or fall? Questions for Thought • Studies indicate that the demand for Florida oranges, Bayer aspirin, watermelons, and airfares to Europe are elastic. Why? – Why is the demand for salt, matches, and gasoline (short-run) inelastic? • Are the following statements true or false? – A 10% reduction in price that leads to a 15% increase in amount purchased indicates a price elasticity of more than 1. – A 10% reduction in price that leads to a 2% increase in total expenditures indicates a price elasticity of more than 1. Demand Estimation • Interviews – Surveys – Focus Groups – Simulated Markets • Price Experimentation – Varying prices across different markets • Statistical Analysis – Estimate demand curves – The problem of ceteris paribus and omitted variables Price Elasticity of Supply • The price elasticity of supply is the percent change in quantity supplied divided by the percent change of the price causing the supply response. – Analogous to the price elasticity of demand. – However, the price elasticity of supply will be positive because the quantity producers are willing to supply is directly related to price. Determinants of Supply Elasticity • Ability of sellers to change the amount of the good they produce. – Beach-front land is inelastic. – Books, cars, or manufactured goods are elastic. • Time period. – Supply is more elastic in the long run.

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posted: | 2/18/2010 |

language: | English |

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