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Principles of Microeconomics This is a PowerPoint presentation on the fundamentals of the concept of “elasticity” as used in principles of economics. A left mouse click or the enter key will add an element to a slide or move you to the next slide. The backspace key will take you back one element or slide. The escape key will get you out of the presentation. R. Larry Reynolds

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Fall '97Economics 205Principles of MicroeconomicsSlide 2 Elasticity ·Elasticity is a concept borrowed from physics ·Elasticity is a measure of how responsive a dependent variable is to a small change in an independent variable(s) ·Elasticity is defined as a ratio of the percentage change in the dependent variable to the percentage change in the independent variable ·Elasticity can be computed for any two related variables

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Fall '97Economics 205Principles of MicroeconomicsSlide 3 Elasticity [cont... ] ·Elasticity can be computed to show the effects of : ·a change in price on the quantity demanded [ “a change in quantity demanded” is a movement on a demand function] ·a change in income on the demand function for a good ·a change in the price of a related good on the demand function for a good ·a change in the price on the quantity supplied ·a change of any independent variable on a dependent variable

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Fall '97Economics 205Principles of MicroeconomicsSlide 4 “Own” Price Elasticity ·Sometimes called “price elasticity” ·can be computed at a point on a demand function or as an average [arc] between two points on a demand function ·e p, are common symbols used to represent price elasticity ·Price elasticity [e p ] is related to revenue ·“How will a change in price effect the total revenue?” is an important question.

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Fall '97Economics 205Principles of MicroeconomicsSlide 5 Elasticity as a measure of responsiveness ·The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much. ·e p [“own”price elasticity] is a measure of that information] ·“If you change price by 5%, by what percent will the quantity purchased change?

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Fall '97Economics 205Principles of MicroeconomicsSlide 6 or, e p % Q % P At a point on a demand function this can be calculated by: e p = Q 2 - Q 1 Q1Q1 P 2 - P 1 P1P1 Q 2 - Q 1 = Q P 2 - P 1 = P = Q Q1Q1 P P1P1

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Fall '97Economics 205Principles of MicroeconomicsSlide 7 Q Q1Q1 P P1P1 ep =ep = Price decreases from $7 to $5 3 PxPx Q x / ut D $5 B 5 $7 A P 1 = P 2 = P 2 - P 1 = 5 - 7 = PP = -2 PP = -2 Q 1 = Q 2 = Q 2 - Q 1 = 5 - 3 = QQ = +2 QQ = +2 +2 7 3 [2/3 =.66667] [-2/7=-.28571] = % Q = 67% % P = -28.5% = -2.3 [rounded] The “own” price elasticity of demand at a price of $7 is -2.3 This is “point” price elasticity. It is calculated at a point on a demand function. It is not influenced by the direction or magnitude of the price change.. There is a problem! If the price changes from $5 to $7 the coefficient of elasticity is different! -2

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Fall '97Economics 205Principles of MicroeconomicsSlide 8 3 PxPx Q x / ut D $5 B 5 $7 A Q Q1Q1 P P1P1 ep =ep = When the price increases from $5 to $7, P 1 = P2 =P2 = PP = +2 +2 5 Q1=Q1= Q2=Q2= QQ = -2 -2 5 [-2/5 = -.4] [+2/5 =.4] = % Q = -40% % P = 40% = -1 [this is called “unitary elasticity] the ep ep = [“unitary”] e p = -1 In the previous slide, when the price decreased from $7 to $5, e p = -2.3 e p = -2.3 The point price elasticity is different at every point! There is an easier way!

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Fall '97Economics 205Principles of MicroeconomicsSlide 9 An easier way! Q1Q1 P P1P1 ep =ep = Q Q1Q1 = Q1Q1 P 1 P * By rearranging terms = P1P1 Q1Q1 * Q P this is the slope of the demand function this is a point on the demand function Q P1P1 Q1Q1 = * P epep Given that when: P 1 = $7, Q 1 = 3 P 2 = $5, Q 2 = 5 P 2 - P 1 = 5 - 7 = P = -2 Q 2 - Q 1 = 5 - 3 = Q = +2 Then, Q P +2 -2 = = - 1 This is the slope of the demand Q = f(P) P 1 = $7, Q 1 = 3 7 3 = -2.33 On linear demand functions the slope remains constant so you just put in P and Q

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Fall '97Economics 205Principles of MicroeconomicsSlide 10 P 1 = $7, Q 1 = 3 P 2 = $5, Q 2 = 5 P 2 - P 1 = 5 - 7 = P = -2 Q 2 - Q 1 = 5 - 3 = Q = +2 3 PxPx Q x / ut D $5 B 5 $7 A The following information was given Q = f (P) The slope of the demand function [ Q = f(P) ] is Q P = +2 -2 = -1 The slope-intercept form Q = a + m P - 1 What is the Q intercept? P x must decrease by 5. The slope [-1] indicates that for every 1 unit increase in Q, P x will decrease by 1. Since P x must decrease by 5, Q must increase by 5 Q increases by 5 Q = 10 Q = 10 when P x = 0 10 The equation for the demand function we have been using is Q = 10 - 1P. A table can be constructed.

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Fall '97Economics 205Principles of MicroeconomicsSlide 11 For a simple demand function: Q = 10 - 1P pricequantityepTotal Revenue $010 $19 $28 $37 $46 $55 $64 $73 $82 $91 $100 The slope is -1 The intercept is 10 using our formula, epep = Q P 1 Q1Q1 * P epep = Q P1P1 Q1Q1 P * the slope is -1, (-1) price is 7 7 at a price of $7, Q = 3 3 = -2.3 -2.3 Calculate e p at P = $9 Q = 1 e p = (-1) 9 1 = -9 Calculate e p for all other price and quantity combinations. -9 0 -.11 -.25 -.43 -.67 -1.5 -4. undefined

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Fall '97Economics 205Principles of MicroeconomicsSlide 12 For a simple demand function: Q = 10 - 1P pricequantityepTotal Revenue $010 $19 $28 $37 $46 $55 $64 $73 $82 $91 $100 -2.3 -9 0 -.11 -.25 -.43 -.67 -1. -1.5 -4. undefined Notice that at higher prices the absolute value of the price elasticity of demand, e p is greater. Total revenue is price times quantity; TR = PQ. 0 9 16 21 24 25 24 21 16 9 0 Where the total revenue [TR] is a maximum, e p is equal to 1 In the range where e p < 1, [less than 1 or “inelastic”], TR increases as price increases, TR decreases as P decreases. In the range where e p > 1, [greater than 1 or “elastic”], TR decreases as price increases, TR increases as P decreases.

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Fall '97Economics 205Principles of MicroeconomicsSlide 13 3 PxPx Q x / ut D $5 B 5 $7 A To solve the problem of a point elasticity that is different for every price quantity combination on a demand function, an arc price elasticity can be used. This arc price elasticity is an average or midpoint elasticity between any two prices. Typically, the two points selected would be representative of the usual range of prices in the time frame under consideration. The formula to calculate the average or arc price elasticity is: epep = Q P 1 + P 2 Q 1 + Q 2 * P The average or arc e p between $5 and $7 is calculated, epep = Q P 1 + P 2 Q 1 + Q 2 * P Slope of demand Q P = - 1 P 1 = $7, Q 1 = 3 P 2 = $5, Q 2 = 5 P 2 - P 1 = 5 - 7 = P = -2 Q 2 - Q 1 = 5 - 3 = Q = +2 P 1 + P 2 = 12 Q 1 + Q 2 = 8 8 = - 1.5 The average ep ep between $5 and $7 is -1.5

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Fall '97Economics 205Principles of MicroeconomicsSlide 14 Calculate the point e p at each price on the table. Calculate the TR at each price on the table. Calculate arc e p at between $10 and $20. Calculate arc e p at between $25 and $28. Calculate arc e p at between $20 and $28. Graph the demand function [labeling all axis and functions], identify which ranges on the demand function are price elastic and which are price inelastic.

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Fall '97Economics 205Principles of MicroeconomicsSlide 15 Calculate the point e p at each price on the table. 80 40 20 8 -. 5 -2 -5 -14 Calculate the TR at each price on the table. TR = PQ $800 $500 $224 Calculate arc e p at between $10 and $20. e p = -1 Calculate arc e p at between $25 and $28. e p = -7.6 Calculate arc e p at between $20 and $28. e p = -4 Graph the demand function [labeling all axis and functions], identify which ranges on the demand function are price elastic and which are price inelastic. At what price will TR by maximized? P = $15

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Fall '97Economics 205Principles of MicroeconomicsSlide 16 Q/ut Price 120 30 e p = -1 15 60 | e p | > 1 [elastic] The top “half” of the demand function is elastic. | e p | < 1 inelastic The bottom “half” of the demand function is inelastic. Graphing Q = 120 - 4 P, TR TR is a maximum where e p is -1 or TR’s slope = 0 When e p is -1 TR is a maximum. When | e p | > 1 [elastic], TR and P move in opposite directions. (P has a negative slope, TR a positive slope.) When | e p | < 1 [inelastic], TR and P move in the same direction. (P and TR both have a negative slope.) Arc or average e p is the average elasticity between two point [or prices] point e p is the elasticity at a point or price. Price elasticity of demand describes how responsive buyers are to change in the price of the good. The more “elastic,” the more responsive to P.

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Fall '97Economics 205Principles of MicroeconomicsSlide 17 Use of Price Elasticity ·Ruffin and Gregory [Principles of Economics, Addison- Wesley, 1997, p 101] report that: ·short run e p of gasoline is =.15 (inelastic) ·long run e p of gasoline is =.78 (inelastic) ·short run e p of electricity is =. 13 (inelastic) ·long run e p of electricity is = 1.89 (elastic) ·Why is the long run elasticity greater than short run? ·What are the determinants of elasticity?

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Fall '97Economics 205Principles of MicroeconomicsSlide 18 Determinants of Price Elasticity ·Availability of substitutes [greater availability of substitutes makes a good relatively more elastic] ·Portion of the expenditures on the good to the total budget [lower portion tends to increase relative elasticity] ·Time to adjust to the price changes [longer time period means there are more adjustment possible and increases relative elasticity ·Price elasticity for “brands” is tends to be more elastic than for the category of goods

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Fall '97Economics 205Principles of MicroeconomicsSlide 19 An application of price elasticity. The price elasticity of demand for milk is estimated between -.35 and -.5. Using -.5 as a reasonable figure, there are several important observations that can be made. What effect does a 10% increase in the P milk have on the quantity that individuals are willing to buy ? e p % Q % P e p % Q % P Since e p = -.5 -.5 = +10% To solve for % Q Multiply both sides by +10% (+10%)x ( ) x (+10%) -5% = % Q A 10% increase in the price of milk would reduce the quantity demanded by about 5%. P milk Q milk D milk P1P1 Q1Q1 P2P2 A 10% increase in P Q2Q2 reduces Q by 5% +10% -5% If price were decreased by 5%, what would be the effect on quantity demanded?

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Fall '97Economics 205Principles of MicroeconomicsSlide 20 e p % Q % P The price elasticity of demand is a measure of the % Q that will be “caused” by a % P. If the price elasticity of demand for air travel was estimated at -2.5, what effect would a 5% decrease in price have on quantity demanded ? -2.5 = % Q % P - 5% = +12.5% change in quantity demanded If the price elasticity of demand for wine was estimated at -.8, what effect would a 6% increase in price have on quantity demanded ? -.8 = % Q % P +6% = -4.8% decrease in quantity demanded

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Fall '97Economics 205Principles of MicroeconomicsSlide 21 If the price elasticity of demand for milk were -.5, the effects of a price change on total revenue [TR] can also be estimated. Since, e p % Q % P When e p < 1, demand is “inelastic. “ This means that the % Q < % P . Since the % price decrease is greater than the % increase in Q, TR [TR = PQ] will decrease. When e p < 1, a price decrease will decrease TR; a price increase will increase TR, Price and TR “move in the same direction.” [inelastic demand with respect to price] When e p > 1, demand is “elastic.” This means that the % Q > % P . When the % price decrease is less than the % increase in Q, TR [TR = PQ] will increase. When e p > 1, a price decrease will increase TR; a price increase will decrease TR, price and TR “move in opposite directions.” [elastic demand wrt price]

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Fall '97Economics 205Principles of MicroeconomicsSlide 22 Graphically this can be shown P Q/ut D at the midpoint, e p = -1 P1P1 Q1Q1 TR TR is a maximum TR TR = PQ, so the maximum TR is the rectangle 0Q 1 EP 1 0 E elastic price rises P 2 Q 2 (P 2 Q 2 ) is less than (P 1 Q 1 ) Loss in TR when P +TR As price rises into the elastic range the TR will decrease. Notice that in this range the slope of demand is negative, the slope of TR is positive Price and TR move in opposite directions

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Fall '97Economics 205Principles of MicroeconomicsSlide 23 P Q/ut D inelastic TR at the midpoint, e p = -1 0 E P1P1 Q1Q1 TR is a maximum TR = P 1 Q 1 [Maximum] TR When price elasticity of demand is inelastic A price decrease P0P0 Q 0 results in a smaller PQ [TR] will result in a decrease in TR [PQ]. notice that both TR and Demand have a negative slope in the inelastic range of the demand function. Price and TR “move in the same direction.” A price decrease will reduce TR; a price increase will increase TR. Note that this information is useful but does not provide information about profits!

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Fall '97Economics 205Principles of MicroeconomicsSlide 24 “Own” Price Elasticity of Demand ·e p is a measure of the responsiveness of buyers to changes in the price of the good. ·e p will be negative because the demand function is negatively sloped. ·A linear demand function will have unitary elasticity at its “midpoint.” AT THIS POINT TR IS A MAXIMUM! ·A linear demand function will be more “elastic” at higher prices and tends to be more “inelastic” in the lower price ranges

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Fall '97Economics 205Principles of MicroeconomicsSlide 25 Elastic e p ·When e p > 1 [greater than 1], the demand is “elastic” % Q > % P this shows buyers are responsive to changes in price ·An increase in the price of the good results in a decrease in total revenue [TR], a decrease in the price increases TR. Price and TR move in opposite directions. ·The demand for a good tends to become more elastic ·as the number of substitutes increases ·“luxury” good more elastic than “necessities” ·% of price [or expenditure on the good] of the budget ·as the amount of time for adjustments increases elasticity

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Fall '97Economics 205Principles of MicroeconomicsSlide 26 Inelastic e p ·When e p < 1 [less than 1] the demand is “inelastic” ·The % Q < % P buyers are not very responsive to changes in price. ·An increase in the price of the good results in an increase in total revenue [TR], a decrease in the price decreases TR. Price and TR move in the same direction

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Fall '97Economics 205Principles of MicroeconomicsSlide 27 P Q/ut D1D1 D 1 is a “perfectly elastic” demand function. e p % Q % P For an infinitesimally small change in price, Q changes by infinity. = undefined perfectly elastic e p = undefined. Buyers are very responsive to price changes. An infinitely small change in price changes Q by infinity. D2D2 perfectly inelastic e p = 0 D 2 is a “perfectly inelastic” demand function, no matter how much the price changes the same amount is bought. Buyers are not responsive to price changes! e p = 0, perfectly inelastic. 0 P 0 = 0. As the demand function becomes more horizontal, [buyers are more responsive to price changes], e p approaches infinity. DeDe

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Fall '97Economics 205Principles of MicroeconomicsSlide 28 Examples ·Goods that are relatively price elastic ·lamb, restaurant meals, china/glassware, jewelry, air travel [LR], new cars, Fords ·in the long run, e p tends to be greater ·Goods that are relatively price inelastic ·electricity, gasoline, eggs, medical care, shoes, milk ·in the short run, e p tends to be less

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Fall '97Economics 205Principles of MicroeconomicsSlide 29 Income Elasticity [normal goods] e y % Q x % Y [Where Y = income] Income elasticity is a measure of the change in demand [a “shift” of the demand function] that is “caused” by a change in income.. Q/ut P D At a price of P 1, the quantity demanded given the demand D is Q1 Q1. P1P1 Q1Q1 D is the demand function when the income is Y 1. For a “normal good” an increase in income to Y 2 will “shift” the demand to the right. This is an increase in demand to D 2. Due to increase in income, demand increases D2D2 The increase in income, Y, increases demand to D 2. The increase in demand results in a larger quantity being purchased at the same Price [ P 1].. Q2Q2 % Y > 0; % Q> 0; therefore, e y >0 [it is positive]

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Fall '97Economics 205Principles of MicroeconomicsSlide 30 Income Elasticity [continued...] [normal goods] ey ey % Q x % Y Q/ut P D1D1 A decrease in income is associated with a decrease in the demand for a normal good. At income Y 1, the demand D 1 represents the relationship between P and Q. At a price [P 1 ] the quantity [Q 1 ] is demanded. P1P1 Q1Q1 For a decrease in income [- Y], the demand decreases; i.e. shifts to the left, A decrease in income, decreases demand D2D2 at the price [P 1 ], a smaller Q 2 will be purchased. Q2Q2 % Y 0 [ positive] For either an increase or decrease in income the e p is positive. A positive relationship [positive correlation] between Y and Q is evidence of a normal good.

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Fall '97Economics 205Principles of MicroeconomicsSlide 31 When income elasticity is positive, the good is considered a “normal good.” An increase in income is correlated with an increase in the demand function. e y % Q x % Y ey ey % Q x % Y + % Y + % Q x + e y A decrease in income is associated with a decrease in the demand function. - % Y - % Q x + e y For both increases and decreases in income, e y is positive. The greater the value of e y, the more responsive buyers are to a change in their incomes. When the value of e y is greater than 1, it is called a “superior good.”. The | % Q x | is greater than the | % Y |. Buyers are very responsive to changes in income. Sometimes “superior goods” are called “luxury goods.”

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Fall '97Economics 205Principles of MicroeconomicsSlide 32 ey ey % Q x % Y D1D1 Income Elasticity [inferior goods] There is another classification of goods where changes in income shift the demand function in the “opposite” direction. An increase in income [+ Y] reduces demand. Q/ut P P1P1 Q1Q1 decreases demand D2D2 Q2Q2 +Y+Y - %Qx- %Qx -%Qx-%Qx -e y =. An increase in income reduces the amount that individuals are willing to buy at each price of the good. Income elasticity is negative: - e y The greater the absolute value of - e y, the more responsive buyers are to changes in income.

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Fall '97Economics 205Principles of MicroeconomicsSlide 33 D1D1 Income Elasticity [inferior goods] A decrease in income [ - Y] increases demand. Q/ut P P1P1 Q1Q1 D2D2 Q2Q2 e y % Q x % Y -Y-Y +%Qx+%Qx Decreases in income increase the demand for inferior goods. +%Qx+%Qx - e y. A decrease in income [- Y] results in an increase in demand, the income elasticity of demand is negative. For both increases and decreases in income the income elasticity is negative for inferior goods. The greater the absolute value of e y, the more responsive buyers are to changes in income

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Fall '97Economics 205Principles of MicroeconomicsSlide 34 Income Elasticity ·Income elasticity [ e y] is a measure of the effect of an income change on demand. [ Can be calculated as point or arc.] ·e y > 0, [positive] is a normal or superior good an increase in income increases demand, a decrease in income decreases demand. ·0 < e y < 1 is a normal good ·1 < e y is a superior good ·e y < 0, [negative] is an inferior good

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Fall '97Economics 205Principles of MicroeconomicsSlide 35 Examples of e y ·normal goods, [0 < e y < 1 ], (between 0 and 1) ·coffee, beef, Coca-Cola, food, Physicians’ services, hamburgers,... ·Superior goods, [ e y > 1], (greater than 1) ·movie tickets, foreign travel, wine, new cars,... ·Inferior goods, [ e y < 0], (negative) ·flour, lard, beans, rolled oats,...

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Fall '97Economics 205Principles of MicroeconomicsSlide 36 Cross-Price Elasticity ·Cross-price elasticity [e xy ] is a measure of how responsive the demand for a good is to changes in the prices of related goods. ·Given a change in the price of good Y [P y ], what is the effect on the demand for good X [Q y ]? · e xy is defined as:

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Fall '97Economics 205Principles of MicroeconomicsSlide 37 Cross-price elasticity of demand, [ e xy ] [substitutes]. When the price of pork increases, it will tend to increase the demand for beef. People will substitute beef, which is relatively cheaper, for pork, which is relatively more expensive. pork/ut [price of pork] PpPp DpDp When pork is $1.50, Q p pork is purchased. 1.50 DbDb beef/ut [price of beef] PbPb QpQp When beef is $2, Q b beef is purchased. 2 QbQb price of pork increases 2 The quantity demanded of pork decreases. Qp’Qp’ -Qp-Qp at P b = $2 more beef will be bought to substitute for the smaller quantity of pork. increase demand Db’Db’ Qb’Qb’ for an increase in P pork, demand for beef increases

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Fall '97Economics 205Principles of MicroeconomicsSlide 38 Cross-price elasticity ·In the case of beef and pork ·the e bp is not the same as e pb ·e bp is the % change in the demand for beef with respect to a % change in the price of pork ·e pb is the % change in the demand for pork with respect to a % change in the price of beef ·beef may not be a good substitute for pork ·pork may not be a good substitute for beef

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Fall '97Economics 205Principles of MicroeconomicsSlide 39 Cross-price elasticity of demand, [ e xy ] [substitutes] The cross elasticity of the demand for beef with respect to the price of pork, e beef-pork or e bp can be calculated: e bp = % Q of beef % P of pork An increase in the price of pork, + P p “causes” an increase in the demand for beef. + Qb+ Qb +e bp positive cross elasticity is positive e bp = % Q of beef % P of pork A decrease in the price of pork, - Pp- Pp “causes” a decrease in the demand for beef. - Q b +e bp positive If goods are substitutes, e xy will be positive. The greater the coefficient, the more likely they are good substitutes.

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Fall '97Economics 205Principles of MicroeconomicsSlide 40 Cross-price elasticity of demand, [ e xy ] [compliments] colour books PcPc crayons PcPc DpDp a decrease in the price of crayons, P1P1 Q1Q1 $3 2000 PoPo Q2Q2 increases the quantity demanded of crayons as more crayons are purchased, the demand for colour books increases. DcDc Dc’Dc’ increase demand 2500 At the same price a larger quantity will be bought e bc = % Q of b % P of c -Pc-Pc - P c + Q b - e bc negative for compliments, the cross elasticity is negative for price increase or decrease.

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Fall '97Economics 205Principles of MicroeconomicsSlide 41 Cross-Price Elasticity ·e xy > 0 [positive], suggests substitutes, the higher the coefficient the better the substitute ·e xy < 0 [negative], suggests the goods are compliments, the greater the absolute value the more complimentary the goods are ·e xy = 0, suggests the goods are not related ·e xy can be used to define markets in legal proceedings

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Fall '97Economics 205Principles of MicroeconomicsSlide 42 Elasticity of Supply ·Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good. ·Elasticity of supply [ e p ] is defined:

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Fall '97Economics 205Principles of MicroeconomicsSlide 43 Q /ut P Given a supply function, supply at a price [P 1 ], Q 1 is produced and offered for sale. P1P1 Q1Q1 At a higher price [P 2 ], P2P2 a larger quantity, Q 2, will be produced and offered for sale. Q2Q2 +P+P +Q+Q The increase in price [ P ], induces a larger quantity goods [ Q]for sale. The more responsive sellers are to P, the greater the absolute value of e s. [The supply function is “flatter”or more elastic] Elasticity of supply e s = % Q supplied %P%P

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Fall '97Economics 205Principles of MicroeconomicsSlide 44 Q /ut P The supply function is a model of sellers behavior. Sellers behavior is influenced by: 1. technology 2. prices of inputs 3. time for adjustment market period short run long run very long run 4. expectations 5. anything that influences costs of production taxes regulations,... SeSe a perfectly elastic supply [ e s is undefined.] SiSi a perfectly inelastic supply, e s = 0 as supply approaches horizontal e s approaches infinity

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Fall '97Economics 205Principles of MicroeconomicsSlide 45 Elasticity ·Price elasticity of demand [ measures a move on a demand function caused by change in price/arc or point ] ·elastic, inelastic or unitary elasticity ·income elasticity [ measures a shift of a demand function associated with a change in income] ·superior, normal, and inferior ·cross elasticity ·measure the shift of a demand function for a good associated with the change in the price of a related good ·[compliment/substitute] ·price elasticity of supply [measures move on a supply curve]

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