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Income Elasticity (Normal Goods)

Income Elasticity (Normal Goods). Elasticity. Income Elasticity (Normal Goods). Elasticity Elasticity is a measure of how responsive a dependent variable is to a small change in an independent variable(s)

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Income Elasticity (Normal Goods)

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  1. Income Elasticity (Normal Goods) Elasticity

  2. Income Elasticity (Normal Goods) Elasticity • 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

  3. Income Elasticity (Normal Goods) 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

  4. Income Elasticity (Normal Goods) “Own” Price Elasticity

  5. Income Elasticity (Normal Goods) • 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 • ep, h, eare common symbols used to represent price elasticity • Price elasticity [ep] is related to revenue • “How will a change in price effect the total revenue?” is an important question.

  6. Income Elasticity (Normal Goods) 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. • ep [“own”price elasticity] is a measure of that information] • “If you change price by 5%, by what percent will the quantity purchased change?

  7. % D Q or, ep º % D P Q2 - Q1 = D Q Q2 - Q1 D Q Q1 Q1 ep = = P2 - P1 = D P P2 - P1 D P P1 P1 At a point on a demand function this can be calculated by:

  8. +2 [2/3 = .66667] 3 % DQ = 67% =-2.3 [rounded] = -2 % DP = -28.5% 7 [-2/7=-.28571] Px A $7 B $5 D Qx/ut 5 3 D Q Q1 ep= D P P1 The “own” price elasticity of demand at a price of $7 is -2.3 Price decreases from $7 to $5 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. P2- P1= 5 - 7 = D P = -2 P1 = D P = -2 Q2 - Q1= 5 - 3 = D Q = +2 P2 = There is a problem! If the price changes from $5 to $7 the coefficient of elasticity is different! D Q = +2 Q1= Q2 = .

  9. [-2/5 = -.4] -2 D Q % DQ = -40% 5 = -1 [this is called “unitary elasticity] = % DP = 40% +2 5 Px A P2= $7 B P1= $5 D Qx/ut Q2= Q1= 5 3 ep= Q1 D P [+2/5 = .4] P1 the ep= -1[“unitary”] When the price increases from $5 to $7, In the previous slide, when the price decreased from $7 to $5, ep= -2.3 The point price elasticity is different at every point! ep= -2.3 ep= -1 D P = +2 There is an easier way! D Q = -2

  10. this is a point on the demand function P1 D Q D Q P1 = * * D P Q1 D P Q1 this is the slope of the demand function P1 = $7, Q1 = 3 7 -1 P2 = $5, Q2= 5 3 P2- P1= 5 - 7 = D P = -2 Q2 - Q1= 5 - 3 = D Q = +2 Then, +2 D Q = D P -2 By rearranging terms An easier way! D Q ep= Q1 = Q1 D P P1 Given that when: D Q P1 ep = -2.33 = * Q1 D P P1 = $7, Q1 =3 On linear demand functions the slope remains constant so you just put in P and Q = -1 This is the slope of the demand Q = f(P)

  11. Px A $7 B $5 D The slope of the demand function [Q = f(P)] is Q increases by 5 D Q +2 Qx/ut = = -1 Q = 10 5 3 D P -2 - 1 Q = f (P) The following information was given P1 = $7, Q1 = 3 What is the Q intercept? P2 = $5, Q2= 5 Q2 - Q1= 5 - 3 = D Q = +2 P2- P1= 5 - 7 = D P = -2 Px must decrease by 5. The slope [-1] indicates that for every 1 unit increase in Q, Px will decrease by 1. Since Px must decrease by 5, Q must increase by 5 The equation for the demand function we have been using is Q = 10 - 1P. A table can be constructed. Q = 10 when Px = 0 The slope-intercept form Q = a + m P 10

  12. D Q P1 ep = * For a simple demand function: Q = 10 - 1P Q1 D P price quantity e p Total Revenue 7 P1 0 D Q $0 10 ep = (-1) * -.11 Q1 3 D P $1 9 -.25 $2 8 -.43 $3 7 -.67 $4 6 -1. 9 $5 5 ep = (-1) -1.5 1 $6 4 $7 3 -4. $8 2 $9 1 undefined $10 0 using our formula, The slope is -1 The intercept is 10 price is 7 the slope is -1, = -2.3 at a price of $7, Q = 3 Calculate ep at P = $9 Q = 1 = -9 -2.3 Calculate ep for all other price and quantity combinations. -9

  13. For a simple demand function: Q = 10 - 1P price quantity e p Total Revenue 0 0 $0 10 -.11 9 $1 9 16 -.25 $2 8 21 -.43 $3 7 24 -.67 $4 6 -1. 25 $5 5 24 -1.5 $6 4 -2.3 21 $7 3 -4. 16 $8 2 9 -9 $9 1 undefined 0 $10 0 Notice that at higher prices the absolute value of the price elasticity of demand, ½ep½, is greater. Total revenue is price times quantity; TR = PQ. Where the total revenue [TR] is a maximum, ½ep ½ is equal to 1 In the range where ½ep ½< 1, [less than 1 or “inelastic”], TR increases as price increases, TR decreases as P decreases. In the range where ½ep ½> 1, [greater than 1 or “elastic”], TR decreases as price increases, TR increases as P decreases.

  14. D Q P1 + P2 = 12 P1 + P2 ep = * Q1 + Q2 D P P1 = $7, Q1 = 3 Px Q1 + Q2 = 8 P2 = $5, Q2= 5 A Q2 - Q1= 5 - 3 = D Q = +2 $7 P2- P1= 5 - 7 = D P = -2 D Q B = - 1 D P $5 D D Q 12 P1 + P2 -1 ep = * 8 Q1 + Q2 D P Qx/ut 5 3 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: The average or arcep between $5 and $7 is calculated, Slope of demand = - 1.5 The average ep between $5 and $7 is -1.5

  15. Given: Q = 120 - 4 P e Price Quantity T R p $ 10 $ 20 $ 25 $ 28 Calculate the point ep at each price on the table. Calculate the TR at each price on the table. Calculate arc ep at between $10 and $20. Calculate arc ep at between $25 and $28. Calculate arc ep 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.

  16. Given: Q = 120 - 4 P e Price Quantity T R p 80 $ 10 $800 - . 5 40 $ 20 -2 $800 $500 20 -5 $ 25 8 $224 -14 $ 28 Calculate the point ep at each price on the table. Calculate the TR at each price on the table. TR = PQ Calculate arc ep at between $10 and $20. ep = -1 Calculate arc ep at between $25 and $28. ep = -7.6 ep = -4 Calculate arc ep 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. At what price will TR by maximized? P = $15

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

  18. Income Elasticity (Normal Goods) 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

  19. Income Elasticity (Normal Goods) % D Q ep º % D P % D Q ep º -.5 = -5% = x (+10%) % D Q (+10%)x ( ) % D P +10% Pmilk P2 +10% P1 Dmilk -5% Qmilk Q1 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. Sinceep = -.5 What effect does a 10% increase in the Pmilk have on the quantity that individuals are willing to buy? To solve for % D Q Multiply both sides by +10% A 10% increase in the price of milk would reduce the quantity demanded by about 5%. If price were decreased by 5%, what would be the effect on quantity demanded? A 10% increase in P reduces Q by 5% Q2

  20. % D Q % D P % D Q -2.5 = % D P - 5% % D Q -.8 = % D P +6% ep º The price elasticity of demand is a measure of the % D Q that will be “caused” by a % D 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 ? = +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 ? = -4.8% decrease in quantity demanded

  21. % D Q % D P If the price elasticity of demand for milk were -.5, the effects of a price change on total revenue [TR] can also be estimated. When |ep|< 1, demand is “inelastic. “ This means that the ê% D Qê < ê% D Pê. Since the % price decrease is greater than the % increase in Q, TR [TR = PQ] will decrease. Since , ep º When |ep| < 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 |ep|> 1, demand is “elastic.” This means that the ê% D Qê > ê% D Pê. When the % price decrease is less than the % increase in Q, TR [TR = PQ] will increase. When |ep| > 1, a price decrease will increase TR; a price increase will decrease TR, price and TR “move in opposite directions.” [elastic demand wrt price]

  22. TR is a maximum TR P elastic +TR E P1 Loss in TR when DP D 0 Q1 Q/ut TR Price and TR move in opposite directions Graphically this can be shown TR = PQ, so the maximum TR is the rectangle 0Q1 EP1 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 P2 at the midpoint, ep = -1 price rises than (P1 Q1) (P2 Q2) is less Q2

  23. TR is a maximum TR P E inelastic P1 P0 results in a smaller PQ [TR] D 0 Q1 Q/ut TR When price elasticity of demand is inelastic 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 at the midpoint, ep = -1 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! TR = P1Q1 [Maximum] Q0

  24. “Own” Price Elasticity of Demand ep is a measure of the responsiveness of buyers to changes in the price of the good. epwill 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 Economics 205Principles of Microeconomics

  25. Inelastic ep When |ep| < 1 [less than 1] the demand is “inelastic” The |%DQ| < |%DP|, 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 Economics 205Principles of Microeconomics

  26. D2 P D1 De ¥ 0 % D Q ep º = 0 ¥ % D P P Q/ut 0 D1is a “perfectly elastic” demand function. perfectly inelastic ep = 0 For an infinitesimally small change in price, Q changes by infinity. Buyers are very responsive to price changes. An infinitely small change in price changes Q by infinity. perfectly elastic |ep| = undefined As the demand function becomes more horizontal, [buyers are more responsive to price changes],|ep|approaches infinity. = undefined D2 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! |ep| = 0, perfectly inelastic. . .

  27. Examples Goods that are relatively price elastic lamb, restaurant meals, china/glassware, jewelry, air travel [LR], new cars, Fords in the long run, |ep| tends to be greater Goods that are relatively price inelastic electricity, gasoline, eggs, medical care, shoes, milk in the short run, |ep| tends to be less Economics 205Principles of Microeconomics

  28. Income Elasticity (Normal Goods) Income Elasticity (Normal Goods)

  29. Income Elasticity [normal goods] % D Qx % D Y P demand increases P1 D2 D Q/ut Income elasticity is a measure of the change in demand [a “shift” of the demand function] that is “caused” by a change in income. ey º The increase in income, DY, increases demand to D2. The increase in demand results in a larger quantity being purchased at the same Price [P1].. [Where Y = income] At a price of P1 , the quantity demanded given the demand D is Q1. Dis the demand function when the income is Y1 . Due to increase in income, For a “normal good” an increase in income to Y2will “shift” the demand to the right. This is an increase in demand to D2. % D Y > 0; % D Q> 0; therefore, ey >0 [it is positive] Q1 Q2 .

  30. % D Qx % D Y P decreases demand P1 D1 D2 Q/ut A decrease in income is associated with a decrease in the demand for a normal good. eyº For a decrease in income [-D Y], the demand decreases; i.e. shifts to the left, At income Y1, the demand D1 represents the relationship between P and Q. At a price [P1] the quantity [Q1] is demanded. at the price [P1 ], a smaller Q2 will be purchased. A decrease in income, % DY < 0 [negative]; % DQ < 0 [negative]; so, ep > 0 [ positive] For either an increase or decrease in income the ep is positive. A positive relationship [positive correlation] between D Y and D Q is evidence of a normal good. Q1 Q2

  31. - % D Qx +% D Qx % D Qx + ey eyº + ey % D Y + % D Y - % D Y % D Qx ey º % D Y 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. A decrease in income is associated with a decrease in the demand function. For both increases and decreases in income, ey is positive The greater the value of ey, the more responsive buyers are to a change in their incomes. When the value of ey is greater than 1, it is called a “superior good.” The |% D Qx| is greater than the |% D Y|. Buyers are very responsive to changes in income. Sometimes “superior goods” are called “luxury goods.” . .

  32. Income Elasticity (Normal Goods) Income Elasticity (Inferior Goods)

  33. -%DQx % D Qx eyº -ey = % D Y +DY P decreases demand P1 D1 -%DQx D2 Q/ut There is another classification of goods where changes in income shift the demand function in the “opposite” direction. An increase in income [+DY] reduces demand. An increase in income reduces the amount that individuals are willing to buy at each price of the good. Income elasticity is negative: - ey The greater the absolute value of - ey,the more responsive buyers are to changes in income Q1 Q2 . .

  34. +%DQx % D Qx ey º - ey P % D Y -DY P1 D2 D1 +%DQx Q/ut Decreases in income increase the demand for inferior goods. A decrease in income [-DY] increases demand. A decrease in income [-D 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 ey, the more responsive buyers are to changes in income Q1 Q2 . .

  35. Income Elasticity Income elasticity [ey] is a measure of the effect of an income change on demand. [Can be calculated as point or arc.] ey > 0, [positive] is a normal or superior good an increase in income increases demand, a decrease in income decreases demand. 0 < ey < 1 is a normal good 1 < ey is a superior good ey < 0, [negative] is an inferior good Economics 205Principles of Microeconomics

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

  37. Income Elasticity (Normal Goods) Cross-price elasticity of demand, [exy] [substitutes]

  38. increase demand 2 1.50 Db’ -DQp When the price of mutton increases, it will tend to increase the demand for beef. People will substitute beef, which is relatively cheaper, for mutton, which is relatively more expensive. When beef is $2, Qb beef is purchased. When mutton is $1.50, Qm is purchased. Pb Pm [price of mutton] at Pb = $2 more beef will be bought to substitute for the smaller quantity of mutton. price of mutton increases [price of beef] The quantity demanded of mutton decreases. 2 for an increase in Pmutton, demand for beef increases Db Dp beef/ut Qb’ Qm’ Qb Qm mutton/ut .

  39. Cross-price elasticity In the case of beef and mutton the ebm is not the same as emb ebm is the % change in the demand for beef with respect to a % change in the price of mutton emb is the % change in the demand for mutton with respect to a % change in the price of beef beef may not be a good substitute for mutton mutton may not be a good substitute for beef

  40. +DQb %D Q of beef +ebm positive ebp = %DP of mutton + DPm - DQb %D Q of beef +ebm positive ebp = %DP of mutton -DPm The cross elasticity of the demand for beef with respect to the price of mutton, ebeef-mutton or ebm can be calculated: An increase in the price of mutton, “causes” an increase in the demand for beef. cross elasticity is positive A decrease in the price of mutton, “causes” a decrease in the demand for beef. If goods are substitutes, exy will be positive. The greater the coefficient, the more likely they are good substitutes.

  41. Income Elasticity (Normal Goods) Cross-price elasticity of demand, [exy] [Compliments]

  42. increase demand -DPc Po Dc’ Q2 + DQb - ebc negative %D Q of b ebc = - DPc %DP of c as more crayons are purchased, the demand for colour books increases. Pc Pc a decrease in the price of crayons, At the same price a larger quantity will be bought P1 $3 Dp Dc crayons colour books Q1 2500 2000 + DQb increases the quantity demanded of crayons for compliments, the cross elasticity is negative for price increase or decrease.

  43. Cross-Price Elasticity exy > 0[positive], suggests substitutes, the higher the coefficient the better the substitute exy < 0[negative], suggests the goods are compliments, the greater the absolute value the more complimentary the goods are exy = 0, suggests the goods are not related Economics 205Principles of Microeconomics

  44. Income Elasticity (Normal Goods) Elasticity of Supply

  45. 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 [ep] is defined: Economics 205Principles of Microeconomics

  46. %DQsupplied es = %DP P supply Q /ut Given a supply function, at a price [P1], Q1 is produced and offered for sale. a larger quantity, Q2, will be produced and offered for sale. At a higher price [P2], P2 The increase in price [ DP ], induces a larger quantity goods [ DQ]for sale. +DP P1 The more responsive sellers are to DP, the greater the absolute value of es. +DQ [The supply function is “flatter”ormore elastic] Q1 Q2

  47. P Si as supply approaches horizontal es approaches infinity Se Q /ut The supply function is a model of sellers behavior. a perfectly inelastic supply, es = 0 Sellers behavior is influenced by: 1. technology 2. prices of inputs a perfectly elastic supply [es is undefined.] 3. time for adjustment market period short run long run very long run 4. expectations 5. anything that influences costs of production taxes regulations, . . .

  48. Income Elasticity (Normal Goods) • Reference: Principles of Economics, 6/e by Karl Cas, Ray Fair • Slides prepared by: Fernando Quijano and YvonnQuijano

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