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1 ELASTICITY n Principles of Microeconomic Theory, ECO 284 n John Eastwood n CBA 247 n 523-7353 n e-mail address: John.Eastwood@nau.edu

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2 Learning Objectives n Define and calculate the price elasticity of demand n Explain what determines the price elasticity of demand n Use the price elasticity to determine whether a price change will increase or decrease total revenue

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3 Learning Objectives (cont.) n Define, calculate and interpret the income elasticity of demand n Define, calculate and interpret the cross- price elasticity of demand n Define and calculate the elasticity of supply n Use elasticities to analyze tax incidence.

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4 Learning Objectives n Define and calculate the price elasticity of demand n Explain what determines the price elasticity of demand n Use the price elasticity to determine whether a price change will increase or decrease total revenue

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5 Elasticity n Elasticity measures the response of one variable to changes in some other variable. n Civil Engineers need to know the elasticity of construction materials. n Economists need to know the elasticity of quantities demanded (and supplied).

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6 Elasticity of Demand n How does a firm go about determining the price at which they should sell their product in order to maximize profit? – Profit = total revenue – total cost = TR - TC – Total Revenue = Price Quantity =PQ n How does the government determine the tax rate that will maximize tax revenue?

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7 Price Elasticity of Demand, e d e d measures the responsiveness of quantity demanded of a product to a change in its own price, ceteris paribus. e d = (percentage change in Q d ) divided by (the percentage change in the P x )

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8 Example n Assume that the price of crude oil has increased by 100%, and that the quantity demanded has fallen by 10% e d = -10% / 100% = -0.1 n For every 1% increase in price, the quantity demanded fell by 0.1%

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9 Computing Elasticity Using the “Arc Formula” n where P 1 represents the first price, P 2 the second price, and Q 1 and Q 2 are the respective quantities demanded. n Elasticity is dimensionless (units divide out).

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10 Arc Formula Notation n Some people prefer to write delta for change, and “overbar” for average.

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11 Calculating Elasticity n The changes in price and quantity are expressed as percentages of the average price and average quantity. – Avoids having two values for the price elasticity of demand n e d is negative; its sign is ignored

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12 Calculating the Elasticity of Demand Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa Original point

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13 Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa Original point New point Calculating the Elasticity of Demand

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14 Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa = $20 = 8 Original point New point Calculating the Elasticity of Demand

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15 Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa Original point New point P ave = $400 = $20 = 8

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16 Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa Original point New point P ave = $400 Q ave = 40 = $20 = 8 Calculating the Elasticity of Demand e d = ?

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17 Quantity (millions of chips per year) Price (dollars per chip) 36 40 44 390 400 410 DaDa Original point New point P ave = $400 Q ave = 40 = $20 = 8 Calculating the Elasticity of Demand e d = 20/5 = 4

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18 Example -- Crude Oil n Assume P 1 = $15/bbl, Q 1 = 105 bbl/day, and that P 2 = $25/bbl, Q 2 = 95 bbl/day Calculate e d using this formula:

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19 Answer: n For every 1% increase in price, Qd fell 0.2%.

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20 Elasticity and Slope e d and slope are inversely related.

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21 Discussing e d Note that e d is always negative (or zero) because of the law of demand. However, when discussing the value of e d, economists almost always use the absolute value. Using | e d |, a larger value means greater elasticity.

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22 Elastic Demand, | e d |>1 n If the percentage change in quantity demanded is greater than the percentage change in price, demand is said to be price elastic. n The demand for luxury goods tends to be price elastic. n Examples – see page 99 of McEachern.

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23 Inelastic Demand, | e d |< 1 n If the percentage change in quantity demanded is smaller than the percentage change in price, demand is said to be price inelastic. n The demand for necessities tends to be price inelastic.

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24 Perfectly Elastic D, e d = infinity n If quantity demanded drops to zero in response to any price increase, demand is said to be perfectly elastic. n This corresponds to a horizontal demand curve. n Sounds unlikely, doesn’t it? n Example: Demand for a small country’s exports

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25 Inelastic and Elastic Demand 6 12 Price Quantity D3D3 Elasticity = Perfectly Elastic

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26 Perfectly Inelastic D, e d =0 n If quantity demanded is completely unresponsive to a change in price, demand is said to be perfectly inelastic. n This corresponds to a vertical demand curve. n Can you think of a vertical demand curve?

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27 Inelastic and Elastic Demand 6 12 Price Quantity D1D1 Elasticity = 0 Perfectly Inelastic

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28 Unit Elastic D, | e d |= 1 n If the percentage change in quantity just equals the percentage change in price, demand is said to be unit elastic. n While there are many goods that could be unit elastic, there aren’t any we can identify without statistical evidence. n Example:

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29 Inelastic and Elastic Demand 6 12 Price Quantity D2D2 1 2 3 Elasticity = 1 Unit Elasticity

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30 e d and Total Revenue (TR) n Note that TR = P times Q = PQ. n Will a change in price raise or lower total revenue? n It all depends on the price elasticity of demand!

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31 When Demand is Elastic, P and TR vary inversely. Since | e d | > 1, the percentage change in Qd is greater than the percentage change in P. n If P rises by, say, 1%, Qd will fall by more than 1%. n Therefore, if price is increased, total revenue will decrease. n If price is reduced, then TR will rise.

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32 When Demand is Inelastic, P and TR vary directly. Since | e d | < 1, the percentage change in Qd is smaller than the percentage change in P. n If P rises by, say, 1%, Qd will fall by less than 1%. n Therefore, if price is increased, total revenue will increase. n If price is reduced, then TR will fall.

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33 When Demand is Unit Elastic, TR does not change. Since | e d | = 1, the percentage change in Qd equals the percentage change in P. n If P rises by, say, 1%, Qd will fall by exactly 1%. n Therefore, if price is increased, total revenue will stay the same. n If price is reduced, TR will not change.

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34 Some Real-World Price Elasticities of Demand Good or ServiceElasticity Elastic Demand Metals1.52 Electrical engineering products1.30 Mechanical engineering products1.30 Furniture1.26 Motor vehicles1.14 Instrument engineering products1.10 Professional services1.09 Transportation services1.03 Inelastic Demand Gas, electricity, and water0.92 Oil0.91 Chemicals0.89 Beverages (all types)0.78 Clothing0.64 Tobacco0.61 Banking and insurance services0.56 Housing services0.55 Agricultural and fish products0.42 Books, magazines, and newspapers0.34 Food0.12

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35 Example: Demand for Oil and Total Revenue n Assume demand is p = 60 - q n TR = price x quantity =PQ n Substituting 60-q for p gives, TR=(60-q)q n Multiply through by q to get an equation for TR, TR = 60q - q 2 n TR will graph as a parabola. n Let’s calculate TR and graph it with D.

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36 Computing Total Revenue

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37 Marginal Revenue, MR MR = Change in TR divided by Change in Quantity. Let Change. TR / Q = TR 2 -TR 1 )/ Q 2 -Q 1 ) (easier for many students). n One could substitute: TR = 60Q - Q 2 TR / Q = 60Q - Q 2 )/ Q = 60-2Q (to be precise).

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38 Demand (P), Total Revenue (TR), and Marginal Revenue (MR)

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39 Total Revenue as an Area

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40 Linear Demand and Point Elasticity e d can be illustrated with geometry. n With a linear D, the slope is constant. n We don’t need an arc to get the slope. n Elasticity is inversely related to slope.

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41 e d and Linear Demand

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42 e d Using Line Segments The formula for e d may be rewritten in terms of the length of line segments. n O is the origin, T is the x-intercept, and M is a point between O and T.

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43 Elasticity at the Midpoint | e d | =MT/OM for any linear demand curve. n If M is the middle, then MT=OM. e d = | -1| = 1 n Unit Elastic at the midpoint.

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44 Elasticity at Higher Prices If M is left of the middle, then MT>OM. | e d | =MT/OM. | e d | > 1 Demand is elastic at higher prices.

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45 Elasticity at Lower Prices If M is right of the middle, then MT

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46 Two Extremes At the point where the demand curve intercepts the vertical axis, e d is infinite or perfectly elastic. At the point where the demand curve intercepts the horizontal axis, e d = 0, that is, demand is perfectly inelastic.

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47 Determinants of e d n Number of substitutes – quality – availability n Budget proportion n Time – to respond – to consume

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48 Other Elasticity Concepts Income Elasticity of Demand, e y Cross Price Elasticity of Demand, e x,z Price Elasticity of Supply, e s

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49 Income Elasticity of Demand, e y e y measures the change in demand for a good (X) in response to a change in income (Y), ceteris paribus. If e y > 0, X is a normal good. If e y < 0, X is an inferior good.

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50 Income Elasticity of Demand, e y If e y > 1, X is a luxury (income elastic ). If e y < 1, X is a necessity (inc. inelastic).

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51 Computing Income Elasticity n With Q 1 and Q 2, find the change in quantity and the average quantity. n Given Y 1 and Y 2, find the change in income and the average income.

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52 Example Computations n Median annual family income rose from $39,000 to $41,000 per year. n The demand for electricity rose from 79,000 GWh to 81,000 GWh. n Normal or inferior?

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53 Answer: n D electricity grew as consumers’ incomes rose. n Electricity is a normal good.

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54 Cross Price Elasticity of D, e x,z e x,z measures the responsiveness of the demand for one good to a change in the price of another good, ceteris paribus. e x,z = (% change in demand for X ) divided by (% change in P Z )

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55 Using Cross Price Elasticity e x,z > 0 tells us the goods X and Z are substitutes. e x,z < 0 tells us the goods X and Z are complements. e x,z = 0 tells us the goods X and Z are unrelated.

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56 Computing Cross-Price Elasticity n With Q X1 and Q X2, find the change in quantity and the average quantity. n Given P Z1 and P Z2, find the change in price and the average price.

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57 Example Computations n The price of gasoline rose from $.75 to $1.25/gal. n The demand for Subarus rose from 9/day to 11/day. n The demand for Cadillacs fell by 10%.

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58 Subaru Example n Let X = Subarus, and Z = gasoline. Find e x,z. n Are Subarus and gasoline related goods? n If so, are they complements or substitutes?

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59 Answer: D Subarus grew when the price of gas rose. Note that Q X measures the shift in D, c.p. n Subarus are substitutes for gasoline.

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60 Cadillac Example n Let X = Cadillacs, and Z = gasoline. Find e x,z. n Are Cadillacs and gasoline related goods? n If so, are they complements or substitutes?

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61 Answer: D Cadillacs fell when the price of gas rose. Note that Q X measures the shift in D, c. p. n Cadillacs and gasoline are complements

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62 Price Elasticity of Supply, e s e s measures the responsiveness of quantity supplied to a change in the good’s price.

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63 Example Computations n The price of corn fell from $3/bu. to $1/bu. n The quantity supplied of corn fell from 101,000 bu to 99,000 bu. n Compute the price elasticity of supply.

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64 Answer: n The quantity supplied fell by only 2% as the price fell by 100%. n The short-run supply of corn is inelastic.

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65 Linear Supply and e s n First draw a positively-sloped straight line from the origin. Label this supply “curve” S u n Next draw a parallel supply curve with a negative y-intercept. Label this one S i n Now draw a parallel supply curve with a positive y-intercept. Label this one S e

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66 e s Along a Supply Curve

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67 e s Using Line Segments Rewrite the formula for e s in terms of point elasticity. Note the relationship with the slope. Use length of line segments to get e s

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68 A Supply Curve with e s = 1 Find e s at point u: n Note that S u is unit elastic at any point.

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69 A Supply Curve with e s <1 Find e s at point i. n S i is inelastic at any point.

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70 Supply Curves May Not Touch the x-axis or y-axis. n S i is unrealistic. n It implies that the firm would supply positive quantities of its product at a price of zero (or at a negative price)! n As we will learn later, a firm will shut down if the price of its product falls too low. Thus, we should draw supply curves that begin at a positive (Q, P).

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71 A Supply Curve with e s >1 Find e s at point e. S e is elastic at any point. As y gets larger, e s gets larger. As P gets larger, e s approaches 1.

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72 Perfectly Elastic Supply e s is infinite when the slope is zero. n Cost per unit is constant. n Example: One consumer may buy as many apples as s/he wishes at the going price.

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73 Perfectly Inelastic Supply e s is zero when the slope is infinite. n Price has no effect on the quantity supplied. n e.g.: Once the crop is ready to harvest, the farmer will do so as long as s/he can earn at least the cost of harvesting it. P min P Q0 S market period D Qs

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74 Determinants of e s : n The degree of substitutability of resources among different productive activities. n Time -- Given more time, producers are able to make more adjustments to their production processes in response to a given change in price.

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75 Elasticity and the Burden of a Tax n The economic incidence of taxation falls on the persons who suffer reduced purchasing power because of the tax. n The legal incidence falls on the persons who are required by law to pay the tax to the government.

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76 Tax Burden n Demand for Tonic: P = $42 - 3Q Let Supply be: P = -3 + 2Q. ( e s <1.) n Solve for equilibrium quantity: – -3 + 2Q e = 42 - 3Q e – 5Q e = 45 – Q e = 9 pints per day (| e d | 7.) n Solve for equilibrium price: – P e = 42 - 3Q e = 42 - 27 = $15 per pint.

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77 Legal incidence on seller: n Add the tax to Supply: P= -3+2Q+10=7+2Q n Solve for new quantity: – 7 + 2Q n = 42 - 3Q n e s >1 – 5Q n = 35 – Q n = 7 pints per day (| e d |=1 if Q=7.) n Solve for gross & net price: – P gross = 42 - 3Q n = 42 - 21 = $21 per pint. – P net = - 3 + 2Q n = -3 + 14 = $11 per pint.

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78 Specific Tax on the Seller

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79 Legal incidence on buyer: n Subtract tax from Demand: P= 42-3Q-10 n Solve for new quantity: – -3 + 2Q n = 32 - 3Q n – 5Q n = 35 – Q n = 7 pints per week (| e d |=1 if Q=7.) n Solve for gross & net price: – P gross = 42 - 3Q n = 42 - 21 = $21 per pint. – P net = 32 - 3Q n = 32 - 21 = $11 per pint.

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80 Specific Tax on the Buyer

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81 Compute|e d | and e s n Before the tax P e = $15/pint and Q e = 9 pints/week The slope of D = -3, while the slope of S = 2.

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82 Now Who Pays the Tax? n Consumers now pay $21 per pint – $6 / pint more than before the tax n Vendors now receive $21 per pint, – but must pay the $10 per pint tax. – Sellers keep only $11 per pint. – $4 / pint less than before n Buyers respond less to a change in price, so they pay more of the tax.

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