Chapter 4. Elasticity

Transcription

1 Chapter 4 Elasticity

2 -comparative static exercises in the supply and demand model give us the direction of changes in equilibrium prices and quantities -sometimes we want to know more we want to know about the magnitudes of these changes -ie. how much of a market adjustment to a new equilibrium comes through price adjustment and how much comes through quantity adjustment? -when only one of the curves shifts the move to a new equilibrium is a movement along either the D curve or the S curve -so we start off by looking at measures of relative responsiveness of price and quantity along either D or S

3 rice Elasticity of Demand (η in your text we will use E D ) -demand is said to be: elastic when quantity demanded is very responsive to changes in the product s price inelastic when quantity demanded is unresponsive to changes in its price -Figure 4-1 same decrease in supply leads to very different changes in price and quantity -elasticity is related to the slope of the demand curve, but it is not exactly the same

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5 The Measurement of rice Elasticity E D = percentage change in quantity demanded percentage change in price E D = % D % E D = ΔD/D Δ/ -why do we include the minus sign in the formula for E D (or take the absolute value of the measure)? -since demand curves have negative slopes, price and quantity demanded move in opposite directions along the demand curve -the changes in price and quantity have opposite signs, so demand elasticity would return a negative number would lead to confusion when speaking about higher or lower elasticity -convert the measure to a positive number

6 -another important point to consider -since we are dealing in percentage changes, elasticity relates the absolute change in and to some base levels of and. -seems simple but raises an important issue -consider the two points A and B in the diagram below. A A B B D A B -if we use the starting points for any move as our base levels we get contradictory measures of elasticity over the same segment of the demand curve depending on which direction we are going.

7 EXAMLE: Suppose A = 100, A = 25 and =50, = B BB 75. Elasticity (A B) using A as the base: Elasticity (B A) using B as the base:

8 Average Arc (or mid-point) Method -to avoid this problem we use average values of and when computing the percentage changes -referred to as the average arc or mid-point method because we are using the average or midpoint in calculating the percentages -in general, the formula for elasticity is given by: B A B A B A B A D B A B A B A B A B A B A B A B A D E E + + = + + = + + = ) ( ) ( ) ( ) ( ) ( ) ( EXAMLE: Using the values from above we obtain:

9 oint Method -if you have a linear equation and wish to calculate elasticity at a certain point E E D D Δ base = Δ base run = rise 1 = slope -base and are the point you are interested in EXAMLE: -in our example, if demand was linear, its equation would be: = 125 or = 125 -so the slope (rise/run) = -1 -calculating the elasticity at our previous midpoint ( = 50, = 75):

10 Calculus Method -if you have a specific demand function (linear or not) and wish to calculate elasticity at a certain point d E D = d -or if you have a demand function with many independent variables E D = Summing Up -you can always use the average arc method to calculate elasticity -if you only have two points just apply formula -if you have an equation pick points above and below the point you are interested in (such that the averages are the point you are interested in and apply the formula

11 Range of Values for E D Inelastic: 0 < E D < 1 -if the percentage change in quantity demanded is less than the percentage change in price, then demand is inelastic Unit Elastic: E D = 1 -if the percentage change in quantity demanded is equal to the percentage change in price, then demand is unit elastic Elastic: E D > 1 -if the percentage change in quantity demanded is greater than the percentage change in price, then demand is elastic

12 What Determines the Elasticity of Demand? Demand is elastic when the product has close substitutes Demand is inelastic when the product has no close substitutes -the availability of substitutes hinges on several factors: The longer the time interval considered, the more elastic is demand. The less a good is a necessity, the more elastic is demand The more specifically a good is defined, the more elastic is its demand

13 rice Elasticity of Demand E D E D = % D (expressed as a positive number) % Special Cases: Constant E D Demand Curves: D1 b D2 D3 a

14 D 1 : D = a (where a > 0 is some constant) D 2 : = b (where b > 0 is some constant) D 3 : D = k/ (where k > 0 is some constant)

15 Downward Sloping Linear Demand Curves: D = c d (where c, d > 0 are constants) = c d 1 d D Δ E D = = ( d) = d Δ c/d midpoint D c

16 Intuition behind this result: -as we have discussed, demand is more elastic for goods with available substitutes -people tend to substitute from high-price goods to low-price goods when they can -consumers have more opportunities to substitute towards lower price goods when the price of the good is high -as the price of a good falls, the number of similar goods that have lower prices falls

17 Elasticity and Total Expenditure Total Expenditure by Consumers (TE) = Total Revenues going to Firms (TR) = E D < 1 % < % -price effect dominates in total revenue E D > 1 % > % -quantity effect dominates in total revenue E D = 1 % = % -effects offset so total revenue is unchanged

18 Back to E D = 1 Everywhere: -if E D = 1 then total revenue is constant along the demand curve -so = k (where k is some constant), or: D = k/ (a rectangular hyperbola) D3

19 Back to Downward Sloping Linear Demand: c/d midpoint D c TR =

20 rice Elasticity of Supply: (η S in your text we will use E S ) E S = percentage change in quantity supplied percentage change in price or E S = % S % or E D = ΔS/S Δ/ -since supply curves have positive slopes, price and quantity demanded move in the same direction along the supply curve -no need to turn it into a positive number -calculate in the same way as E D only along the supply curve - i.e. use the average arc (mid-point) method -or if you have an equation, use the point method

21 Determinants of Elasticity of Supply -the elasticity of supply depends on how easy it is for producers to switch between the production of different products -this depends on: $the technical ease of substitution in production $the nature of production costs -clearly again we would expect a difference in $short run versus long run -in the short run existing firms can hire more of only some inputs to increase production -in the long run can expand their use of all factors (new plant, etc.) -also in the long run, higher prices may bring entry

22 SSR SLR Range of Values for E S Inelastic: 0 < E S < 1 -if the percentage change in quantity supplied is less than the percentage change in price, then supply is inelastic Elastic: E S > 1 -if the percentage change in quantity supplied is greater than the percentage change in price, then supply is elastic

23 Special Cases: S1 b S2 a S 1 : S = a (where a > 0 is some constant) S 2 : = b (where b > 0 is some constant)

24 Other Demand Elasticities: -the following elasticities are associated with changes in variables other than the price of the good in question -therefore we are dealing with shifts of the demand curve rather than movements along it D D

25 Income Elasticity of Demand (η Y in your text we will use E I ) E I = percentage change in quantity demanded percentage change in income or E D = % D % I Range of Values for E I E I < 0 inferior goods E I > 0 normal goods 0 < E I < 1 -income-inelastic normal goods E I > 1 -income-elastic normal goods

26 Cross rice Elasticity of Demand (η XY in your text we will use E XY ) E XY = % change in quantity demanded of good X % change in price of good Y Range of Values for E XY E XY < 0 complements E XY > 0 substitutes E XY = 0 unrelated goods

27 Important Example Where Elasticity Matters Tax Incidence Who bears the burden of a tax? Short Answer: -doesn t matter who the government says owes the tax, or is responsible for collecting the tax on a transaction -GST vs sales tax on private used car sales -what matters is how the tax affects the market and its participants How much more do buyers pay because of the tax? How much less do sellers receive because of the tax?

28 Basic Analytics: -suppose the government levies (institutes) a tax of $t per unit on sales of a good -puts a wedge between what consumers pay and what sellers ultimately receive -sellers pay the gov t $t for every unit they sell -there are now 3 prices to consider * before-tax consumer and producer price T after-tax consumer price T t after-tax producer price -what is the effect of the tax on sellers? -since sellers must give the gov t $t per unit sold, then they must receive $t more from consumers to be willing to provide the same quantity as before the tax -this is true for any quantity -supply curve shifts up by t (the other way to think about this is that for any given price paid by consumers, since sellers keep less of it, they are willing to supply fewer units)

29 S * D * Consumers pay roducers pay -on a per unit basis Total burden on a per unit basis? -key insight is that the burden is shared between buyers and sellers Upon what does this tax burden sharing depend?

30 Taxes and E D : -the more elastic is demand, the less of the burden is borne by consumers -therefore the more of the burden is borne by producers t ST S * DE DI * -intuition is that, with an elastic demand, sellers are less able to pass on the burden to buyers in the form of higher prices

31 But E S Matters Too: -we will show this by considering the special cases of supply elasticity E S = perfectly elastic supply curve * t ST S D * Consumers pay: roducers pay: -intuition is that, with perfectly elastic supply, sellers cannot be forced to bear any of the burden

32 E S = 0 perfectly inelastic supply curve S = ST * D * roducers pay: Consumers pay: -intuition is that, with perfectly inelastic supply, sellers cannot avoid any of the burden