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Or, how I learned to love percentages

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Direction of Change versus Sensitivity A summary of the all of the determinants of demand and supply are given in their respective functions. These functions assist in distinguishing between a movement from a shift of a curve AND the direction of change for each of the determinants. To increase the explanatory power of the demand and supply model, and to make it more interesting, we need to not only know the direction of change but how much each of the determinants affects demand and supply. This concept of responsiveness is called elasticity.

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Measuring Responsiveness or Sensitivity The initial candidate for measuring sensitivity is the concept of slope. Slope tells us the change in the quantity demanded or demand from a change in one of its determinants (i.e. Q d /P in the case of prices) The problems with slope are: Slope is unit dependent. If the units in which the currency (dollars to pesos) or quantity changes (boxes of apples to individual apples) it will change the slope. For example, the change from dollars to pesos will decrease the slope. Slope gives no indication of the beginning point. It also doesnt tell us where we started (e.g. a stock goes up by a $1. A large increase if the purchases price was $1 a small increase if the purchase price was $1,000) Therefore, we use percentage changes. Percentages are not unit dependent. If the measure of quantity is changed from boxes to individual apples the percentage change will remain the same. Percentages always refer to a starting point. Since percentage are always taken from a starting point, the base, they better measure the extent of change. We will return to this point shortly when we calculate elasticities along a straight-line (constant slope) demand curve.

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Various Elasticities Ep = Price elasticity of demand = %change in quantity demanded/% change in price Ey = Income elasticity of demand = %change in demand/% change in income Ex =Cross-price elasticity of demand = %change in demand/% change in the price of a related good Or, any other elasticity is simply the %change in something/% change in something else

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An Intuitive Approach to Elasticity Since price elasticity of demand (Ep) is always negative (law of demand) we ignore the negative sign and take the absolute value of price elasticity. %Q d = Output Effect and %P = Price Effect E p > 1 or Elastic %Q d > %P a given %P creates a larger %Q d or Output Effect > Price Effect Quantity demanded is sensitive to price. If price falls slightly, quantity demanded will increase by a large amount, or vice versa. E p < 1 or Inelastic %Q d < %P a given %P creates a smaller %Q d or Output Effect < Price Effect Quantity demanded is not sensitive to price. If price falls significantly, quantity demanded will increase slightly, or vice versa. E p = 1 or Unit Elastic %Q d = %P a given %P creates an equal %Q d or Output Effect = Price Effect If price falls, quantity demanded will increase by the same relative amount, or vice versa. Note, in the above descriptions percentages are a easier and clearer way of explaining sensitivity.

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Using Elasticity: The Relationship between P, Q and TR As P the law of demand tells us that Q . What happens to TR is not clear (P x Q = TR ?) The increase in price, the price effect, increases TR, ceteris paribus, but the decrease in quantity demanded, the output effect, ceteris paribus, would increase would TR. So, change in TR hinge about the relative strength of the price and output effects. Elasticity provides the key because it tells us the size of the price and output effect. The strength of the price effect is measured by the %P and that of the output effect by the %Q d. For example, if the %P = 5% and the %Qd =10%, the output effect is larger that the price effect. So if P the Q will strong enough to cause TR . Second example, For example, if the %P = 10% and the %Qd =5%, the price effect is larger that the output effect. So, the P will be stronger than the Q and TR .

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Summary of P, Q and TR E p > 1 Responsive or elastic %Q d > %P or Output Effect > Price Effect - if P goes down (up) total revenue goes up (down) E p < 1 Not responsive or inelastic %Q d < %P Output Effect < Price Effect - if P goes down (up) total revenue goes down (up) E p = 1 unit elastic %Q d = %P Output Effect = Price Effect - if P goes down (up) total revenue stays the same

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Price and Output Effects So, far we have defined the output and price effects using percentage changes. The Price Elasticity is simply the ratio of the OE and the PE in percentage terms. We can also define the price and output effects in absolute or dollar terms. If P falls, Output Effect = Pnew x Q = Pnew x (Qnew-Qold) this is extra revenue you get from selling additional units at the new price. If P falls, Price Effect = P x Qold = (Pnew-Pold) x Qold this is the revenue you lose from selling the old units at a new lower price. If P increases: Output Effect = Pold x Q = Pold x (Qnew-Qold) Price Effect = P x Qnew = (Pnew-Pold) x Qnew Change in TR = OE +PE

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Figure 2 Total Revenue Copyright2003 Southwestern/Thomson Learning Demand Quantity Q P 0 Price P Q = $400 (revenue) $4 100

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Figure 2 Total Revenue Demand Quantity Q 0 Price $4 100 $3 120 P -$1 Q =100TR = -$100 $300 Q +20 P=$3 TR= $+60 Price Effect Output Effect

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The Mid-point Formula: Calculating Price Elasticity Economists, when calculating elasticity, using the midpoints between the new (P 1 and Q 1 ) and old (P 0 and Q 0 ) prices and quantities, rather than the old price and quantity that others typically use. E p = %Q d / %P = (Q 1 - Q 0 )/[(Q Q + Q 1 )/2] (P 1 - P 0 )/[(P 0 + P 1 )/2]

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Calculating Price Elasticity the Price Elasticity of Demand Demand is price elastic $5 4 Demand Quantity 100050 Price

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Linear Demand Curve:Elasticity

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E>1 E=1 E

Other Demand Elasticities Income Elasticity of Demand - Sign is important: Normal Good E Y >0 Inferior Good E Y 1 Income-elastic and a luxury good because as Y the % of Y spend on the good (TE/Y) E Y 0 (P R Q R Q ) Complement Ex

Elasticity and Tax Incidence A tax drives a wedge between the price the buyer pays and the seller receives. Before Tax: P e =P B =P S After Tax: P B >P S by the amount of the tax. Example: Per unit tax of $1. If the buyer pays $6 for one unit of the good, the seller receives $5 and $1 goes to the government in tax. P B MC to buyers Q D Tax Wedge P S MB to sellers Q S Taxes can be imposed on the buyer or the seller, but the government usually imposes them on the seller for ease of collection. Tax imposition determines who nominally pays the tax, but who really pays the tax depends on elasticities of demand and supply (and doesnt depend upon whether the buyers or the seller pays the tax!). Who really pays the tax, the tax incidence or burden, depends upon how buyers and sellers respond to price changes. If the buyers can respond relatively more to price changes more than suppliers, suppliers pay more of the tax. If the suppliers can respond relatively more than the buyers, then the buyers pay more of the tax. Remember the water fight example!

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Graphing Tax Incidence If the buyer pays the tax, a new demand curve is created to reflect the fact that sellers receive lower prices. If the seller pays the tax, a new supply curve is created to reflect the fact that buyers pay higher prices. In either case, the higher price to buyers causes buyers to decrease their quantity demanded and the sellers to decrease their quantity supplied. Thus both the buyers and the sellers will likely both pay part of the tax. The tax incidence or burden is related to how each responds to price changes or their price elastiticies. If E D >E S then buyers pay less of the tax and sellers more of the tax. If E D< E S then buyers pay more of the tax and sellers less of the tax. Note that the tax incidence or burden does NOT depend upon who pays the tax to the government!

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Extreme examples: Perfectly elastic demand Perfectly elastic supply Perfectly inelastic demand Perfectly inelastic supply Less extreme examples (e.g. the luxury tax)

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Applications Getting to Mr./Ms. Rich: Luxury Tax on Yachts Case study The payroll tax: Federal Insurance Contribution Act (FICA) for Social Security and Medicare