# Lecture 4 Elasticity. Readings: Chapter 4 Elasticity 4. Consideration of elasticity Our model tells us that when demand increases both price and quantity.

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Lecture 4 Elasticity

Elasticity 4. Consideration of elasticity Our model tells us that when demand increases both price and quantity will increase. It does not tell us whether the price or quantity increase will be relatively big or small. To make these sorts of predictions we need information on the price sensitivity of the demand and supply relationships.

Elasticity Q: How should price sensitivity be measured? The Demand and Supply equations have slope parameters that measure price sensitivity. Recall: Q d = a - bP and Q s = c +dP b = ∆Q d / ∆P = (Q d 2 - Q d 1 ) / (P 2 - P 1 ) d = ∆Q s / ∆P = (Q s 2 - Q s 1 ) / (P 2 - P 1 )

Elasticity Problem: The slope parameters depend on the units used to measure price and quantity. If there is inflation, the slope parameter will change every year. Comparisons of price sensitivity will be meaningless. Comparisons of the slope parameters in different countries are meaningless because of different national currencies. Comparisons of the price sensitivity of different commodities will also be impossible because of the differing units used to measure different commodities.

Elasticity Solution: Elasticity provides a universal measure that is immune to inflation and is comparable across national borders and across different commodities. Q: What is elasticity? Elasticity = % Δ (dependent variable) % Δ (independent variable) It is a unit free measure because it is a ratio of %.

Elasticity Q: What are the important elasticities? We will use four: η d = │(%ΔQ d ) / (%ΔP)│ = Price Elasticity of Demand η s = (%ΔQ s ) / (%ΔP) = Price Elasticity of Supply η m = (%ΔQ d ) / (%ΔIncome) = Income Elasticity of D η xy = (%ΔQ x d ) / (%ΔP y ) = Cross-price Elasticity of D High elasticity  dependent variable highly responsive to changes in the independent variable Low elasticity  dependent variable unresponsive to changes in the independent variable

Elasticity The price elasticity of demand tells us the price sensitivity of the quantity demanded. P Q D Elastic Demand Q P D Inelastic Demand

Elasticity The price elasticity of supply tells the price sensitivity of the quantity supplied. P Q S Elastic Supply Q P S Inelastic Supply

Q: How do we use data to calculate the elasticity of demand? The arc elasticity of demand: Where: Elasticity

Example: Consider the demand for pop (D pop ) when P falls from \$1.50 to \$1.00 η d = │(∆Q d / Q average )/(∆P / P average )│ η d =│ 5 / 7.5 │ = │ +66.6% │ = │ -1.67 │= 1.67 │-0.5/1.25│ │ - 40% │

Elasticity This is an approximation of the elasticity on the region of the demand curve between P = \$1.50 and \$1.00. It is most accurate at the midpoint of this region.

Elasticity Q: What about the other elasticities? They have similar arc elasticity formulas:

Elasticity Q: How does knowledge of the elasticity of demand help us understand the market? Knowing the elasticity of demand we can: 1. Predict the relative movements of price and quantity to changes in supply. 2. Predict what will happen to industry revenue if price changes.

Elasticity Predicting the relative movements of P and Q. η d > 1 0<η d < 1

Elasticity Predicting the relative movements of P and Q. η d > 1 0<η d <1

Elasticity Predictions: Elastic (η d >1) Increasing Supply causes small decline in P and large increase in Q. Inelastic (η d <1) Increasing Supply causes large decline in P and small increase in Q. Elastic (η d > 1) Decreasing P causes increase in Industry Revenue. Inelastic (η d <1) Decreasing P causes decline in Industry Revenue. Exercise: If supply is elastic how will P and Q respond to demand changes? What if supply is inelastic?

Elasticity Q: Does a straight line demand curve have a constant elasticity? A straight-line demand curve has a constant slope, but elasticity declines with P. η d < 1 η d > 1 η d = 1 P Q

Elasticity Q: How is the slope of a straight line demand curve related to the elasticity? b = ∆Q / ∆P η d = │∆Q / Q avg │ = │(∆Q /∆P)(P avg /Q avg ) │ =b(P avg /Q avg ) │ ∆P / P avg │ This is an approximation of the elasticity on a region of the demand curve. At a particular point (Q,P) on the demand curve, the point elasticity of demand will be η d = b(P/Q)

Elasticity With a little thought, you can see why the mid-point has unit elasticity. ● η d = b (P/Q) = 1 P Q 2P 2Q

Elasticity Q: How is the straight-line demand curve related to revenue? Q Q P R Revenue: R = PQ η d = 1 η d > 1 η d < 1

Elasticity Q: Is there a point elasticity of supply equation? Yes. If the supply equation is Qs = c + dP then the point elasticity of supply is η s = d(P/Q). Supply: Q s = c + dP η s = d (P/Q) P Q

Elasticity Q: What about the income elasticity of demand? Recall: η m = ∆Q d / Q avg, ∆m / m avg If η m > 0 then the good is a normal good and a rise in income will cause the demand curve to shift right (demand increases). If η m < 0 then the good is an inferior good and a rise in income will cause the demand curve to shift left (demand declines).

Elasticity Q: What about the cross-price elasticity of demand? Recall: η xy = ∆Q d x / Q x,avg ∆P y / P y,avg If η xy > 0, then and increase in the price of y causes the quantity of x demanded to increase, and hence x and y are substitutes. If η xy < 0, then x and y are complements.