ALGEBRAIC REPRESENTATION

Transcription

1 Elasticity - 1

2 ALGEBRAIC REPRESENTATION Demand curve: QD = a b P Supply curve: QS = c + d P At equilibrium, QD = QS Solving for the values of P and Q will give the following answers: Equilibrium price: P0 = (a-c)/(b+d) Equilibrium quantity: Q0 = (ad + bc)/(b+d)

3 BEER The demand curve for beer is QD = 500 5P where QD is the quantity demanded of beer (in millions of barrels per year) and P is the price (in dollars per barrel). If the supply curve for beer is a vertical line QS = 400 million barrels of beer per year, what is the equilibrium price of a barrel of beer?

4 P S BEER At equilibrium, QD = QS, or 500 5P = 400. Solving for P, the equilibrium price is $ D Q

5 BUTTER The supply curve for butter is QS = P, where QS is quantity supplied (in millions of pounds per year) and P is the price of butter (in dollars per pound). If the demand curve for butter is a vertical line at QD = 106 millions of pounds per year), and the government imposes a price floor of $1 per pound of butter, will there be an excess supply or excess demand of butter, and how big will it be? If the government s floor price is set at $3, will there be an excess supply or excess demand for butter, and how big will it be? Source: Mansfield, Microeconomic Problems

6 At equilibrium, the price should be $2. When government imposes a price floor of $1, there will be no shortage or surplus. When government sets a price floor of $3, QS = P = 109. Since QD = 106, there will be a surplus of 3 million pounds per year. BUTTER P QS = P 106 = P P = 2 D S FLOOR FLOOR Q

7 Price of of Chicken (in centavos) pesos) HOW RESPONSIVE IS Q TO P? P = = 50 = 5000 Q = = Slope = P/ Q = - 50/80 = Slope = P/ Q = /80 = Q/ P = Q/ P = The Demand Curve for Chicken P Q Question: If there is another demand curve where Q/ P = , is Q less responsive to P? Quantity of Chicken (in kilos) We can not use the slope as a measure of responsiveness because it is affected by units of measurement.

8 PRICE ELASTICITY OF DEMAND Price elasticity of demand: measures the responsiveness of changes in quantity demanded to changes in price Elasticity is defined as the percentage change in quantity demanded divided by the percentage change in price ɛp = % QD/ % P How to compute for elasticity (Point Method) A B Point P Q A B % QD = (160-80)/80 = 1 % P = ( )/150 = - 1/3 ɛp = - 3.0

9 CATEGORIES OF ELASTICITIES Price elasticity: ɛp = % Q/% P Interpretation: ɛp > 1: Elastic (a 1% change in price will lead to more than 1% change in quantity demanded) ɛp < 1: Inelastic (a 1% change in price will lead to less than 1% change in quantity demanded) ɛp = 1: Unitary (a 1% change in price will lead to an equivalent 1% change in quantity demanded) ɛp = : Infinitely elastic (quantity demanded is infinite for every price change) ɛp = 0: Perfectly inelastic (a change in price will not affect quantity demanded)

10 COMPUTING FOR ELASTICITY 150 A Point P Q A B Using point A as denominator: % QD = (160-80)/80 = 1 % P = ( )/150 = - 1/3 ɛp = B For the price level, the midpoint between 150 and 100 is 125. Using point B as denominator: % QD = (160-80)/160 = 1/2 % P = ( )/100 = - 1/2 ɛp = - 1 Solution: Do not use A or B as the denominator. Use the midpoint between A and B. For quantity demanded, the midpoint between 80 and 160 is 120. Using the midpoints: % QD = (160-80)/120 = 0.67 % P = ( )/125 = ɛp =

11 COMPUTING FOR ELASTICITY Point elasticity: value of the elasticity computed using the point method Arc elasticity: value of the elasticity computed using the midpoint method This is the preferred measure of responsiveness of quantity demanded to price: not affected by units, not affected by base Formula for Arc Elasticity ɛp = (P1+P2/Q1+Q2)(Q2-Q1/P2-P1) ɛp = (P1+P2/Q1+Q2)( Q/ P)

12 GASOLINE PRICES Suppose the price of gasoline was reduced from P50/liter to P48/liter. If the price elasticity of demand for gasoline is -1.5, by how much will the quantity demanded of gasoline increase (in %)? The %-age change in gasoline prices is computed as follows: % P = (- 2/49)*100 = (midpoint method) Since ɛp = % Q/% P 1.5 = % Q/ Hence, the quantity demanded of gasoline will increase by 6.12%.

13 GRAPHICAL REPRESENTATION Perfectly inelastic demand: An increase in price leaves the quantity demanded unchanged Infinitely elastic demand: Quantity demanded is infinite at a given price level Above that price level, quantity demanded is zero At and below that price level, quantity demanded is infinite Perfectly Inelastic Infinitely elastic

14 GRAPHICAL REPRESENTATION Perfectly inelastic demand: An increase in price leaves the quantity demanded unchanged Infinitely elastic demand: Quantity demanded is infinite at a given price level Above that price level, quantity demanded is zero At and below that price level, quantity demanded is infinite Unitary Inelastic Elastic

15 SLOPE AND ELASTICITY Is this demand curve elastic, inelastic, or unitary? A B C P Q P A B The slope of this line is C Q Infinite elasticity At point A, elasticity is (elastic). At point B, elasticity is -1.0 (unitary). At point C, elasticity is (inelastic). Zero elasticity The slope of a linear demand curve is constant. Its elasticity changes depending on the location on the curve.

16 DETERMINANTS OF ELASTICITY Availability of substitutes: availability of substitutes tends to make demand more elastic (more substitutes, more elastic) Relative importance: When a product represents a relatively small part of our total budget, we are not likely to respond much to price changes (less important, more inelastic) Time: In the long-run, demand is more elastic (longer time period, more elastic) Over time, households are able to adjust consumption patterns, look for substitutes