Concordia University Econ 201

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1 Concordia University Econ 01 Department of Economics Shih-tse (Fred) Lo NOTE 5: ELASTICITY * Motivation for Elasticity: Imagine that you are the CEO of a business. Assume that your goal is to maximize the total revenue of your firm. (This assumption is not common in economics Economists in general assume that firms are to maximize their profits. Here I use this revenue maximization assumption just to give you a sense why we care about elasticity.) Apparently, you have two options, either to raise the price of your product and sell a smaller number of your products, or to decrease the price and sell more units of your commodity. Which way should you choose? The answer indeed depends on the elasticity of demand for your product. Price Elasticity measures the responsiveness of the % change in quantity demanded (Q D ) (or quantity supplied (Q S )) relative to a % change in price (P), of the same good. Price Elasticity Formula Let E P represent the price elasticity coefficient. P 1 and P represent two different prices, and Q 1 and Q represent the quantities associated with those prices. E P % Q = % P Note: If the quantity used in the numerator is Q D, then this formula will calculate the price elasticity of demand. If the quantity used in the numerator is Q S, then this formula will calculate the price elasticity of supply. Q - Q 1 E P = Q + Q 1 P - P 1 P + P 1 Interpretation of Price Elasticity Coefficients The use of percentage changes enables us to compare the consumer (or producer) responsiveness to changes in the prices of different products. The absolute value of the percentage change allows us to determine how elastic the consumer (or producer) responsiveness is relative to the change in price. Note 5 1 of 6 Econ 01

2 Note: Price elasticities of demand will have a minus sign prior to conversion to absolute value because of the inverse relationship between quantity demanded and price. Price elasticities of supply will always be positive due to the direct relationship between quantity supplied and price. Economists sometimes avoid use of the minus sign by giving the price elasticity of demand as E D. Similarly the price elasticity of supply would be E S. 3 Elasticity Cases 1) Elastic the percentage change in quantity demanded (or supplied) will exceed the percentage change in price. That is, % D Q D > % D P and E P > 1 ) Unit Elastic the percentage change in quantity demanded (or supplied) is equal to the percentage change in price. That is, % D Q D = % D P and E P = 1 3) Inelastic the percentage change in quantity demanded (or supplied) is less than the percentage change in price. That is, % D Q D < % D P and E P < 1. Some Examples In our previous example of the movie market, calculate the price elasticity of demand for movies given your market demand in (a) from P = 6 to P = 5, and from P = 4 to P = 3. Is demand elastic, unit elastic, inelastic? Explain in detail. Elasticity Determinants 1) Substitutability the greater the availability of substitute goods, the greater the elasticity and visa versa. Depends how narrowly the product is defined, i.e. price elasticity of soft drinks < price elasticity of colas < price elasticity of Pepsi. ) Proportion of Income the higher the price of the good is relative to income, the greater the elasticity and visa versa. Price elasticity of homes > price elasticity for cappuccinos. 3) Degree of Need price elasticity of luxuries is greater than that of necessities. 4) Time over time adjustments are easier to make for a variety of reasons. Note 5 of 6 Econ 01

3 Graph 1: Elasticity Extremes Demand Perfectly Elastic Demand E P = (Compare with Relative Elasticity) Perfectly Inelastic Demand E P = 0 (Compare with Relative Inelasticity) Demand Price Elasticity and Total Revenue for an ordinary D-Curve, there are 3 cases to consider in the relationship between P and TR: 1) Elastic Demand when P falls and D is elastic, TR will rise and visa versa. E p > 1 As P fl, TR and visa versa ) Unit Elastic Demand when P falls or rises and D is unit elastic, TR will stay the same. E p = 1 As P fl or, TR stays the same 3) Inelastic Demand when P falls and D is inelastic, TR will fall and visa versa E p < 1 As P fl, TR fl and visa versa Note 5 3 of 6 Econ 01

4 Graph Demand Price Elasticity and Total Revenue Note 5 4 of 6 Econ 01

5 Graph 3: Elasticity Extremes Supply Perfectly Elastic Supply E P = (Compare with Relative Elasticity) Perfectly Inelastic Supply E P = 0 (Compare with Relative Inelasticity) Time is the key determinant of supply price elasticity. Note 5 5 of 6 Econ 01

6 Types of Elasticity Price Elasticity Income Elasticity Cross Elasticity % Q D E P = % P % Q D E I = % I % Q D X E X,Y = % P Y Q - Q 1 Q + Q 1 E P = P - P 1 P + P 1 Q - Q 1 Q + Q 1 E I = I - I 1 I + I 1 Q X - Q 1 X Q X + Q 1 X E X,Y = P Y - P 1 Y P Y + P 1 Y If E P is + Supply E P is - Demand E p = Perf. Inelas. = 0 E p = Perf. Elas. = E P > 1 : Elastic E P = 1 : Unit Elastic E P < 1 : Inelastic If E I is + Sup/Normal E I is - Inferior E I is 0 Neutral E I > 1 : Elastic E I = 1 : Unit Elastic E I < 1 : Inelastic If E X,Y is + Substitute E X,Y is - Complement E X,Y is 0 Unrelated E X,Y > 1 : Elastic E X,Y = 1 : Unit Elastic E X,Y < 1 : Inelastic Materials come from Anne Bresnock s lecture notes. Note 5 6 of 6 Econ 01

Elasticity. McGraw-Hill/Irwin. Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Elasticity. McGraw-Hill/Irwin. Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved. 04 Elasticity McGraw-Hill/Irwin Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved. LO1 4-2 Price Elasticity of Demand Measures buyers responsiveness to price changes Elastic demand