1 Demand and Supply: Elasticity Principles Microeconomics Professor Dalton ECON 202 – Spring 2013 Boise State University

2 Elasticity  Elasticity - measure of responsiveness  Measures how much a dependent variable changes due to a change in an independent variable  Elasticity = %Δ X / %Δ Y Elasticity can be computed for any two related variables

3 Elasticity Measures  Elasticities economists are interested in: a change in price on the quantity demanded a change in income on the demand function for a good a change in the price of a related good on the demand function for a good a change in the price on the quantity supplied

4 Price Elasticity of Demand  The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much.  The price elasticity of demand, ε, is a measure of that information  “If you change price by 5%, by what percent will the quantity purchased change?

5 ε  %  Q %  P At a point on a demand function this can be calculated by: ε = Q 2 - Q 1 Q1Q1 P 2 - P 1 P1P1 Q 2 - Q 1 =  Q P 2 - P 1 =  P =  Q Q1Q1  P P1P1 Price Elasticity of Demand

6  Q Q1Q1  P P1P1 ε =ε = Price decreases from $7 to $5 3 PxPx Qx/tQx/t D $5 B 5 $7 A P 1 = P 2 = P 2 - P 1 = = PP = -2  PP = -2 Q 1 = Q 2 = Q 2 - Q 1 = = QQ = +2  QQ = [2/3 =.66667] [-2/7= ] = %  Q = 67% %  P = -28.5% = -2.3 [rounded] The “own” price elasticity of demand at a price of $7 is -2.3 This is “point” price elasticity. It is calculated at a point on a demand function. It is not influenced by the direction or magnitude of the price change.. There is a problem! If the price changes from $5 to $7 the coefficient of elasticity is different! -2

7 3 PxPx Qx/tQx/t D $5 B 5 $7 A  Q Q1Q1  P P1P1 ε =ε = When the price increases from $5 to $7, P 1 = P2 =P2 =  PP = Q1=Q1= Q2=Q2=  QQ = = %  Q = -40% %  P = 40% = -1 [this is called “unitary elasticity] the ε = [“unitary”] e p = -1 In the previous slide, when the price decreased from $7 to $5, ε = -2.3 e p = -2.3 The point price elasticity is different at every point! There is an easier way!

8 An easier way! Q1Q1  P P1P1 ε =ε =  Q Q1Q1 = Q1Q1 P 1  P * By rearranging terms = P1P1 Q1Q1 *  Q  P this is the slope of the demand function this is a point on the demand function  Q P1P1 Q1Q1 = *  P ε Given that when: P 1 = $7, Q 1 = 3 P 2 = $5, Q 2 = 5 P 2 - P 1 = =  P = -2 Q 2 - Q 1 = =  Q = +2 Then,  Q  P = = - 1 This is the slope of the demand Q = f(P) P 1 = $7, Q 1 = = On linear demand functions the slope remains constant so you just put in P and Q

9 Use of Price Elasticity  Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that: short run  ε  of gasoline is =.15 (inelastic) long run  ε  of gasoline is =.78 (inelastic) short run  ε  of electricity is =. 13 (inelastic) long run  ε  of electricity is = 1.89 (elastic)  Why is the long run elasticity greater than short run?  What are the determinants of elasticity?

10 Determinants of Price Elasticity  Availability of substitutes greater availability of substitutes makes a good more elastic  Proportion of budget expended on good higher proportion – more elastic  Time to adjust to the price changes longer time period means more adjustments possible and increases elasticity  Price elasticity for “brands” tends to be more elastic than for the category

11 P Q/t D1D1 D 1 is a “perfectly elastic” demand function. ε  ε  %  Q %  P For an infinitesimally small change in price, Q changes by infinity.  = undefined perfectly elastic  ε  = undefined. Buyers are very responsive to price changes. An infinitely small change in price changes Q by infinity. D2D2 perfectly inelastic ε = 0 D 2 is a “perfectly inelastic” demand function, no matter how much the price changes the same amount is bought. Buyers are not responsive to price changes!  ε  = 0, perfectly inelastic. 0 P 0  = 0. As the demand function becomes more horizontal, [buyers are more responsive to price changes],  ε  approaches infinity. DeDe

12 Income Elasticity  Income elasticity [ e y] is a measure of the effect of an income change on demand.  When e y > 0, the good is a normal or superior good an increase in income increases demand, a decrease in income decreases demand.  0 < e y < 1 is a normal good  1 < e y is a superior good  When e y < 0, the good is an inferior good

13 Examples of Income Elasticity  normal goods, [0 < e y < 1 ], (between 0 and 1) coffee, beef, Coca-Cola, food, Physicians’ services, hamburgers,...  Superior goods, [ e y > 1], (greater than 1) movie tickets, foreign travel, wine, new cars,..  Inferior goods, [ e y < 0], (negative) “top ramen,” flour, lard, beans,...

14 Cross-Price Elasticity  Cross-price elasticity [e xy ] is a measure of how responsive the demand for a good is to changes in the prices of related goods.  Given a change in the price of good Y, what is the effect on the demand for good X?  e xy is defined as:

15 Cross-Price Elasticity  In the case of beef and pork the e bp is not the same as e pb e bp is the % change in the demand for beef with respect to a % change in the price of pork e pb is the % change in the demand for pork with respect to a % change in the price of beef

16 The cross elasticity of the demand for beef with respect to the price of pork, e beef-pork or e bp can be calculated: e bp = %  Q of beef %  P of pork An increase in the price of pork, +  P p “causes” an increase in the demand for beef. + Qb+ Qb +e bp positive cross elasticity is positive e bp = %  Q of beef %  P of pork A decrease in the price of pork, - Pp- Pp “causes” a decrease in the demand for beef. -  Q b +e bp positive If goods are substitutes, e xy will be positive. The greater the coefficient, the more likely they are good substitutes. Cross-Price Elasticity

17 Cross-Price Elasticity e xy > 0 suggests substitutes, the higher the coefficient the better the substitute e xy < 0 suggests the goods are complements, the greater the absolute value the more complimentary the goods are e xy = 0 suggests the goods are not related e xy can be used to define markets in legal proceedings

18 Elasticity of Supply  Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good.  Elasticity of supply [ e s ] is defined:

19 Q /t P Given a supply function, supply at a price [P 1 ], Q 1 is produced and offered for sale. P1P1 Q1Q1 At a higher price [P 2 ], P2P2 a larger quantity, Q 2, will be produced and offered for sale. Q2Q2 +P+P +Q+Q The increase in price [  P ], induces a larger quantity goods [  Q]for sale. The more responsive sellers are to  P, the greater the absolute value of e s. [The supply function is “flatter”or more elastic] Elasticity of supply e s = %  Q supplied %P%P

20 Q /ut P The supply function is a model of sellers behavior. Sellers behavior is influenced by: 1. technology 2. prices of inputs 3. time for adjustment market period short run long run very long run 4. expectations 5. anything that influences costs of production taxes regulations,... SeSe a perfectly elastic supply [ e s is undefined.] SiSi a perfectly inelastic supply, e s = 0 as supply approaches horizontal e s approaches infinity

21 Elasticity  Price elasticity of demand elastic, inelastic or unitary elasticity  Income elasticity superior, normal, and inferior  Cross-Price elasticity complements/substitutes  Price elasticity of supply Elastic, inelastic