1. Demand and Elasticity

2. Consider the following cases: 4 Making Sales Targets 4 A Public Transportation Problem: Can the daily ridership fluctuations be controlled through a pricing strategy? 4 The Airliners’ Pricing Problem: How can an airliner fill its plains while maximizing its profit?

3. 4 220 TR 0 = 220 x 120 = 26,400 TR 1 = 180 x 140 = 25,200 TR 2 = 180 x 200 = 36,000 120 180 0 Q D 2 D 1 140200

4. Note: Slope and Scale o o A B

5. Elasticity A general definition: “Elasticity” is a (standard) measure of the degree of sensitivity ( or responsiveness) of one variable to changes in another variable. The price elasticity of Demand The (self) price elasticity of demand is a measure of the degree of sensitivity of demand to changes in the (self) price, ceteris paribus.

6. Determining Price Elasticity Percentage Change in Quantity Ep = Percentage Change in Price Change in Quantity Quantity Ep = Change in Price Price

7. Ep (a --- b) = (10/8)/(-2/10) = -6.25 Ep (c ---d ) = (10/80)/(-2/4) = -.25 P Q D a b c d 2 4 8 10 8 18 8090

8. What does the elasticity “measure” really measure? 4 The elasticity measure is a ratio between two percentage measures: the percentage change in one variable over the percentage change in another variable 4 A price elasticity of -6.25 means that for each one percent change in price the quantity demanded will change by 6.25 percent.

9. Arc (Price) Elasticity P Q D 2 4 Note that if we increased the price, (from 8 to 10 or 2 to 4) the original P and Q would be 2 and 8 and 18 and 90, respectively. Ep = (-10/18)/(2/8) = -2.22 Ep = (-10/90)/(2/2) = -.11 8 10 8188090 a b c d

10. Arc Elasticity To get the average elasticity between two points on a demand curve we take the average of the two end points (for both price and quantity) and use it as the initial value: Q2-Q110 (Q1+Q2) 8+18 Ea = = -3.49 P2-P1-2 (P1+P2) 10+8

11. Elasticity and the Price Level Along a linear demand curve as the price goes up, |elasticity | increases. Note that between points "a" and "b" the (arc) elasticity of the above demand curve is -3.49, whereas between "c" and "d" it is -.17. P D 8188090 a b c d 2 4 8 10 | Ep | > 1 : Elastic | Ep | < 1 : Inelastic | Ep | = 1 : Unit-elastic E =-3.49 E = -.17

12. Point Elasticity Q --------- Q 1 +Q 2 Q P 1 +P 2 Q P E = ------------ = -------. ------- = -------. ------ P P Q 1 +Q 2 P Q --------- P 1 +P 2 dQ P Or, = ------. ----- dP Q

13. P,MR Q Q TR 0 0 | E | = 1 Q = C - b P C 1 P = ----- - ----- Q b b C 2 MR = ------ - ------ Q b b C D MR Note: In the demand equation dQ/dP = -b That means P E p = -b ----- Q

14. A note about marginal revenue: Recall: TR = P.Q ; P = f (Q ) 4 Marginal Revenue = Change in TR resulting from producing (selling) one additional unit of output. TR (P.Q) d P d Q MR = ------ = -------- = ------.Q + ------.P Q Q d Q d Q d P Q P 1 = ( -----. ----- + ------ ).P = P. ( ------- + 1 ) d Q P P E

15. 0 Q Q = C - b P Slope= -1/b Slope=-2/b D MR C P, MR dQ ---- = - b d p dQ P P E = -----. ----- = -b. ------ d p Q Q 1 MR = P. ( 1 + ---- ) E

16. Special Cases P D D Q0 0 Q Infinitely (price) elasticInfinitely price inelastic

17. Important Observations When demand is elastic, a decrease in price will result is an increase in the revenue (sales). When demand is inelastic, a decrease in price will result is a decrease in the revenue (sales). When demand is unit-elastic, an increase (or a decrease) in price will not change the revenue (sales).

18. What Determines Elasticity 4 Necessities versus luxuries Eating at restaurants Groceries 4 Availability of substitutes Chicken versus beef 4 How much of our income a good takes Salt versus Nike sneakers 4 The passage of time

19. Elasticity and Passage of Time DoDo D1D1 D2D2 D3D3 Qo Q’o Q1Q2 Q3 Q P O

20. Other Elasticity Measures Recall: “Elasticity” is a (standard) measure of the degree of sensitivity ( or responsiveness) of one variable to changes in another variable. 4 Income Elasticity: a measure of the degree of sensitivity of demand for a good (or service) to changes in consumers’ (buyers’) income 4 Cross Price Elasticity: a measure of the degree of sensitivity of demand for a good (or service) to changes in the price of another good or service

21. Income Elasticity of Demand A measure of the degree of responsiveness of demand (for a good) to a change in income, ceteris paribus. (Shift of the demand curve) Q 2 -Q 1 Q 2 +Q 1 d Q I E I = = or = ------. ------ I 2 -I 1 d I Q I 1 +I 2

22. Cross (Price) Elasticity A measure of the degree of responsiveness of the demand for one good (X) to a change in the price of another good (Y): (Shift of demand curve) Q x2 - Q x1 Q x2 +Q x1 d Qx Py Ec = or = -----------. ------- P y2 - P y1 d Py Qx P y1 +P y2