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Demand and Elasticity

Demand and Elasticity. Consider the following cases:. Making Sales Targets A Public Transportation Problem: Can the daily ridership fluctuations be controlled through a pricing strategy? The Airliners’ Pricing Problem:

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Demand and Elasticity

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  1. Demand and Elasticity

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

  3. TR 0 = 220 x 120 = 26,400TR1= 180 x 140 = 25,200TR2 = 180 x 200 = 36,000 D 2 D 1 220 180 Q 0 140 200 120

  4. Note: Slope and Scale o o B A

  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. Thepriceelasticity 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. P a 10 b 8 Ep (a --- b) = (10/8)/(-2/10) = -6.25 Ep (c ---d ) = (10/80)/(-2/4) = -.25 c 4 d 2 D Q 80 90 8 18

  8. What does the elasticity “measure” really measure? • The elasticity measure is a ratio between two percentage measures: the percentage change in one variable over the percentage change in another variable • 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. P 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 Arc (Price) Elasticity a b 10 8 c 4 d 2 D Q 8 18 80 90

  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-Q1 10 (Q1+Q2) 8+18 Ea = = -3.49 P2-P1 -2 (P1+P2) 10+8

  11. 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 Elasticity and the Price Level | Ep | > 1 : Elastic | Ep | < 1 : Inelastic | Ep | = 1 : Unit-elastic a E =-3.49 b 10 8 E = -.17 c 4 d D 2 8 18 80 90

  12. Point Elasticity Q --------- Q1+Q2 QP1+P2 Q P E = ------------ = ------- . ------- = ------- . ------ P P Q1+Q2 P Q --------- P1+P2 dQ P Or, = ------ . ----- dP Q

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

  14. A note about marginal revenue: Recall: TR = P.Q ; P = f (Q ) • 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. Q = C - b P dQ P P E = ----- . ----- = -b . ------ d p Q Q dQ ---- = - b d p P, MR 1 MR = P. ( 1 + ---- ) E Slope= -1/b Slope=-2/b D MR Q 0 C

  16. Special Cases P D D 0 Q Q 0 Infinitely (price) elastic Infinitely 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 • Necessities versus luxuries Eating at restaurants Groceries • Availability of substitutes Chicken versus beef • How much of our income a good takes Salt versus Nike sneakers • The passage of time

  19. Elasticity and Passage of Time P Do D1 D3 D2 Q O Qo Q’o Q2 Q1 Q3

  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. • Income Elasticity: a measure of the degree of sensitivity of demand for a good (or service) to changes in consumers’ (buyers’) income • 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) Q2-Q1 Q2+Q1 d Q I EI = = or = ------ . ------ I2-I1 d I Q I1+I2

  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) Qx2- Qx1 Qx2+Qx1 d Qx Py Ec = or = ----------- . ------- Py2- Py1 d Py Qx Py1+Py2

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