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: How can an airliner fill its plains while maximizing its profit? TR 0 = 220 x 120 = 26,400 TR1 = 180 x 140 = 25,200 D2 TR2 = 180 x 200 = 36,000 D1 220 180 0 Q 120 140 200 Note: Slope and Scale o o A B 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. Determining Price Elasticity Percentage Change in Quantity Ep = Percentage Change in Price Change in Quantity Quantity Ep = Change in Price Price P a 10 b 8 c 4 2 d 8 18 80 D 90 Ep (a --- b) = (10/8)/(-2/10) = -6.25 Ep (c ---d ) = (10/80)/(-2/4) = -.25 Q 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. Arc (Price) Elasticity Note that if we increased P the price, (from 8 to 10 or 2 to 4) the original P and Q would 10 8 be 2 and 8 and 18 and 90, respectively. Ep = (-10/18)/(2/8) = -2.22 a b c 4 d 2 Ep = (-10/90)/(2/2) = -.11 8 18 80 90 D Q 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 (P1+P2) -2 10+8 Elasticity and the Price Level P 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. 10 8 | Ep | > 1 : Elastic | Ep | < 1 : Inelastic | Ep | = 1 : Unit-elastic a E =-3.49 b c E = -.17 d 4 2 D 8 18 80 90 Point Elasticity Q --------Q1+Q2 Q P1+P2 Q P E = ------------ = ------- . ------- = ------- . -----P P Q1+Q2 P Q --------P1+P2 dQ P Or, = ------ . ----dP Q P,MR Q = C - b P |E|=1 C 1 P = ----- - ----- Q b b D MR Q 0 TR C 2 MR = ------ - ------ Q b b C Note: In the demand equation dQ/dP = -b That means Q 0 P E p = -b ----Q 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 dQ MR = ------ = -------- = ------ .Q + ------ .P Q Q dQ dQ dP Q P 1 = ( -----. ----- + ------ ).P = P. ( ------- + 1 ) dQ P P E dQ P P E = ----- . ----- = -b . -----dp Q Q Q = C - b P dQ ---- = - b dp P, MR 1 MR = P. ( 1 + ---- ) E Slope= -1/b Slope=-2/b MR 0 D Q C Special Cases P D D 0 Q Infinitely (price) elastic 0 Infinitely price inelastic Q 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). 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 Elasticity and Passage of Time P D3 D2 Do D1 Q O Q3 Q2 Q1 Q’o Qo 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 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 EI = I2-I1 I1+I2 d Q I = or = ------ . -----d I Q 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 Ec = or = Py2- Py1 Py1+Py2 d Qx Py ----------- . ------d Py Qx