Section 3 Elasticity Presented by MOHAMED ABD-ELMOHSEN Assistant lecture Economic department Faculty of commerce Suez canal university

(PED) Definition The price elasticity of demand (PED)is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on buyers’ plans remain the same. Calculating Elasticity The price elasticity of demand is calculated by using the formula: Percentage change in quantity demanded Percentage change in price

If the quantity demanded doesn’t change when the price changes, the price elasticity of demand is zero and the good as a perfectly inelastic demand. If the percentage change in the quantity demanded equals the percentage change in price, the price elasticity of demand equals 1 and the good has unit elastic demand. Between the two previous cases, the percentage change in the quantity demanded is smaller than the percentage change in price so that the price elasticity of demand is less than 1 and the good has inelastic demand.

If the percentage change in the quantity demanded is infinitely large when the price barely changes, the price elasticity of demand is infinite and the good has perfectly elastic demand If the percentage change in the quantity demanded is greater than the percentage change in price, the price elasticity of demand is greater than 1 and the good has elastic demand. If demand is elastic, a 1 percent price cut increases the quantity sold by more than 1 percent, and total revenue increases.

If demand is inelastic, a 1 percent price cut decreases the quantity sold by more than 1 percent, and total revenues decreases. If demand is unitary elastic, a 1 percent price cut increases the quantity sold by 1 percent, and total revenue remains unchanged. If a price cut increases total revenue, demand is elastic If a price cut decreases total revenue, demand is inelastic. If a price cut leaves total revenue unchanged, demand is unit elastic

Types of price Elasticity Demand(PED ) Elastic >1Unit elastic = 1Inelastic <1Zero elastic =0Perfectly elastic= ∞ ppppP ∆Q > ∆p∆Q = ∆p∆Q < ∆p∆Q not change ∆p not change Total Revenue = P × QD Total Revenue = P × QD (not change) Total Revenue = P × QD Total Revenue = P × QD Total Revenue = P × QD

1- Calculate the Price elasticity of demand when: a.The price fall from $25 to15. B. The price fall from $15 to 10. C. The price fall from $10 to 0. D. Interpret your results in a, b, and c. a.The price fall from $25 to15. B. The price fall from $15 to 10. C. The price fall from $10 to 0. D. Interpret your results in a, b, and c. Original point New point Price2515 QD020

A)Fall from B) fall from 15 to 10 PED= ( %∆ Q) / (% ∆ p) (%∆ Q)= (QD (N) – QD (O) ) / QD (avreg) ∆ Q = (20-0 ) ∕ 10 =2 (% ∆ p)= (P (N) –p (o) ) / Op = (15- 25) / 20 = PED= (2∕- 0.5) =- 4 When the price increase about 1% the demand fall about 4 % (Elastic) & indirect relation between price & QD PED= ( %∆ Q) / (% ∆ p) (%∆ Q)= (QD (N) – QD (O) ) / QD (avreg) ∆ Q = (20-0 ) ∕ 10 =2 (% ∆ p)= (P (N) –p (o) ) / Op = (15- 25) / 20 = PED= (2∕- 0.5) =- 4 When the price increase about 1% the demand fall about 4 % (Elastic) & indirect relation between price & QD Original point New point Price2515 QD020 PED= ( %∆ Q) / (% ∆ p) ∆ Q= (QD (N) – QD (O) ) / QD (avereg) %∆ Q= (30-20)/25 = 0.4 ∆ p= (10-15)/ 12.5= -0.4 PED=(0.4 / -0.4 ) PED= -1 When the price increase 1% the demand fall 1% (unit Elastic) PED= ( %∆ Q) / (% ∆ p) ∆ Q= (QD (N) – QD (O) ) / QD (avereg) %∆ Q= (30-20)/25 = 0.4 ∆ p= (10-15)/ 12.5= -0.4 PED=(0.4 / -0.4 ) PED= -1 When the price increase 1% the demand fall 1% (unit Elastic) Original pointNew point Price1510 QD2030

C- The price fall from $10 to 0. PED= ( %∆ Q) / (% ∆ p) %∆ Q= (QD (N) – QD (O) ) / QD (avreg) %∆ Q= (50-30)/40 = 0.5 %∆p =( p (n) - p (o) ) p (avredge) ∆p = (0 -10 ) /5 = -2 PED= (0.5/ -2) = When the price rise about 1% the quantity fall about 0.25% (inelastic) PED= ( %∆ Q) / (% ∆ p) %∆ Q= (QD (N) – QD (O) ) / QD (avreg) %∆ Q= (50-30)/40 = 0.5 %∆p =( p (n) - p (o) ) p (avredge) ∆p = (0 -10 ) /5 = -2 PED= (0.5/ -2) = When the price rise about 1% the quantity fall about 0.25% (inelastic) Original point New point Price100 QD3050 When the price rise about 1% the quantity fall about 0.25% (inelastic) When the price rise about 1% the quantity fall about 0.25% (inelastic)

2)The price elasticity of demand is defined as the magnitude of A)The change in quantity demanded divided by the change in price B)The change in price divided by the change in quantity demanded C)The percentage change in quantity demanded divided by the percentage change in price D)The percentage change in price divided by the percentage change in quantity demanded

3 ) If a 20 percent increase in the price of a used car results in a 10 percent decrease in the quantity of used cars demanded, then the price elasticity of demand equals A) 0.5. B) 1.0. C) 2.0. D) 10.0.

4) The demand schedule for hotel rooms is: Price (dollars per night) Q D (millions of rooms per night) A- What happens to total revenue if the price falls from $400 to $250? B- What happens to total revenue if the price falls from $250 to $200? C- At what price is the total revenue at a maximum? Explain and interpret your answer? D- Is the demand for hotel room’s elastic, unit elastic, or inelastic?

A- if the price falls from $400 to $250? ( nothing change in Total revenue ) b- price falls from $250 to $200? (nothing change) c- Total Revenue is constant at all points PriceQDQD Total Revenue (dollars per night)(millions of rooms per night) P * QD Because, The percentage change in quantity demanded = the percentage change in price D- the demand for hotel room’s is unit elastic Because, The percentage change in quantity demanded = the percentage change in price D- the demand for hotel room’s is unit elastic

5) Consider the market of CDs Qd= 120 – 10 p A- Find the equilibrium price and equilibrium quantity. B- Find the Price Elasticity of Demand (PED) at equilibrium. C- Find the Price Elasticity of Supply (PES) at equilibrium. A- Find the equilibrium price and equilibrium quantity. B- Find the Price Elasticity of Demand (PED) at equilibrium. C- Find the Price Elasticity of Supply (PES) at equilibrium. Qs= 30p Equilibrium price=3, Equilibrium Q= 90

PED= ( %∆ Q) / (% ∆ p) ( %∆ Q )= ( QD (n)- QD (o) )/ QD (avre) = ( ) /90 = (%∆ p)= (P (n) – p (o) )/ p (avre) = (4-2 )/3 = PED= (-0. 22/ 0.66) = PED= ( %∆ Q) / (% ∆ p) ( %∆ Q )= ( QD (n)- QD (o) )/ QD (avre) = ( ) /90 = (%∆ p)= (P (n) – p (o) )/ p (avre) = (4-2 )/3 = PED= (-0. 22/ 0.66) = priceQD=120-10pQs=30p PES = ( %∆ QS) / (% ∆ p) ( %∆ QS)= QS (n) - QS (o) )/ QS (avre) = (120-60)/ 90= (% ∆ p)= (P(n) – p(o) )/ p (avre) = (4- 2)/ 3 = PES= (0.666/ 0.666) = 1 PES = ( %∆ QS) / (% ∆ p) ( %∆ QS)= QS (n) - QS (o) )/ QS (avre) = (120-60)/ 90= (% ∆ p)= (P(n) – p(o) )/ p (avre) = (4- 2)/ 3 = PES= (0.666/ 0.666) = 1