# Elasticity of demand Which one is the most elastic if I apply the same force on them?

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Elasticity of demand

Which one is the most elastic if I apply the same force on them?

To measure the responsiveness ( 反應 ) of the change in Qd as a result of a change in one of its determinants, ceteris paribus. (1)Price, Or (2) income, Or (3) price of related good

The determinants can be: (1)The price of the good – price elasticity of demand %∆Qd %∆Qd %∆Price %∆Price (2)The income of the consumer – income elasticity of demand %∆Qd %∆ income (3) The price of another good – cross elasticity of demand = =

Measures the responsiveness of quantity demanded of a good to a change in the price of the good. (1)Price Elasticity of demand ( 價格需求彈性 ) Ed= % ∆Qd % ∆P 1.Action 2. Response Q2-Q1 Q1 P2-P1 X 100% P1 = 新一舊 舊 X 100%

Why the Elasticity measured as the %∆ rather than absolute change ( 減數 )? Case 1 if P 1 = \$10  Qd = 100 if P 2 = \$9  Qd = 110 Case 2 if P 1 = \$10  Qd = 10000 if P2 = \$9  Qd = 10010 P↓ \$ 1 Absolute change Qd↑10units Does the absolute change show the Elasticity? Then which case is more elastic when P ↓ ? No!

Remarks:  Case 1 is more elasticity than case 2 when calculated by the percentage change Consideration of percentage change of quantity demand not absolute changes ( 減數 )

Why price elasticity of demand is always negative ? Price Ed = -1 or -2 or -0.8 … etc Price Ed = -1 or -2 or -0.8 … etc Hint: P Vs Qd relationship is? Hint: P Vs Qd relationship is? Price and quantity demand is negatively related Price and quantity demand is negatively related (When P ↓  Qd ↑ or P ↑  Qd ↓ ) (When P ↓  Qd ↑ or P ↑  Qd ↓ ) We ignore the sign of price Ed We ignore the sign of price Ed  high Ed or low Ed is in absolute value  high Ed or low Ed is in absolute value  Ed = -1 = 1; -2 = 2 ; -0.8 = 0.8  Ed = -1 = 1; -2 = 2 ; -0.8 = 0.8  Price Ed = 2 > Ed = 1 > Ed = o.8  Price Ed = 2 > Ed = 1 > Ed = o.8

What is the data of P Ed wants to show us? if P Ed = -0.8 = absolute value = 0.8 P Ed = = 0.8 1%∆P ↓ 1% % ∆Qd ↑0.8% Action 反應 Response Since % ∆Qd in response is less than %∆P in action (0.8% < 1% )  Response < Action  in economic we call it inelastic or less elastic You can apply in different elastic range….

2 ways to calculate Price Ed: (a)Arc elasticity: To measure the elasticity between two points on a demand curve **weakness: a different Price Ed when the direction of price movement is reversed. 3 1 P Qd Ed= 2.25 Ed=0.85 D

(b) Point elasticity of Ed To measure the elasticity on a point of the demand curve. The ∆Qd and ∆P are infinitely small (very very small) Ed= % ∆Qd % ∆P

Types of Price elasticity of demand. P Ed may vary form o to ∞ 1.Perfectly inelastic demand (%∆ Qd = 0) Ed = 0 2.Inelastic demand; %∆Qd < %∆P 1> Ed > 0 e.g. 0.1, 0.8, 0.3.. 3.unitarily Ed; Ed = 1 %∆Qd = %∆P;  rectangular hyperbola TR = P ↑ X Qd ↓ Q P D P↑ Q D TR gain TR Loss P ↑ Qd ↓ P Q

Continues…. 4.Elastic demand ∞ >Ed > 1 %∆Qd > %∆P  反應大 5.perfectly elastic demand Ed = ∞ %∆Qd = ∞ > %∆P  反應無限大 D Q P

(1)Price Elasticity of demand ( 價格需求彈性 ) Ed = % ∆P P2-P1 P1 Q1 Q2-Q1 Ed= % ∆Qd = X Q2-Q1 Q1 X P2-P1 P1 Q1P2-P1 Q2-Q1 = = P1 Q1 P2-P1 Q2-Q1 Slope of the ray from pt (0,0) to (P1, Q1) Slope of the demand curve (P1,Q1), (P2,Q2) Ed

Use slopes or angles to measure the Price elasticity demand A linear demand curve P Q D M (0,0) ab (P2,Q2 ) If ray form the origin slope = D curve slope ∠ a = ∠ b  Ed = 1 at M Unitarily range If ray from the origin slope > D curve slope ∠ a > ∠ b  Ed >1 elastic range If ray from the origin slope < D curve slope ∠ a < ∠ b  Ed <1 inelastic range P1

5.4The price Ed varies along a straight line demand curve Mid point, Ed = 1 (unitarily Ed) P1 Ed>1 (elastic) Ed < 1 (inelastic) Ed = 0 Ed = infinitive Qd P So don’t think that a flat demand curve will be elastic !! Q P 100 10 P 100 10 Upper p range Lower p range

Compare the elasticities of D1 & D2 P D2 (0,0) Q (P2,0 ) Ed at D1, P1 = P1 D1 Q1Q1 ’ Slope of the ray from the origin to P1 Slope of D1 P1/Q1 (P2-P1)/(0 – Q1) P1,Q1 ’ = P1,Q1 P1/Q1 (P2-P1)/ Q1 = = P1 P2-P1 (P1,Q1); (0,0) (P2,0); (P1,Q1) = Ed at D2, P1 = (P1,Q1 ’ ); (0,0) (P2,0); (P1,Q1 ’ ) P1/Q1 ’ (P2-P1)/(0 – Q1 ’ ) = = = P1/Q1 ’ (P2-P1)/ Q1 ’ P1 P2-P1 Since P2 is the same intercept on both curve,  Ed of D1 = D2.

If both D curves intercept on the Y-axis at the same point, their Ed are the same Ed = 6.33 Ed = 3.1 Ed = 0.69 Ed = 0.16 Ed = 0.69 Ed = 3.1 Q P

Compare the elasticities of D2 & D3 P D3 (0,0) Q (P2 ’,0 ) Ed at D3, P1 = P1 D2 Q1Q1 ’ Slope of the ray from the origin to P1 Slope of D1 P1/Q1 ’ (P2 ’ -P1)/(0 – Q1 ’ ) P1,Q1 ’ = P1,Q1 P1/Q1 ’ (P2 ’ -P1)/ Q1 ’ = = P1 P2 ’ -P1 (P1,Q1 ’ ); (0,0) (P2 ’,0); (P1,Q1 ’ ) = Ed at D2, P1 = (P1,Q1 ); (0,0) (P2,0); (P1,Q1 ) P1/Q1 (P2-P1)/(0 – Q1) = = = P1/Q1 (P2-P1)/ Q1 P1 P2-P1 Since P2’>P2,  Ed of D3< D2 (P2,0)

Compare Ed between D1 &D2 P Q D1 D2 P1 P2 ’ P2 P1/(P2-P1) for D1 > P1/(P2 ’ -P1) for D2 D1 has a greater price elasticity of demand than D2.

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