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Elasticity of demand

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

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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

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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 = =

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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%

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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!

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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 )

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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

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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….

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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

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(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

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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

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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

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(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

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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

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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

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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.

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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

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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)

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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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