© Pilot Publishing Company Ltd Chapter 6 Elasticities of Demand

© Pilot Publishing Company Ltd Elasticity of Demand Elasticity of Demand Classification of Elasticities of Demand Classification of Elasticities of Demand Price Elasticity of Demand Price Elasticity of Demand Price Elasticity & Demand Curve Price Elasticity & Demand Curve Price Elasticity of Demand, Total Revenue & Total Expenditure Price Elasticity of Demand, Total Revenue & Total Expenditure Income Elasticity of Demand Income Elasticity of Demand Cross Elasticity of Demand Cross Elasticity of Demand Contents:

© Pilot Publishing Company Ltd Advanced Material 6.1: Price Consumption Curve and Price Elasticity Advanced Material 6.1: Price Consumption Curve and Price Elasticity Advanced Material 6.2: Income Consumption Curve and Income Elasticity Advanced Material 6.2: Income Consumption Curve and Income Elasticity Contents:

© Pilot Publishing Company Ltd Elasticity of Demand

© Pilot Publishing Company Ltd Elasticity of demand ( 需求彈性, E d ) is a measure of the responsiveness of the quantity demanded of a good to a change in an exogenous variable. Elasticity of demand % change in X_________ % change in exogenous variable Why?

© Pilot Publishing Company Ltd Classification of Elasticities of Demand

© Pilot Publishing Company Ltd Type of elasticity of demand Exogenous variable concerned Price elasticity of demand ( 價格需求彈性, p E d ) Income elasticity of demand ( 所得需求彈性, i E d ) Cross elasticity of demand ( 交叉需求彈性, c E d ) Classification according to the exogenous variable concerned Price of the good Income Price of related good

© Pilot Publishing Company Ltd Classification according to the formula adopted in calculation Point elasticity of demand % Δ = X 2 – X 1 x 100% X 1 Situations applied: when the % change are _________ Arc elasticity of demand % Δ = X 2 – X 1 x 100% (X 1 + X 2 )/2 Situations applied: when the % change are _________ very small significant

© Pilot Publishing Company Ltd vertical Classification according to the size of the elasticity 1. Perfectly inelastic (E d = 0) The exogenous variable changes but X remains unchanged i.e. % Δ in X =_______. In the case of price elasticity, the demand curve is _________. D 0 vertical PxPx X 0

© Pilot Publishing Company Ltd Classification according to the size of the elasticity 2. Inelastic (E d < 1) %  in X ____ %  in exogenous variable 3. Unitarily elastic (E d = 1) %  in X ____ %  in exogenous variable    4. Elastic (E d > 1) %  in X ____ %  in exogenous variable

© Pilot Publishing Company Ltd horizontal D Classification according to the size of the elasticity 5. Perfectly elastic (E d = infinity) A negligible change in the exogenous variable brings an infinite change in Qd i.e. % Δ in X =_________. In the case of price elasticity, the demand curve is ___________. infinity horizontal PxPx X 0

© Pilot Publishing Company Ltd Price Elasticity of Demand

© Pilot Publishing Company Ltd What is price elasticity? Price elasticity of demand ( 價格需求彈性, p E d ) is equal to the percentage change in quantity demanded of a good divided by the percentage change in its own price.

© Pilot Publishing Company Ltd What is price elasticity? (Con’t) According to the first law of demand,  p E d is ________. negative positive However, if Giffen good existed,  its p E d would be ________.

© Pilot Publishing Company Ltd ΔPxΔPx ΔXΔX X X1X1 P1P1 0 C B A Px Px DC Point elasticity of demand -- on a linear demand curve (DC) Mathematical measure: p E d at point A: Graphical measure:

© Pilot Publishing Company Ltd ΔPxΔPx ΔXΔX Point elasticity of demand – on a non-linear DC X X1X1 P1P1 0 C B A P x DC Mathematical measure: p E d at point A: Graphical measure:

© Pilot Publishing Company Ltd Price Elasticity & Demand Curve

© Pilot Publishing Company Ltd X 0 P x Demand curve M (mid-point): | p E d |= 1 (unitarily elastic) |pEd| > 1 (elastic) |pEd| < 1 (inelastic) Point elasticity of demand -- on a linear DC

© Pilot Publishing Company Ltd A D d1d1 d2d2 X O Px Px B C P E p E d at point A on d 1 = BA AC = OP PC ED DC = = p E d at point D on d 2 Price elasticity at points on different DCs If two linear DCs have the same y-intercept  they will have the same p E d at every price.

© Pilot Publishing Company Ltd p E d at point A on d 1 (with a smaller y-intercept) = OP PF ED DF = p E d at point D on d 2 (with a larger y-intercept) > Price elasticity at points on different DCs AD X O P x B C P E d1d1 d2d2 F OP PC = BA AC = If 2 linear DCs have different y-intercepts  The curve with a smaller y-intercept will have a larger price elasticity than the curve with a larger y-intercept at every price.

© Pilot Publishing Company Ltd D (on d 2 ) X O P x A on (d 1 ) B C P E F d1d1 d2d2 p E d at point A on a d 1 (with a larger slope) OP PF ED DF = = p E d at point D on d 2 (with a smaller slope) < Price elasticity of points on different DCs OP PC = BA AC = If 2 linear DCs intersect,  the one with a gentler slope will have a larger price elasticity at the intersection point.

© Pilot Publishing Company Ltd Price Elasticity of Demand, Total Revenue & Total Expenditure

© Pilot Publishing Company Ltd Total expenditure paid by a consumer = Price x Quantity transacted (or P x Q) = Total revenue received by a producer Price elasticity, total expenditure (TE) and total revenue (TR)

© Pilot Publishing Company Ltd Change in TE and TR When demand or supply changes, price & quantity transacted vary. Subsequently, total expenditure & total revenue are affected.

© Pilot Publishing Company Ltd D2D2 P2P2 X2X2 in TR  in TR Increase in demand D   P  & Q   TR  PxPx X D1D1 S1S1 P1P1 X1X1 0

© Pilot Publishing Company Ltd D2D2 P2P2 X2X2 Decrease in demand D   P  & Q   TR  PxPx X D1D1 S1S1 P1P1 X1X1 0 in TR in TR

© Pilot Publishing Company Ltd Increase in supply P  but X  Δ in TR depends on the relative % Δ in P & Q, i.e., the p E d. X S2S2 PxPx D S1S1 P1P1 X1X1 P2P2 X2X2 0

© Pilot Publishing Company Ltd S2S2 a. Demand is elastic P2P2 X2X2 When supply increases, if demand is elastic, %  in X  %  in P TR  PxPx X D S1S1 P1P1 M  in TR  in TR X1X1 0

© Pilot Publishing Company Ltd S2S2 b. Demand is unitarily elastic %  in X  %  in P TR remains constant  in TR  in TR P2P2 X2X2 PxPx X D S1S1 P1P1 M X1X1 0

© Pilot Publishing Company Ltd S2S2 c. Demand is inelastic %  in X  %  in P TR  PxPx X D S1S1 P1P1 M  in TR  in TR X1X1 P2P2 X2X2 0

© Pilot Publishing Company Ltd P  but X  Decrease in supply PxPx X D S1S1 S2S2 P2P2 P1P1 X1X1 X2X2 0 Δ in TR depends on the relative % Δ in P & Q, i.e., the p E d

© Pilot Publishing Company Ltd S2S2 a. Demand is elastic When supply decreases, if demand is elastic, %  in X  %  in P Δ in TR  PxPx X D S1S1 P2P2 X2X2 P1P1 M X1X1  in TR  in TR

© Pilot Publishing Company Ltd S2S2 b. Demand is unitarily elastic %  in X = %  in P TR remains constant PxPx X D S1S1 P1P1 M  in TR  in TR X1X1 P2P2 X2X2

© Pilot Publishing Company Ltd S2S2 c. Demand is inelastic %  in X  %  in P Δ in TR  P2P2 X2X2 D M PxPx X S1S1 P1P1 X1X1  in TR  in TR

© Pilot Publishing Company Ltd Q6.6: (a) If the demand is inelastic, to increase the TR, should a producer raise the price or should he cut the price? (b) After raising the price of a good, a producer finds that the total revenue falls. What is the reason?

© Pilot Publishing Company Ltd Unit elasticity and total revenue % Δ in X = % Δ in P TR remains constant despite a change in P or Q. If one spends the whole amount (or a fixed amount) of his income on a good no matter what its price is, its p E d must be equal to / greater than /smaller than one. For a unitarily elastic demand: equal to

© Pilot Publishing Company Ltd X x

1.Number of close substitutes: more close substitutes  more elastic demand. Factors affecting price elasticity Why? 2. Degree of necessity: necessities & habit-forming goods  less elastic demand.

© Pilot Publishing Company Ltd Number of possible uses: more different uses  more elastic demand. Factors affecting price elasticity (Con’t) Why? 4. Durability: more durable  more elastic demand. 5. Proportion of income spent: a larger proportion of one’s expenditure  more elastic demand. Why?

© Pilot Publishing Company Ltd Time of adjustment: longer time for adjustment  more elastic demand (Second law of demand) Shift of DC as time passes PxPx X P0P0 P1P1 X0X0 X3X3 X2X2 X1X1 X4X4 0 Why?

© Pilot Publishing Company Ltd Q6.7: The demand for salt is inelastic. List all possible reasons.

© Pilot Publishing Company Ltd Income Elasticity of Demand

© Pilot Publishing Company Ltd Income elasticity of demand ( 所得需求彈性, i E d ) is equal to the percentage change in quantity demanded divided by the percentage change in income. What is income elasticity?

© Pilot Publishing Company Ltd Superior good  X is _________ related to income.  i E d is ________. luxuries necessities positive (Options: positive / negative / luxuries / necessities / positively / negatively ) i E d  1   i E d  1   positively

© Pilot Publishing Company Ltd Inferior good  X is _________ related to income.  i E d is __________. negative (Options: positive / negative / luxuries / necessities positively / negatively) negatively

© Pilot Publishing Company Ltd X I I1I1 X1X1 C 0 B A ΔXΔX Δ I Good X is an inferior good Graphical measure: Mathematical measure: X I I1I1 X1X1 C 0 B A ΔXΔX Δ I Good X is a superior good

© Pilot Publishing Company Ltd Cross Elasticity of Demand

© Pilot Publishing Company Ltd Cross elasticity of demand ( 交叉需求彈性, c E d ) is equal to the percentage change in quantity demanded of a good (e.g., good X) divided by the percentage change in price of another good (e.g., good Y). What is cross elasticity?

© Pilot Publishing Company Ltd The cross elasticity of substitutes is positive, why? The cross elasticity of complements is negative, why? Cross elasticity of demand when P Y   Y  and X (substitute of Y)  thus, P Y and X are positively related. when P Y   Y  and X (complement of Y)  thus, P Y and X are negatively related.

© Pilot Publishing Company Ltd Graphical measure: Mathematical measure: PYPY X C 0 B A ΔXΔX ΔPYΔPY X1X1 P Y1 Good X and good Y are substitutes PYPY X C 0 B A ΔXΔX ΔPYΔPY X1X1 P Y1 Good X and good Y are complements

© Pilot Publishing Company Ltd Q6.9: For each of the following commodities, suggest a good with a positive cross elasticity and a good with a negative cross elasticity related to the commodity. Shoes Pencil Broom Camera Map

© Pilot Publishing Company Ltd Advanced Material 6.1: Price elasticity and price consumption curve As income remains unchanged and the expenditure on good Y , the expenditure on good X must __________. As the expenditure on good X  (when Px  and X  ), the %  in X must be ___________ the %  in P X. the demand for good X must be So, the demand for good X must be _______. If PCC is _upward sloping_, when Px , both the consumption of good X and good Y __________. PCC Y X 0 increase decrease smaller than inelastic

© Pilot Publishing Company Ltd Shape of PCC Consumption and expenditure on Y Expenditure on X (= I - P Y Y) Relative size of % Δ in X (  ) and P x (  ) Price elasticity of demand for X Upward sloping  %  in X %  in P x Horizontal Unchanged %  in X %  in P x Downward sloping  %  in X %  in P x < Inelastic > = Elastic Unitarily elastic

© Pilot Publishing Company Ltd Price elasticity and price consumption curve Graphical measure: PCC (| p E d |<1) Y X 0 PCC (| p E d |=1) Y X 0 PCC (| p E d |>1) Y X0

© Pilot Publishing Company Ltd ICC 1 ICC 2 ICC 5 ICC 4 ICC 3 Shape of ICC i E d of X i E d of Y ICC 1 ICC 2 ICC 3 ICC 4 ICC 5 Y X I1I1 I3I3 I2I2 0 Advanced Material 6.2: Income elasticity and income consumption curve +ve -ve +ve 0 0 -ve+ve

© Pilot Publishing Company Ltd Correcting Misconceptions: 1. The gentler the slope of a demand curve, the larger its price elasticity. 2. A price rise must raise the total revenue. 3. If one spends a fixed amount of his income on a good, his demand for the good is perfectly inelastic. 4. It is impossible for all the goods consumed to be luxuries, because one must consume some necessities.

© Pilot Publishing Company Ltd Survival Kit in Exam Question 6.1: After a rise in the price of coffee, what will happen to the total revenues of (a) coffee, (b) sugar and (c) tea respectively?