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Price, Income and Cross Elasticity

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Elasticity – the concept The responsiveness of one variable to changes in another When price rises, what happens to demand? Demand falls BUT! How much does demand fall?

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Elasticity – the concept If price rises by 10% - what happens to demand? We know demand will fall By more than 10%? By less than 10%? Elasticity measures the extent to which demand will change

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Elasticity 4 basic types used: Price elasticity of demand Price elasticity of supply Income elasticity of demand Cross elasticity

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Elasticity Price Elasticity of Demand –The responsiveness of demand to changes in price –Where % change in demand is greater than % change in price – elastic –Where % change in demand is less than % change in price - inelastic

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Elasticity The Formula: Ped = % Change in Quantity Demanded ___________________________ % Change in Price If answer is between 0 and -1: the relationship is inelastic If the answer is between -1 and infinity: the relationship is elastic Note: PED has – sign in front of it; because as price rises demand falls and vice-versa (inverse relationship between price and demand)

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Elasticity Price (£) Quantity Demanded The demand curve can be a range of shapes each of which is associated with a different relationship between price and the quantity demanded.

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Elasticity Price Quantity Demanded (000s) D The importance of elasticity is the information it provides on the effect on total revenue of changes in price. £5 100 Total revenue is price x quantity sold. In this example, TR = £5 x 100,000 = £500,000. This value is represented by the grey shaded rectangle. Total Revenue

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Elasticity Price Quantity Demanded (000s) D If the firm decides to decrease price to (say) £3, the degree of price elasticity of the demand curve would determine the extent of the increase in demand and the change therefore in total revenue. £5 100 £3 140 Total Revenue

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Elasticity Price (£) Quantity Demanded 10 D % Δ Price = -50% % Δ Quantity Demanded = +20% Ped = -0.4 (Inelastic) Total Revenue would fall Producer decides to lower price to attract sales Not a good move!

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Elasticity Price (£) Quantity Demanded D Producer decides to reduce price to increase sales 7 % Δ in Price = - 30% % Δ in Demand = + 300% Ped = - 10 (Elastic) Total Revenue rises Good Move!

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Elasticity If demand is price elastic: Increasing price would reduce TR (%Δ Qd > % Δ P) Reducing price would increase TR (%Δ Qd > % Δ P) If demand is price inelastic: Increasing price would increase TR (%Δ Qd < % Δ P) Reducing price would reduce TR (%Δ Qd < % Δ P)

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Price Elasticity of Demand Definition: Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us how much more. The degree of sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand. Price elasticity formula: Ed = percentage change in Qd / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qd = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd. Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price. Putting the two above equations together: Ed = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative number. But, we focus on the magnitude of the change by neglecting the minus sign and use absolute value Examples: 1. If the price of Product A increased by 10%, the quantity demanded decreased by 20%. Then the coefficient for price elasticity of the demand of Product A is: Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2 2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased from $2 to $4 per unit, the coefficient for Ed is: Ed = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {( ) / 1/2( )} / {(2 - 4) / 1/2 (2+4)} = Take the absolute value of , Ed = 0.16

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Elasticity Income Elasticity of Demand: –The responsiveness of demand to changes in incomes Normal Good – demand rises as income rises and vice versa Inferior Good – demand falls as income rises and vice versa

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Elasticity Income Elasticity of Demand: A positive sign denotes a normal good A negative sign denotes an inferior good

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Income Elasticity of Demand Definition: Income elasticity of demand (Ey, here y stands for income) tells us the relationship a product's quantity demanded and income. It measures the sensitivity of quantity demand change of product X to a change in income. Price elasticity formula: Ey = percentage change in Quantity demanded / percentage change in Income If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd, and Q2 = new Qd. Percentage change in Y = (Y1-Y2) / [1/2 (Y1 + Y2)] where Y1 = initial Income, and Y2 = New income. Putting the two above equations together: Ey = {(Q1-Q2) / [1/2 (Q1+Q2)] } / (Y1-Y2) / [1/2 (Y1 + Y2)] Characteristics: Ey > 1, Qd and income are directly related. This is a normal good and it is income elastic. 0< Ey<1, Qd and income are directly related. This is a normal good and it is income inelastic. Ey < 0, Qd and income are inversely related. This is an inferior good. Ey approaches 0, Qd stays the same as income changes, indicating a necessity. Example: If income increased by 10%, the quantity demanded of a product increases by 5 %. Then the coefficient for the income elasticity of demand for this product is:: Ey = percentage change in Qx / percentage change in Y = (5%) / (10%) = 0.5 > 0, indicating this is a normal good and it is income inelastic.

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Elasticity For example: Yed = - 0.6: Good is an inferior good but inelastic – a rise in income of 3% would lead to demand falling by 1.8% Yed = + 0.4: Good is a normal good but inelastic – a rise in incomes of 3% would lead to demand rising by 1.2% Yed = + 1.6: Good is a normal good and elastic – a rise in incomes of 3% would lead to demand rising by 4.8% Yed = - 2.1: Good is an inferior good and elastic – a rise in incomes of 3% would lead to a fall in demand of 6.3%

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Elasticity Cross Elasticity: The responsiveness of demand of one good to changes in the price of a related good – either a substitute or a complement Xed = % Δ Qd of good t __________________ % Δ Price of good y

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Elasticity Goods which are complements: –Cross Elasticity will have negative sign (inverse relationship between the two) Goods which are substitutes: –Cross Elasticity will have a positive sign (positive relationship between the two)

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Cross Elasticity of Demand Definition: Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity demand change of product X to a change in the price of product Y. Formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 = new Qd of X. Percentage change in Py = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y. Putting the two above equations together: Exy = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} Characteristics: Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes. Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not related. Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements. Examples: 1. If the price of Product A increased by 10%, the quantity demanded of B increases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating A and B are substitutes. 2. If the price of Product A increased by 10%, the quantity demanded of B decreases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = < 0, indicating A and B are complements.

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Elasticity Price Elasticity of Supply: –The responsiveness of supply to changes in price –If Pes is inelastic - it will be difficult for suppliers to react swiftly to changes in price –If Pes is elastic – supply can react quickly to changes in price Pes = % Δ Quantity Supplied ____________________ % Δ Price

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Price Elasticity of Supply Definition: Law of supply tells us that producers will respond to a price drop by producing less, but it does not tell us how much less. The degree of sensitivity of producers to a change in price is measured by the concept of price elasticity of supply. Price elasticity formula: Es = percentage change in Qs / percentage change in Price. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qs = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qs, and Q2 = new Qs. Percentage change in P = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price, and P2 = New Price. Putting the two above equations together: Es = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} Because of the direct relationship between Qs and Price, the Es coefficient will always be a positive number. Examples: 1. If the price of Product A increased by 10%, the quantity supplied increases by 5%. Then the coefficient for price elasticity of the supply of Product A is: Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = If the quantity supplied of Product B has decreased from 1000 units to 200 units as price decreases from $4 to $2 per unit, the coefficient for Es is: Es = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [1/2 (P1 + P2)]} = {( ) / 1/2( )} / {(4-2) / 1/2 (4+2)} = 2

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Characteristics & Determinants Characteristics: Es approaches infinity, supply is perfectly elastic. Producers are very sensitive to price change. Es > 1, supply is elastic. Producers are relatively responsive to price changes. Es = 1, supply is unit elastic. Producers’ response and price change are in same proportion. Es < 1, supply is inelastic. Producers are relatively unresponsive to price changes. Es approaches 0, supply is perfectly inelastic. Producers are very insensitive to price change. It is impossible to judge elasticity of a supply curve by its flatness or steepness. Along a linear supply curve, its elasticity changes. Determinants: 1. Time lag: How soon the cost of increasing production rises and the time elapsed since the price change influence the Es. The more rapidly the production cost rises and the less time elapses since a price change, the more inelastic the supply. The longer the time elapses, more adjustments can be made to the production process, the more elastic the supply. 2. Storage possibilities: Products that cannot be stored will have a less elastic supply. For example, produces usually have inelastic supply due to the limited shelf life of the vegetables and fruits.

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Determinants of Elasticity Time period – the longer the time under consideration the more elastic a good is likely to be Number and closeness of substitutes – the greater the number of substitutes, the more elastic The proportion of income taken up by the product – the smaller the proportion the more inelastic Luxury or Necessity - for example, addictive drugs

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Importance of Elasticity Relationship between changes in price and total revenue Importance in determining what goods to tax (tax revenue) Importance in analysing time lags in production Influences the behaviour of a firm

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