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Elasticity Appendix (chapter 5)

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**Calculating Elasticity**

The price elasticity of demand 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 demand Percentage change in price

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Types of Elasticity > 1, demand is said to be elastic < 1, demand is said to be inelastic = 1, demand is said to be unitary elastic = 0, demand is said to be perfectly inelastic

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**COMPUTING PRICE ELASTICITY WITH INITIAL VALUES AND MIDPOINTS**

Quantity Data Initial $20 100 New 22 80 Computation with Initial-value method Percentage change Price elasticity of demand Computation with Midpoint method

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Practice Problem 1 When the price of a good increased by % 10, the quantity demanded of it decreased % 2. 1. Calculate the price elasticity of demand for this good. 2. Explain how the total revenue from the sale of the good has changed.

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**Solution 1. Price elasticity of demand = 2 ÷ 10 or 0.2.**

Price elasticity of demand = Percentage change in the quantity demanded Percentage change in price 1. Price elasticity of demand = 2 ÷ 10 or 0.2. 2. An elasticity less than 1 means that demand is inelastic. When demand is inelastic, a price rise - increases total revenue.

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**Music giant shops price to combat downloads**

Practice Problem 2 Music giant shops price to combat downloads In 2003, when music downloading first took off, Universal Music slashed the price of a CD from $21 to $15. The company said that it expected the price cut to boost the quantity of CDs sold by % 30. Source: Globe and Mail, September 4, 2003 What was Universal Music’s estimate of the price elasticity of demand for CDs and is the demand estimated to be elastic or inelastic?

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Solution Price elasticity of demand = Percentage change in the quantity demanded ÷ Percentage change in price. % change in price = (P2 - P1) / ((P1 + P2)/2) x 100% [($21 – $15)/($21+15)/2] × 100, which is 33.3 percent. The Percentage change in the quantity is 30 percent. So the estimated price elasticity of demand is 30 percent ÷ 33.3 percent, or 0.9. An estimated elasticity of 0.9 means that demand is estimated to be inelastic.

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**The quantity demanded at various prices is shown in the table below:**

Practice Problem 3 The quantity demanded at various prices is shown in the table below: 1. Draw demand curve. 2. Calculate the price elasticity of demand (when price rises from $1 to $2). 3. Calculate the price elasticity of demand (when price rises from $5 to $6).

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**Solution The demand curve is shown in Figure.**

2.When price rises from $1 to $2 (a % increase) [(1-2)/((1+2)/2)) x %100] = % 66.67 quantity demanded falls from 60 to 30 (a 66.67% decrease). Therefore, the price elasticity of demand is equal to one. 3. When price rises from $5 to $6 (an 18.18% increase), quantity demanded falls from 12 to 10 (an 18.18% decline). Again the price elasticity is equal to one.

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**Practice Problem 4 Suppose that the monthly demand for housing is**

QD = –10P. Using the formula for elasticity we have described in class, suppose that the initial price is $400 dollars, calculate the price elasticity of demand between a price of $500 and $400. Explain the meaning of your answer using the concept of elasticity.

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**Solution QD at P = $500 is equal to 5,000 and**

QD is 6,000 when P = $400. Using the formula for price elasticity of demand we have, Demand is inelastic and is equal to A one percentage increase in the price of housing results in a decline of housing of roughly .82%, or a 10%’age increase in the price of housing results in a decline of housing of roughly 8.2%.

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**Calculating the Price Elasticity of Demand **

Elasticity Changes Along a Straight-Line Demand Curve Consider the following demand curve: the price elasticity of demand (moving from point A to point B) ? (use midpoint method)

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**Calculating the Price Elasticity of Demand **

Elasticity Changes Along a Straight-Line Demand Curve % change in price = (P2 - P1) / ((P1 + P2)/2) x 100% % change in quantity= (Q2 - Q1) / ((Q1 + Q2)/2) x 100% (9-10)/((10+9)/2)x100%= -10.5%. (4-2)/(2+4)/2)x100%= 66.7%. moving from point A to point B: the price elasticity of demand is 66.7%/(-10.5%) = -6.4. demand is elastic between those two points. (2-3)/((3+2)/2)x100%= -40%. (18-16)/(16+18)/2)x100%= 11.76%. moving from point C to point D: 11.76%/(-40%) = -0.29 demand is inelastic between those two points. As you move to the right along a demand curve, the price elasticity of demand will always fall. Demand curves are more elastic at higher prices and less elastic at lower prices.

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