2Calculating Elasticity Theprice elasticity of demandis 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 ElasticityThe price elasticity of demand is calculated by using the formula:Percentage change in quantity demand Percentage change in price
3Types 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
4COMPUTING PRICE ELASTICITY WITH INITIAL VALUES AND MIDPOINTS QuantityDataInitial$20100New2280Computation with Initial-value methodPercentage changePrice elasticity of demandComputation with Midpoint method
6Practice Problem 1When 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.
7Solution 1. Price elasticity of demand = 2 ÷ 10 or 0.2. Price elasticity of demand = Percentage change in the quantity demanded Percentage change in price1. 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.
8Music giant shops price to combat downloads Practice Problem 2Music giant shops price to combat downloadsIn 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, 2003What was Universal Music’s estimate of the price elasticity of demand for CDs and is the demand estimated to be elastic or inelastic?
9SolutionPrice 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.
10The quantity demanded at various prices is shown in the table below: Practice Problem 3The 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).
11Solution The demand curve is shown in Figure. 2.When price rises from $1 to $2 (a % increase)[(1-2)/((1+2)/2)) x %100] = % 66.67quantity 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), quantitydemanded falls from 12 to 10 (an 18.18% decline).Again the price elasticity is equal to one.
12Practice 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.
13Solution 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 toA 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%.
14Calculating the Price Elasticity of Demand Elasticity Changes Along a Straight-Line Demand CurveConsider the following demand curve:the price elasticity of demand (moving from point A to point B) ?(use midpoint method)
15Calculating 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 is66.7%/(-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%) = -0.29demand 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.