2 Calculating 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
3 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
4 COMPUTING PRICE ELASTICITY WITH INITIAL VALUES AND MIDPOINTS QuantityDataInitial$20100New2280Computation with Initial-value methodPercentage changePrice elasticity of demandComputation with Midpoint method
6 Practice 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.
7 Solution 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.
8 Music 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?
9 SolutionPrice 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.
10 The 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).
11 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] = % 66.67quantity 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.
12 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.
13 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 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%.
14 Calculating 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)
15 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 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.