Elasticity Appendix (chapter 5)

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

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

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

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.

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.

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?

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.

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).

Solution The demand curve is shown in Figure. 2.When price rises from $1 to $2 (a 66.67 % 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.

Practice Problem 4 Suppose that the monthly demand for housing is QD = 10000 –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.

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 0.8181. 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%.

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)

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.