# 2 Price Elasticity of Demand

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1 1 1.1 Goals of this class Goals of this class Expand on supply and demand: how much do quantities change in responses to: changes in price? changes in income? changes in price of related goods? Learn implications for total revenue, taxes. 2 Price Elasticity of Demand 2.1 Computing Elasticity Elasticity Recall law of demand: all other things remaining equal, the higher the price of the good, the lower is the quantity demanded. Price elasticity of demand: Answers how responsive demand is to changes in price. When the price increases by 1%, by how much does the quantity demanded decrease? Formula: Price elasticity of dem. = Average Percentage Changes Usual percentage change: Perc. Change in Quantity Demanded Perc. change in price % Q d = Q 2 Q 1 Q 1 or.. Average percentage change: % Q d = Q 1 Q 2 Q 2 % Q d = Q 2 Q 1 Q ave

2 Computing Elasticity Elasticity of demand: e d = % Q d % P = Q 2 Q 1 Q ave P 2 P 1 P ave Compute the elasticity of demand between these two points. 2.2 Elastic vs. Inelastic Demand Elastic vs. Inelastic Demand Demand is elastic if demand is very responsive to changes in price. Elastic demand: when an increase (decrease) in price causes a greater percentage decrease (increase) in quantity demanded. When demand is elastic, e d < 1. Demand is inelastic if demand is not very responsive to changes in price. 2

3 Inelastic demand: when an increase (decrease) in price causes a smaller percentage decrease (increase) in quantity demanded. When demand is inelastic, 1 < e d < 0. Perfectly Inelastic Demand is perfectly inelastic when quantity demanded does not change at all due to changes in price. i.e. consumers will buy the same amount at any price. Perfectly inelastic demand e d = 0. If a demand curve is perfectly inelastic, what will be the shape/slope? Perfectly Elastic Demand is perfectly elastic when quantity demanded changes by infinitely large amounts due to small changes in price. i.e. consumers are completely inflexible to increases in price. Perfectly elastic demand e d =. If a demand curve is perfectly elastic, what will be the shape/slope? Straight Line Demand Curve Elasticity at a single point for a straight line demand curve: e d = 1 ( ) P m Q Compute elasticities at each point: Last name A-D: compute point A. Last name E-I: compute point B. Last name J-N: compute point C. Last name M-P: compute point D. Last name Q-Z: compute point D. 3

4 2.3 Total Revenue Elasticity and Total Revenue If a firm increases its price, what will happen to the quantity demanded? If a firm increases its price, what will happen to total revenue? Total Revenue = (Price) x (Quantity) If demand is inelastic percentage increase in price is larger increase revenue. If demand is elastic percentage increase in quantity is larger decrease revenue. What are some goods that have extra large sales taxes? 2.4 Determinants of Elasticity Determinants of Elasticity Closeness of substitutes. If there are more substitutes available and/or if the substitutes are very similar, the demand will be more elastic. Goods that are necessities are usually inelastic. Proportion of income spent on good. Goods that require large proportions of income are more elastic. Example: doubling the price of cars vs. table salt. Time elapsed since price change. As time progresses, the good becomes more elastic. Example: gasoline. 3 More Demand Elasticities 3.1 Cross-Price Elasticity Cross-Price Elasticity Cross-Price Elasticity: measures how much the demand for one good changes in response to a change in the price of a related good. e x,y = Percentage change in demand of X Percentage change in price of Y 4

5 e x,y = % Q X % P y = Q x,2 Q x,1 Q x,ave P y,2 P y,1 P y,ave Example: Suppose the price of Coke increases from \$1 to \$1.50, and as a result, the quantity of Pepsi sold increases from 300 to 700. Substitutes vs. Complements If two goods are substitutes, the cross-price elasticity will be. If two goods are complements, the cross-price elasticity will be. The closer the relationship between the two goods, the larger will be the magnitude of the elasticity. 3.2 Income Elasticity Income Elasticity Income Elasticity: measures how much the demand for one good changes in response to a change in income. e I = Percentage change in demand of X Percentage change in income e I = % Q X % I = Q x,2 Q x,1 Q x,ave I 2 I 1 I ave Example: Suppose your income increases from \$8,000 to \$12,000 and as a result your demand for MP3s increases from 60 to 140. Types of Goods Normal goods: income elasticity is positive. Inferior goods: income elasticity is negative. Necessities: income elasticity is between 0 and 1. Luxury goods: income elasticity is greater than 1. 5

6 4 Price Elasticity of Supply 4.1 Computing Supply Price Elasticity of Supply Price Elasticity of Supply: changes in price. Price elasticity of supply = e s = % Q s % P = 4.2 Elastic and Inelastic Supply Elastic and Inelastic Supply measures how responsive supply is to Perc. Change in Quantity Supplied Perc. change in price Q 2 Q 1 Q ave P 2 P 1 P ave Inelastic supply: when the percentage change in quantity supplied is less than percentage change in price. 0 < e s < 1 Elastic supply: when the percentage change in quantity supplied is greater than percentage change in price. e s > 1 Perfectly elastic supply: when a small change in price leads to an infinitely large change in quantity supplied. Perfectly inelastic supply: when quantity supplied does not change in response to changes in price. 4.3 Determinants of Supply Elasticity Determinants of Supply Elasticity Resource substitution possibilities: items that require unique factors of production have an inelastic supply. Time since price change: Very short run: immediately following a change in price, sometimes supply cannot be changed at all perfectly inelastic supply. Short-run: some technological changes and substitutions are possible supply becomes more elastic. Long-run: long enough for all technological changes and substitutions possible. Could involve: building or destroying new factories, entire industries, educating populations, etc. 6

7 5 5.1 What We Have Learned Measure how responsive demand is to changes in price: price elasticity of demand. Measure how substitutable goods are: cross-price elasticity. Measure how demand responds to income: income elasticity. Measure how responsive supply is to changes in price: price elasticity of price. Learned what can influence elasticity. Learned implications for total revenue. 7

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### 3. CONCEPT OF ELASTICITY

3. CONCET OF ELASTICIT The quantity demanded of a good is affected mainly by - changes in the price of a good, - changes in price of other goods, - changes in income and c - changes in other relevant factors.