Elasticity of Demand and Supply Chapter 5 Elasticity of Demand and Supply © 2006 Thomson/South-Western

Price Elasticity of Demand Price elasticity of demand measures how responsive consumers are to price change; elasticity is another word for responsiveness Price elasticity of demand = Percentage change in quantity demanded / Percentage change in price

Exhibit 1: Demand Curve for Tacos For the price elasticity to be a useful measure, we should come up with the same result between points a and b as we get between b and a. To do this we must take the average of the initial price and the new price and use that as the base in computing the percent change in price $1.10 a Price 0.90 b D 95 105 Thousands per day Price elasticity between a and b = 10% / - 20% = - 0.5

Price Elasticity of Demand Generalize the price elasticity formula

Price Elasticity of Demand Because the average quantity and average price are used as a base for computing percent change, the same elasticity results whether going from the higher price to the lower price or the other way around Since the focus is on the percent change, we need not be concerned with how output or price is measured

Price Elasticity of Demand Because price and quantity demanded are inversely related, the price elasticity of demand has a negative sign This tends to be cumbersome, thus it is commonplace to discuss the price elasticity of demand as an absolute value  positive number For example, absolute value of the elasticity for tacos computed earlier will be referred to as 0.5 rather than –0.5

Categories of Price Elasticity Three general categories Percent change in quantity demanded is smaller than the percent change in price, the price elasticity has an absolute value between 0 and 1.0  demand is inelastic  quantity demanded is relatively unresponsive to a change in price Percent change in quantity demanded just equals the percent change in price  a price elasticity with an absolute value of 1.0  unit-elastic demand Percent change in quantity demanded exceeds the percent change in price, the price elasticity has an absolute value exceeding 1.0  demand is said to be elastic  quantity is responsive to changes in price

Elasticity and Total Revenue Total revenue (TR) is the price (p) multiplied by the quantity demanded (q) at that price  TR = p x q What happens to total revenue when price decreases? Lower price  producers get less for each unit sold  total revenue declines Lower price  increases quantity demanded  total revenue increases Overall impact of lower price on total revenue depends on the net result of these opposite effects

Elasticity and Total Revenue When demand is elastic, the percent increase in quantity demanded exceeds the percent decrease in price  total revenue increases When demand is unit elastic, the two are equal  total revenue remains unchanged When demand is inelastic, the percent increase in quantity demanded is more than offset by the percent decrease in price  total revenue decreases

Exhibit 2: Demand, Price Elasticity and Total Revenue

Exhibit 2: Demand, Price Elasticity and Total Revenue (a) Demand and Price Elasticity $100 Panel (a) shows the linear demand curve and panel (b) shows the total revenue generated by each price-quantity combination along the demand curve Because the demand curve is linear, its slope is constant: a given decrease in price always causes the same unit increase in price However, the price elasticity of demand is larger on the high end of the demand curve than it is on the low price end 90 80 70 60 50 Price per unit 40 30 20 10 D 100 200 500 800 900 1,000 Quantity per period (b) Total Revenue TR = p x q $25,000 T o t a l r e v n u Total revenue 500 1,000 Quantity per period

Exhibit 2: Demand, Price Elasticity and Total Revenue Consider a movement from point a to point b on the demand curve. The 100-unit increase in quantity demanded is a percent change of 100/150 = 0.67% while the $10 drop in price is a percent change of 10/85 = 12%  the price elasticity of demand here is 5.6 Between points d and e, the 100 quantity increase is a 12% change and the $10 price decrease is a 67% price decrease  price elasticity of 0.2 (a) Demand and Price Elasticity $100 90 a 80 b 70 60 50 c 40 30 Price per unit 20 d 10 e D 100 200 500 800 900 1,000 Quantity per period

Exhibit 2: Demand, Price Elasticity and Total Revenue (a) Demand and Price Elasticity $100 When demand is elastic, a decrease in price (from a to b) will increase total revenue because the gain in revenue from selling more units (blue box) exceeds the loss in revenue from selling all units at a lower price (red box) When demand is elastic, a price decrease (from d to e) reduces total revenue because the gain in revenue from selling more units (blue box) is less than the loss in revenue at the lower price (red box) 90 a Elastic ED > 1 80 b 70 60 Unit elastic ED = 1 50 c Price per unit 40 Inelastic ED < 1 30 20 d 10 e D 100 200 500 800 900 1,000 Quantity per period (b) Total Revenue TR = p x q $25,000 T o t a l r e v n u Total revenue 500 1,000 Quantity per period

Exhibit 3: Constant Elasticity Demand Curves (a) Perfectly elastic demand curve (b) Perfectly inelastic demand curve (c) Unit elastic demand curve D' t i t n i i t n n u ¥ u u E = 1 r D e E = r r e e p D p D p p e E = e D e c c c $10 a r i i r i r P P P b 6 D" Quantity Q Quantity 0 60 100 Quantity per period per period per period This demand curve indicates consumers will demand all that is offered at the given price, p. If the price rises above p, quantity demanded drops to zero. This demand curve indicates that quantity demanded does not vary when the price changes; no matter how high the price, consumers will purchase the same quantity. This demand curve is unit-elastic everywhere: any percent change in price results in an identical offsetting percent change in quantity demanded.

Availability of Substitutes The greater the availability of substitutes for a good and the closer the substitutes, the greater the good’s price elasticity of demand The number and similarity of substitutes depend on how we define the good  the more broadly we define a good, the fewer the substitutes and the less elastic the demand

Proportion of Consumer’s Budget Because spending on some goods represents a large share of the consumer’s budget, a change in the price of such a good has a substantial impact on the amount consumers are able to purchase Generally, the more important the item is as a share of the consumer’s budget, other things constant, the greater will be the income effect of a change in price, the more price elastic will be the demand for the item

Exhibit 5: Demand Becomes More Elastic over Time Suppose the price increases from the initial price of $1.00 to $1.25. Dw shows that one week after the price increase, the quantity demanded has not changed much, from 100 to 95 After one month, Dm, it has declined to 75, and after one year, Dy, to 50 The longer the time period the larger the response to a given price change $1.25 1.00 Price per unit Dy Dm Dw 50 75 95 100 Quantity per period

Price Elasticity of Supply The price elasticity of supply measures how responsive producers are to a price change Equals the percent change in quantity supplied divided by the percent change in price Since the higher price usually results in an increased quantity supplied, the percent change in price and the percent change in quantity supplied move in the same direction  the price elasticity of supply is usually a positive number

Exhibit 7: Price Elasticity of Supply

Exhibit 7: Price Elasticity of Supply If the price increases from p to p', the quantity supplied increases from q to q‘ The price elasticity of Es is Where  q is the change in quantity supplied and  p is the change in price.

Categories of Supply Elasticity The terminology for supply elasticity is the same as for demand elasticity If supply elasticity is less than 1.0, supply is inelastic If it equals 1.0, supply is unit elastic If it exceeds 1.0, supply is elastic Exhibit 8 illustrates some special cases of supply elasticity to consider

Exhibit 8: Constant-Elasticity Supply Curves (a) Perfectly elastic (b) Perfectly inelastic (c) Unit elastic S' i t t t i i n n n S" u u u r ¥ r r E = 1 e E = e e S p S S p p $10 e p e E = e c c S c i i i r r r P P P 5 Quantity per period Quantity per period Quantity per period 10 20 Q At one extreme is the horizontal supply curve. Here producers will supply none of the good at a price below p, but will supply any amount at a price of p The most unresponsive relationship is where there is no change in the quantity supplied regardless of the price where the supply curve is perfectly vertical. Any supply curve that is a straight line from the origin such as shown above is a unit-elastic supply curve.

Determinants The responsiveness of sellers depends on how easy it is to alter output when price changes If the cost of supplying additional units rises sharply as output expands, then a higher price will elicit little increase in quantity supplied But if the marginal cost rises slowly as output expands, the lure of a higher price will prompt a large increase in output

Length of Time Supply also becomes more elastic over time as producers adjust to price changes The longer the time period under consideration, the more able producers are to adjust to changes in relative prices

Exhibit 9: Supply Becomes More Elastic over Time Sw is the supply curve when the period of adjustment is a week. Sm is the supply curve when the adjustment period is one month; supply more elastic and quantity supplied increases to 140 After one year the supply curve becomes Sy and the quantity supplied increases to 200 Quantity per period Sw Sm Sy 100 110 140 200 $1.25 Price 1.00

Income Elasticity of Demand Measures how responsive demand is to a change in income Equals the percent change in demand divided by the percent change in income Categories Goods with income elasticities less than zero are called inferior goods  demand declines when income increases

Income Elasticity of Demand Normal goods have income elasticities greater than zero  demand increases when income increases Normal goods with income elasticities greater than zero but less than 1 are called income inelastic goods  demand increases but not as much as does income Goods with income elasticity greater than 1 are called income elastic  demand not only increases when income increases but increases by more than does income

Exhibit 11: The Demand for Grain

Exhibit 12: Effect of Increases in Supply and Demand on Farm Revenue Over time, technological advances in farming have sharply increased the supply of grain In addition, increases in household income over time have increased the demand for farm products But because increases in the supply of grain have exceeded increases in demand, the combined effect has been a drop in the market price and a fall in total farm revenue S S' Price per bushel $8 4 D' D 10 14 Billions of bushels per year

Cross-Price Elasticity of Demand Since firms often produce an entire line of products, it has a special interest in how a change in the price of one product will affect the demand for another The responsiveness of the demand for one good to changes in the price of another good is called the cross-price elasticity of demand

Cross-Price Elasticity of Demand Defined as the percent change in the demand of one good divided by the percent change in the price of another good If an increase in the price of one good leads to an increase in the demand for another good, their cross-price elasticity is positive  the two goods are substitutes If an increase in the price of one good leads to a decrease in the demand for another, their cross-price elasticity is negative  the two goods are complements