ELASTICITY: A MEASURE OF RESPONSE Elasticity is the ratio of the percentage change in a dependent variable to the percentage change in an independent variable $100 90 -20 A 80 Price per unit 70 60 -10 +10 +20 B 50 40 Demand 30 20 10 190 Quantity per period 180 130 80 60 0 Calculating Elasticities ep = percentage change in quantity demanded percentage change in price WRINKLE #1 ep = = 60 - 40 ep = 40 - 60 60 70 - 80 80 60 80 - 70 70 50 = 14.3 -12.5 = -4 -33.3 = - 2.3 Calculating Elasticities Arc elasticity is computed by calculating percentage changes relative to the average value of each variable between two points. A to B B to A Q 20 -20 ep = Q P = (60+40)/2 = -10 P 10 (80+70)/2 = -3 (60+40)/2 (80+70)/2 = -3 Price Elasticities Along the Demand Curve WRINKLE #2 The price elasticity of demand varies between different pairs of points along a linear demand curve. The higher the price and the lower the quantity demanded, the greater the absolute value of the price elasticity of demand. 20 20 $100 90 80 ep = Price per unit 50 40 ep = = -3.0 A = -1.0 -10 -10 (55+45)/2 (80+70)/2 70 60 (90+110)/2 (60+40)/2 20 B (140+160)/2 C ep = = -0.3 D -10 (30+20)/2 30 E 20 F 10 190 0 Quantity per period Price Elasticity of Demand and Changes in Total Spending • If the absolute value of the price elasticity of demand > 1 demand is price elastic. • If the absolute value of the price elasticity of demand = 1 demand is unit price elastic. • If the absolute value of the price elasticity of demand < 1 demand is price inelastic. Price Elastic Price Total Spending Price Total Spending Price Inelastic Price Total Spending Price Total Spending When the price of a good or service changes, the quantity demanded changes in the opposite direction (law of demand). Total spending will move in the direction of the variable that changes by the larger percentage. If quantity demanded changes by a larger percentage than price, total spending will change in the direction of the quantity change [demand is price elastic]. When a change in price results in a smaller percentage change in quantity demanded [demand is price inelastic], total spending will move in the direction of the price change. Two Examples: Gasoline: Orange Juice: Suppose that 1,000 gallons per day are demanded at $1.25/gallon. Total spending equals $1,250 per day. But if the price increases to $1.40, the quantity demanded decreases to 950 gallons. What is total spending? Suppose that 1,000 cans of frozen orange juice per month are demanded at $1.00/can. Total spending equals $1,000 per month. But if the price increases to $1.10, the quantity demanded decreases to 880 cans. What is total spending? ep = -50 975 -5.13% = 11.32% = -0.45 0.15 1.325 Price Inelastic ep = -120 940 -12.77% = 9.52% = -1.45 0.10 1.05 Price Elastic Changes in Total Spending and a Linear Demand Curve Elastic region $100 Moving from point s A to B implies a reduction in price and an increase in quantity demanded. Demand is elastic between these two points. Total spending, indicated by the red rectangle, rises. When we move from points E to F, which is the region of inelastic demand, total spending falls. 80 70 A Price per unit B C Unit elastic demand Inelastic region 30 E 20 F 190 60 0 Quantity per period The demand curve below is given by the equation Q = 1-/P. The equation yields the combinations of prices and quantities shown in the table. The price elasticity of demand can be calculated between any two points on the demand curve. What can you note about the price elasticity of demand in this example? Point A B C D E F G H I J Price $10 9 8 7 6 5 4 3 2 1 Quantity 1.00 1.11 1.25 1.43 1.67 2.00 2.50 3.33 5.0 10 A 0.11 (1.11 + 1.00)/2 10 B ep = 9 = -1.0 -1 8 Price per unit 7 C 0.33 (10 + 9)/2 (2.00+ 1.67)/2 D ep = = -1.0 6 -1 E 5 (6 + 5)/2 F 4 5 G (10.00 + 5.00)/2 3 ep = H 2 -1 I 1 0 J 1 2 3 4 = -1.0 5 6 7 8 9 10 (2 + 1)/2 Quantity per period Here elasticity of price demand is constant and is unit price elastic. Notice that total spending (TS), as given by the red, green, and magenta rectangles, is always the same. Indeed, the area of a rectangle drawn from any point on this demand curve will equal $10. A price change does not affect total spending when demand is unit price elastic. 10 A TS = $10 5 F J 1 1 2 10 Determinants of the Price Elasticity of Demand The greater the absolute value of the price elasticity of demand, the greater the responsiveness of quantity demanded to changes in price. Depending on whether demand is relatively elastic, unit elastic, or relatively inelastic, total spending may fall, remain unchanged, or rise in response to a price change. What determines whether demand is relatively more or less elastic? •Availablity of substitutes •Importance in Household Budgets •Time CHANGES IN TOTAL SPENDING AS A RESULT OF A SHIFT IN DEMAND $100 The shift in demand depicted here by the change from D to D’ results in the following changes in total spending: From Point B to B’, TS = ($70 x 60) - ($70 x 20) = $2,800 80 From Point E to E’, TS = ($30 x 140) - ($30 x 100) = $1,200 A 70 B’ B C D 30 E’ D E F D’ 190 60 0 P When the percentage changes in quantity demanded are very great relative to percentage changes in price, we may say that demand is very price elastic. Q Very Price Elastic Demand P When the percentage changes in quantity demanded are very small relative to percentage changes in price, we may say that demand is very price inelastic. Q Very Price Inelastic Demand INCOME ELASTICITY OF DEMAND ey = percentage change in Q percentage change in y If ey is positive, then the demand for Good A rises as incomes rise or decreases as incomes decrease [normal good]; If ey is negative, then the demand for Good A rises as incomes decrease or decreases as incomes rise [inferior good]. CROSS PRICE ELASTICITY OF DEMAND ecp = percentage change in QA percentage change in PB If ecp is positive, then the quantity demanded of Good A rises as the price of Good B rises or decreases as the price of Good B decreases [substitutes]; If ecp is negative, then the quantity demanded of Good A falls as the price of Good B rises or rises as the price of Good B decreases [complements].