SOLUTIONS 2 Microeconomics ACTIVITY 2-3 Elasticity: An Introduction Student Alert: Elasticity measures the strength of your response to a change in a variable. In many circumstances, it is not enough for an economist, policymaker, firm, or consumer to simply know the direction in which a variable will be moving. For example, if I am a producer, the law of demand tells me that if I increase the price of my good, the quantity demanded by consumers will decrease. The law of demand tells me the direction of the consumer response to the price change, but it does not tell me the strength of the consumer response. The law of demand doesn’t tell me what will happen to my total revenue (the price of the good times the number of units sold). Whether total revenue increases or decreases depends on how responsive the quantity demanded is to the price change. Will total revenue increase or decrease by a little or a lot? Throughout the discipline of economics, in fact, the responsiveness of one variable to changes in another variable is an important piece of information. In general, elasticity is a measurement of how responsive one variable is to a change in another variable, ceteris paribus (holding all other variables constant). Because elasticity measures responsiveness, changes in the variables are measured relative to some base or starting point. Each variable’s change is measured as a percentage change. Consider the following elasticity measurements: The price elasticity of demand, εd percentage change in quantity demanded of Good X ε = . d percentage change in price of Good X The income elasticity of demand, εI percentage change in quantity demanded of Good X ε = . I percentage change in income The cross-price elasticity of demand, εCP percentage change in quantity demanded of Good X ε = . CP percentage change in price of Good W The price elasticity of supply, εS percentage change in quantity supplied of Good X ε = . S percentage change in price of Good X Advanced Placement Economics Microeconomics: Teacher Resource Manual © Council for Economic Education, New York, N.Y. 203 CEE-APE_MACROSE-12-0101-MITM-Book.indb 203 26/07/12 5:25 PM SOLUTIONS 2 Microeconomics ACTIVITY 2-3 (CONTINUED) Part A: Bonus Pay at Work 1. You have a job stocking items on the shelves at the local home improvement store. To increase productivity, your boss says a bonus will be paid based on how many items you put on the shelves each hour. Write the equation of the “elasticity of productivity” for this situation: percentage change in number of items stocked ε = . productivity percentage change in pay 2. Assume your boss wants you to double your output, which would be a 100 percent increase in the number of items you shelve each hour. Underline the correct answer in each of these statements. (A) If your productivity is very responsive to a pay increase, then a given increase in your pay results in a large increase in your hourly output. In this case, your boss will need to increase the bonus pay by (more than / less than / exactly) 100 percent. (B) If your productivity is not very responsive to a pay increase, then a given increase in your pay results in a small increase in your hourly output. In this case, your boss will need to increase the bonus pay by (more than / less than / exactly) 100 percent. Part B: The Price Elasticity of Demand It’s easy to imagine that there are many applications for the elasticity concept. Here we will concentrate on the price elasticity of demand for goods and services. For convenience, the measure is repeated here: percentage change in quantity demanded of Good X ε = . d percentage change in price of Good X Note the following points: ■ Price elasticity of demand is always measured along a demand curve. When measuring the responsiveness of quantity demanded to a change in price, all other variables must be held constant. ■ Because of the law of demand, which states that price and quantity demanded move in opposite directions, when you calculate the value of the price elasticity of demand, expect it to be a negative number. When we interpret that value, we consider the absolute value of εd. ■ Along a linear, downward sloping demand curve, there are price ranges over which demand is elastic, unit elastic, and inelastic. 204 Advanced Placement Economics Microeconomics: Teacher Resource Manual © Council for Economic Education, New York, N.Y. CEE-APE_MACROSE-12-0101-MITM-Book.indb 204 26/07/12 5:25 PM SOLUTIONS 2 Microeconomics ACTIVITY 2-3 (CONTINUED) Table 2-3.1 Relationship between Changes in Quantity Demanded and Price %DQd compared to %DP Absolute value of εd Interpretation %DQd > %DP > 1 Elastic %DQd = %DP = 1 Unit elastic %DQd < %DP < 1 Inelastic Part C: Calculating the Arc Elasticity Coefficient The arc elasticity calculation method is obtained when the midpoint or average price and quantity are used in the calculation. This is reflected in the formula below. QQ2 – 1 ∆Q percentage change inquantity demanded ()QQ2 + 1 / 2 (QQ2 + 1 ) / 2 εd = = = . perrcentage change in price PP– ∆P 2 1 PP+ / 2 + P / 2 ()2 1 ()P2 1 theactualchangeinQ theaverage valueeofQ εd = . theactualchangeinP theaveeragevalue of P Suppose in Figure 2-3.1 that price is decreased from P1 to P2 and so quantity demanded increases from Q1 to Q2. Figure 2-3.1 Calculating the Arc Elasticity Coefficient P1 PRICE P2 D Q1 Q2 QUANTITY Advanced Placement Economics Microeconomics: Teacher Resource Manual © Council for Economic Education, New York, N.Y. 205 CEE-APE_MACROSE-12-0101-MITM-Book.indb 205 26/07/12 5:25 PM SOLUTIONS 2 Microeconomics ACTIVITY 2-3 (CONTINUED) Because price decreased, our calculations will show the percentage change in price is negative. Because quantity demanded increased, the percentage change in quantity demanded is positive. The ratio of the two percentage changes thus will have a negative value. When we interpret the calculated value of εd, we consider its absolute value in deciding whether demand over this price range is elastic, unit elastic, or inelastic. Note that we have used the average of the two prices and the two quantities. We have done this so that the elasticity measured will be the same whether we are moving from Q1 to Q2 or the other way around. Part D: Coffee Problems Suppose Moonbucks, a national coffee-house franchise, finally moves into the little town of Middleofnowhere. Moonbucks is the only supplier of coffee in town and faces the weekly demand schedule as shown in Table 2-3.2. Answer the questions that follow. Table 2-3.2 Cups of Coffee Demanded per Week Price (per cup) Quantity demanded Price (per cup) Quantity demanded $10 0 $4 120 $9 20 $3 140 $8 40 $2 160 $7 60 $1 180 $6 80 $0 200 $5 100 3. What is the arc price elasticity of demand when the price changes from $1 to $2? –0.18 ()160 – 180 –20 ()160 + 180 /2 –111.8% ε = ==170 =.–0.18 d ($2.00 – $1.00) +$1.00 +66.7% ()$2.00 + $1.00 /2 $1.50 So, over this range of prices, demand is (elastic / unit elastic / inelastic). 4. What is the arc price elasticity of demand when the price changes from $5 to $6? –1.22 ()80 – 100 –20 ()80 +100 /2 –22.22% ε = ==90 =.–1.22 d ()$6.00 – $5.00 +$1.00 +18.2% ($$6.00 + $5.00) /2 $5.50 So, over this range of prices, demand is (elastic / unit elastic / inelastic). 206 Advanced Placement Economics Microeconomics: Teacher Resource Manual © Council for Economic Education, New York, N.Y. CEE-APE_MACROSE-12-0101-MITM-Book.indb 206 26/07/12 5:25 PM SOLUTIONS 2 Microeconomics ACTIVITY 2-3 (CONTINUED) Part E: Comparing Slope and Price Elasticity of Demand Now, consider Figure 2-3.2, which graphs the demand schedule given in Table 2-3.2. Recall that the slope of a line is measured by the rise over the run: slope = rise / run = DP / DQ. Figure 2-3.2 Elasticity of Demand for Coffee 10 9 8 7 6 5 PRICE 4 3 2 Demand 1 0 20 40 60 80 200 100 120 140 160 180 QUANTITY 5. Using your calculations of DP and DQ from Question 3, calculate the slope of the demand curve between the prices of $1 and $2. ∆P $2 –$1 +$1 Slope = = = =–0.05. ∆Q 160 – 180 –20 6. Using your calculations of DP and DQ from Question 4, calculate the slope of the demand curve between the prices of $5 and $6. ∆P $6 –$5 +$1 Slope = = = =–0.05. ∆Q 80 – 100 –20 7. The law of demand tells us that an increase in price results in a decrease in the quantity demanded. Questions 5 and 6 remind us that the slope of a straight line is constant everywhere along the line. Anywhere along this demand curve, a change in price of $1 generates a change in quantity demanded of 20 cups of coffee a week. You’ve now shown mathematically that while the slope of the demand curve is related to the price elasticity of demand, the two concepts are not the same thing. Briefly discuss the relationship between where you are along the demand curve and the price elasticity of demand. How does this tie into the notion of responsiveness? The unit change in Q in response to a given dollar change in P will be the same all along a downward-sloping, straight-line demand curve because the curve has constant slope.