Chapter 6 Elasticity


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1 Goldwasser AP Microeconomics Chapter 6 Elasticity BEFORE YOU READ THE CHAPTER Summary This chapter develops the concept of elasticity, which provides a numerical measure of the responsiveness of quantity to changes in prices or income. The price elasticity of demand measures the responsiveness of the quantity demanded to changes in the price of the good, while the price elasticity of supply measures the responsiveness of the quantity supplied to changes in the price of the good. Income elasticity of demand measures the responsiveness of the quantity demanded to changes in income. Crossprice elasticity of demand measures the responsiveness of the quantity demanded to the changes in the price of another good. This chapter also discusses the factors that influence these elasticities. Chapter Objectives Objective #1. The price elasticity of demand measures the responsiveness of the percentage change in quantity demanded to the percentage change in the price of the good. Thus, the price elasticity of demand can be written as Since demand curves typically slope downward, a positive change in price (i.e., a price increase) results in a negative change in the quantity demanded (i.e., a decrease in quantity demanded). Thus, the price elasticity of demand is usually a negative number. By convention, economists measure the price elasticity of demand in absolute value terms so that negative sign is eliminated. A. The calculations of the percentage change in the quantity demanded of good X can be found using the formula B. The calculation of the percentage change in the price of good X can be found by using the formula
2 C. To generate consistent measures for price elasticities, regardless of an increase or decrease in price, economists calculate the percentage changes using the midpoint method. For example consider two points on a demand curve: (Q 1,P 1 ) and (Q 2,P 2 ). The percentage change in quantity demanded using the midpoint method can be expressed as While the percentage change in price is expressed as Using these two formulas, the price elasticity of demand formula using the midpoint method can be written as Objective #2. Consider a numerical example illustrating the mathematical relationships described in Objective 1. Suppose the demand curve for good X is given by the equation P = Q and you are asked to compute the price elasticity of demand when the quantity increases from 80 units to 90 units on this demand curve. First you need to calculate the price demanders are willing to pay when the quantity demanded is equal to 90 units: this price is $10. Then, you need to calculate the price demanders are willing to pay when the quantity demanded is equal to 80 units: this price is $20. Figure 6.1 below provides a graph of this demand curve with point A on the demand curve corresponding to a price of $10 and a quantity demanded of 90 units and point B on the demand curve corresponding to a price of $20 and a quantity of 80 units.
3 Using this information, you can then calculate the percentage change in the quantity demanded of good X and the percentage change in the price of good X using the midpoint method. Thus, The percentage change in the quantity demanded of good X = [(8090)/2]/[( )/2] x 100 =5.9 The percentage change in the price of good X = [(2010)/2]/[( )/2] x 100 = 33.2 To find the price elasticity of demand, take the absolute value of the percentage change in the quantity demanded of good X divided b the percentage change in the price of good X. Thus, The price elasticity of demand = 5.9/33.3 =.18 Suppose that the price had originally been $10 and that the price had increased to $20. Does the price elasticity of demand change if you move from along the demand curve from the point (90, 10) to the point (80, 20)? The midpoint method of calculating the price elasticity of demand insures that the calculation of elasticity does not depend upon the direction of movement along the demand curve from one point to another. To see this recalculate the price elasticity of demand moving from point B to point A. The percentage change in the quantity demanded of good X = [(90 80)/2]/ [(90 +80)/2] x 100 = 5.9 The percentage change in the price of good X = [(1020)/2] / [( )/2] x 100 = To find the price elasticity of demand, take the absolute value of the percentage change in the quantity demanded of good X divided by the percentage change in the price of good X. Thus, The price elasticity of demand = 5.9/33.3 =.18 The midpoint method of calculating the price elasticity of demand results in the price elasticity of demand being the same whether we move from point A to point B or from point B to point A. Objective #3. A vertical demand curve indicates that the quantity demanded is completely unresponsive to price changes. A vertical demand curve is perfectly inelastic and its measure of price elasticity of demand equals zero. Objective #4. A horizontal demand curve indicates that the quantity demanded is extremely responsive to price changes: even a small increase in price results in demand dropping to zero units, while a small decrease in price results in an extremely large increase in the quantity demanded. A horizontal demand curve is perfectly elastic and its measure of price elasticity of demand equals infinity.
4 Objective #5. A large value for the price elasticity of demand indicates that consumers are highly responsive to price changes in the price of the good. Referring to the formula for the price elasticity of demand (the general formula given in Objective 1), a price elasticity of demand value that is greater than one implies that the percentage change in the quantity demanded in absolute value terms is greater than the percentage change in the price of the good in absolute value terms. When the price elasticity of demand is greater than one, demand is elastic. Objective #6. A small value for the price elasticity of demand indicates that consumers are less responsive to changes in the price of the good. A price elasticity of demand value that is less than one implies that the percentage change in the quantity demanded in absolute value terms is less than the percentage change in the price of the good in absolute value terms. Thus, when price changes, consumers respond with a relatively small change in the quantity of the good the demand. When the price elasticity of demand is less than one, demand is inelastic. Objective #7. When the price elasticity of demand equals one, the demand is unit elastic. A price elasticity of demand of one implies that the percentage change in the quantity demanded of good X is exactly equal to the percentage change in the price of good X in absolute value terms. Objective #8. For a straight line demand curve that intersects both the vertical and horizontal axes, the midpoint of that demand curve is the unit elastic point. Above the midpoint, demand is elastic, while below the midpoint, demand is inelastic. Figure 6.2 illustrates this idea. Objective #9. Total revenue is affected by the price elasticity of demand. If demand is inelastic, then an increase in price causes total revenue to increase. If demand is elastic, then an increase in price causes total revenue to decrease. An increase in price that moves symmetrically around the unit elastic point has no effect on total revenue.
5 Objective #10. A change in price affects total revenue in two ways: first, the price effect is the change in total revenue due to the change in the price of the good, and second the quantity effect is the change in total revenue due to the change in the number of units of the good sold. The price effect is stronger that the quantity effect when demand is inelastic; the quantity effect is stronger than the price effect when demand is elastic; and the price effect and the quantity effect exactly offset each other when demand is unit elastic. A. Figure 6.3 illustrates the effect on total revenue of an increase in price when demand is relatively inelastic. Starting at point E, total revenue is initially P 1 Q 1 or the sum of the areas B and A. When price increases to P 2 (point F), total revenue changes to P 2 Q 2, or the sum of areas C and B. In this example, area A represents the quantity effect, while area C represents the price effect. When price increases, that quantity effect on total revenue is negative while the price effect on total revenue is positive, with the price effect dominating the quantity effect and leading to an increase in total revenue. B. Figure 6.4 illustrates the effect on total revenue of an increase in price when demand is relatively elastic. When demand is elastic, the effect on total revenue of the quantity effect (area A) is larger thank the price effect (area C).
6 C. The table below summarizes the relationship between the price elasticity of demand and the effect of changes in price on total revenue, the price effect, and the quantity effect. Demand Price Total Revenue Price effect Quantity Effect Elastic Increases Decreases Dominates Elastic Decreases Increases Dominates Inelastic Increases Increases Dominates Inelastic Decreases Decreases Dominates Unit elastic Increases No effect Exactly offsets quantity effect Exactly offsets price effect Unit elastic Decreases No effect Exactly offsets quantity effect Exactly offsets price effect Objective #11. Price elasticity of demand is affected by the number of available substitutes, whether the good is a necessity or a luxury, and the time period for adjustment to the price change. Demand is more elastic when there are close substitutes, when the good is a luxury, and/or when there is more time to adjust to the price change. Demand is less elastic when there are no close substitutes, when the good is a necessity, and/or when there is little time to adjust to the price changes. Objective #12. The crossprice elasticity of demand between goods A and B is equal to the percentage change in the quantity demanded of good A divided by the percentage change in the price of good B. That is, Cross price elasticity of demand may be a positive or negative number, and the sign of the crossprice elasticity of demand is critical to the interpretation of the meaning of a particular crossprice elasticity value. A positive crossprice elasticity of demand indicates that good A and good B are substitutes: if the price of good B increases, this leads to an increase in the quantity of good A demanded. A negative cross price elasticity of demand indicates that good A and good B are complements: if the price of good B increases, this leads to a decrease in the quantity of good A demanded. Objective #13. The income elasticity of demand is equal to the percentage change in the quantity demanded of the good divided by the percentage change in income. That is, Income elasticity of demand may have either a positive or a negative value. A positive income elasticity of income value indicates that income and the quantity demanded move in the same direction: an increase in income leads to an increase in the quantity demanded, and thus the good is a normal good. A negative income elasticity of demand value indicates an inferior good: as income increases, the quantity of the good demanded decreases. A. A good that is income elastic has an income elasticity of demand that is greater than one. When income increases, demand for incomeelastic goods rises faster than income. Luxury goods tend to be income elastic. B. Income elastic goods have income elasticities of demand that are positive but less than one. When income increases, demand for incomeinelastic good rises slower than income. Necessities tend to be income inelastic.
7 Objective #14. The price elasticity of supply is defined as the percentage change in the quantity supplied of good A divided by the percentage change in the price of good A. TO get consistent measures of the price elasticity of supply, the percentage changes in quantity supplied and price are both calculated by using the midpoint method. Thus the price elasticity of supply can be expressed as Or, for two points (Q 1,P 1 ) and (Q 2,P 2 ) on a supply curve A. A vertical supply curve has a price elasticity of supply equal to zero and is an example of a perfectly inelastic supply. B. A horizontal supply curve has a price elasticity of supply to infinity and is an example of a perfectly elastic supply curve. Objective #15. The price elasticity of supply is affected by the availability of inputs and the time period for adjustment. Supply is the more price elastic the great the availability of inputs and/or in the long run when full adjustment to price has occurred. Key Terms Notes price elasticity of demand the ratio of the percentage change in the quantity demanded to the percent change in the price as we move along the demand curve (dropping the minus sign). midpoint method a technique for calculating the percentage change in which changes in a variable are compared with the average, or midpoint, of the starting and final values. perfectly inelastic demand the case in which the quantity demanded does not respond to at all to changes in the price, the demand curve is a vertical line. perfectly elastic demand the case in which any price increase will cause the quantity demanded to drop to zero, the demand curve is a horizontal line.
8 elastic demand when the price elasticity of demand is greater than 1. inelastic demand when the price elasticity of demand is less than 1. unitelastic demand the case in which the price elasticity of demand is exactly 1 total revenue the total value of sales of a good or service (the price of the good or service multiplied by the quantity sold). cross price elasticity of demand a measure of the effect of the in this price of one good on the quantity demanded or the other: it is equal to the percentage change in the quantity demanded on one good divided by the percent change in the price in the price of another good. Income elasticity of demand the percent change in the quantity of a good demanded when a consumer s income changes divided by the percent change in the consumer s income Incomeelastic demand when the income elasticity of demand for a good is greater than 1. Incomeinelastic demand when the income elasticity of demand for a good is positive but less than 1. price elasticity of supply a measure of the responsiveness of the quantity of a good supplied to the price of that good; the ratio of the percentage change in the quantity supplied to the percent change in the price as we move along the supply curve. perfectly inelastic supply the case in which the price elasticity of supply is zero, that that the changes in the price of the good have no effect on the quantity supplied; the perfectly inelastic supply curve is a vertical line. perfectly elastic supply the case in which even a tiny increase or reduction in the price will lead to very large changes in the quantity supplied, so that the price elasticity of supply is infinite; the perfectly elastic supply curve is a horizontal line.
9 AFTER YOU READ THE CHAPTER Tips Tip #1 Economists calculate a variety of elasticities because this measures provide important insights into the relationship between two different variables. All elasticities are calculated as the ratio between the percentage changes in quantity (either the quantity demanded of the quantity supplied) to the percentage change in some other related variable. Elasticities are unitfree, making them an ideal measure of sensitivity of one variable to changes in another variable. In general, we can think of elasticity as being defined as Tip #2 In general, to find the percentage change in a variable requires dividing the change in the variable by its initial value and then multiplying this value by 100. That is Tip #3 The midpoint method is used in calculating the price elasticity of demand and the price elasticity of supply. This method modifies the formula given in Tip 2 so that the results of the elasticity calculation provide a measure that is not dependent on which point on the demand or supply curve is designated the initial point. Objective 1C provides the formula for the midpoint method of calculating the price elasticity of demand, and Objective 13 provides the formula for the price elasticity of supply. Tip #4 Total revenue is equal to the price per unit times the quantity. Total revenue at any given price is equal to the area of a rectangle whose height is the price and whose width is the quantity demanded at this price. Figure 6.5 illustrates this concept of total revenue for the given demand curve.
10 At point A, the price is P 1 and the quantity demanded is Q 1. The total revenue for the firm when the price equals P 1 is P 1 x Q 1 (the shaded area in the graph). Tip #5 For a given demand curve, a change in price causes total revenue to change because of two effectsthe price effect and quantity effect. Figure 6.6 illustrates these effects. Suppose we are initially at point A with price P 1 and quantity Q 1. Then total revenue equals P 1 Q 1, or the sum of the areas C and D. If price decreases to P 2, then this causes a movement along the demand curve to point B with price P 2 and quantity Q 2. Total revenue is now equal to P 2 Q 2, or the sum of the areas D and E. The price effect on total revenue is measured by area C: it reflects the change in revenue (in this case a loss in revenue) that arises from selling the original quantity of Q 1 for the new price of P 2 instead of the initial price of P 1. The quantity effect on total revenue is measured by area E: it reflects the change in total revenue (in this case a gain in revenue) that arises from selling an additional Q 2 Q 1 units of the good at the new price P 2. A similar argument holds for increases in price: you will find it helpful to redo this example starting at point B and moving to point A and thinking about this price and quantity effects.
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