# Measuring Elasticity of Demand

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1 C H A P T E R E I G H T P r i c e e l a s t i c i t y o f d e m a n d Measuring Elasticity of Demand Demand curves can have many different shapes and so it is important to derive a way to convey their shape with some precision. For example how would you describe the difference between the two following curves? P P D D Without a precise means of measuring differences you would be forced to conclude that one curve is steeper than the other. Still, people can interpret the word steeper differently. To avoid confusion about the shapes of these curves a more scientific approach should be taken. To explain the shapes of demand curves with precision refer to their price elasticity of demand or in simple terms their elasticity. Elasticity is the responsiveness of a change in one variable to a change in another. Consumers generally respond to prices changes thus economists call this measurement the price elasticity of demand. To calculate the price elasticity of demand this simple formula is used: Elasticity = the percentage change in quantity demanded divided by the percentage change in price. Putting this definition into mathematical symbols yields: E = % in d / % in P

2 Where the % in d (the numerator) is calculated by solving 2-1 / 1, and similarly the % in P (the denominator) is calculated by P2-P1 / P1. The price elasticity formula then appears as: E = 2-1 / 1 P2-P1 / P1 The P s & s in this formula represent the coordinates for two different points along a demand curve. After making the appropriate substitutions into this formula you will note that an elasticity coefficient results. Coefficients will be greater than one, less than one, or equal to one. Demand and supply curves are then named based upon their elasticity coefficients. When the coefficient is greater than one the curve is known as elastic. If the coefficient is less than one the curve is said to be inelastic. And of unitary elasticity when equal to one. While calculating elasticity is simple some caution should be exercised when working with linear demand curves. Due to the construction of the elasticity formula coefficients will vary depending upon the points selected for the calculation. Coordinates to the left of the midpoint of the line will always yield a coefficient greater than one. Based on that coefficient one would be forced to conclude that the curve is elastic. Coordinates selected to the right of the midpoint will yield coefficients less than one. This would lead to the conclusion that the curve is inelastic. Finally, coordinates selected at the midpoint will yield a coefficient equal to one and a conclusion of unitary elasticity. Thus three entirely different conclusions could be made about the shape of this one curve based on the injudicious selection of coordinates. Therefore, if the elasticity measurement is being used to convey the overall shape of a demand curve then it is important to select coordinates that are to the left and right of the midpoint. Elasticity greater than one P Elasticity = one Elasticity less than one elasticity: Given the following information draw the demand curve and calculate its

3 P Using the two extreme points in this example and substitution them into the elasticity formula yields the following steps and calculations: 1. E = 2-1 / 1 P2-P1 / P1 2. E = 54-7 / / E = 47/ 7-52/ E = E = The curve is considered to be elastic. Goods that have elastic curves show greater price sensitivity. This can be observed as you move downward to the right along a demand curve. As the price declines notice how quantity demanded rises. Now in the above case the elasticity coefficient of means that for each one percent change in price the quantity demanded changes by 12.90%. Alternatively, a ten percent change in price would yield a 67.10% change in quantity demanded. Goods with inelastic curves are said to be relatively price insensitive. In this case notice how as price increases the quantity demanded does not decrease dramatically. This means the consumer was insensitive to that price increase. The determinants of elasticity are:

4 1. Availability of substitutes the greater the number of substitutes the more price sensitive the consumer can be because more choices are available. 2. Whether they are luxuries or necessities luxuries tend to cost more making the consumer more sensitive to their price than the price of necessities. 3. What share of the budget they represent the more a product costs the more cautious we become as consumers because we have limited incomes to satisfy all our desires. There is also a measurement known as the cross elasticity of demand. This is calculated by taking the percentage change in quantity demanded of good A divided by the percentage in price of good B. This measurement is used to measure good A s sensitivity to changes in the price of good B. If the cross elasticity of demand is positive, two commodities are substitutes. If the cross elasticity is negative the commodities are complements. Using our understanding about elasticity lets examine how producers and government may use this information. Producers: The producers concern is to maximize revenues. The sum of all their revenue or total revenue (TR) is simply price times quantity (Px = TR). The question before us is at what point is total revenue for our product maximized when faced with a particular demand curve? Given the following demand schedule construct the curve, calculate its total revenue, and relate your observations to elasticity. P TR Notice that when the firm reduces its price from \$100 to \$80 that total revenue rises. Total revenue again rises when the price falls to \$60. Between \$100 and \$60 the firm is operating in the elastic portion of its demand curve. In this region consumers are price sensitive. Any decrease in price will be met with an increase in the volume of sales. Accordingly the firm reduces its price. Notice however that when the firm reduces price again to \$40 total revenue begins to fall. This implies that the firm is now operating in the inelastic portion of its demand curve. Therefore, if a firm wants to maximize its total revenue it will sell its product at the price at which elasticity of demand is equal to one. At that level of price and output no change in price can produce greater revenue. Thus firms are very concerned about how much each unit of output contributes to total

5 revenue. if an increase in output causes total revenue to increase it will be continued. If an increase in output causes total revenue to decline it is likely to be discontinued. The difference in total revenue that results from a unit change in quantity sold is called marginal revenue (MR). Using the former table we can calculate marginal revenue. P TR MR If a firm is operating in the area where MR is positive a price reduction will continue to yield greater total revenue. For firms operating in a price range where marginal revenue is negative, a price reduction will yield less total revenue TR MR Now since a firm is interested in maximizing total revenue (TR) it attempts to effect the demand curve by either shifting the demand curve outward to the right, or influencing the shape of the demand curve (making it more elastic or inelastic). Government Government is concerned about the shape of demand curves because it also must raise revenues. The revenues in this case are in the form of taxes. Government is interested in maximizing revenues but minimizing the impact of those taxes on the economy. If the government plans to impose a tax on some specific item it must consider its demand curve. Taxes imposed on luxury items (goods to which consumers are price sensitive) will increase their cost while decreasing the quantity demanded. If the quantity demanded decreases significantly then instability will enter the market. For this reason

6 you will notice that taxes are generally imposed on goods with inelastic demand curves. The price increase associated with the increased taxes in this case does not dramatically decrease the quantity demanded because the consumer is insensitive to the price increase. Slight price increases on elastic goods results in dramatic declines in quantity demanded. P8 P6 1 2 Major price increases on inelastic goods results in modest declines in quantity demanded. P8 P6 1 2

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