# Mr Sydney Armstrong ECN 1100 Introduction to Microeconomics Lecture Note (4) Price Elasticity of Demand

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1 Mr Sydney Armstrong ECN 1100 Introduction to Microeconomics Lecture Note (4) Price Elasticity of Demand The law of demand tells us that consumers will buy more of a product when its price declines and less when its price increases. But how much more or less will they buy? The amount varies from product to product and over different price ranges for the same product. The responsiveness (or sensitivity) of consumers to a price change is measured by a product s price elasticity of demand. For some products for example restaurant meals, consumers are highly responsive to price changes. Moderate price changes cause very large changes in quantity purchased. Economists say that the demand for such products is relatively elastic or simply elastic. For other products like salt for example, consumers pay less attention to price changes. Substantial price changes causes only small changes in the amount purchased. The demand for such products is relatively inelastic or simply inelastic. The Price Elasticity Coefficient and Formula (point) Economists measure the degree of price elasticity or inelasticity of demand with the coefficient Ed, defined as: Ed = % change in quantity demanded/ % change in Price Elimination of the minus Sign We know from the down sloping demand curve that price and quantity demanded are inversely related. Thus the price elasticity coefficient of demand Ed will always be a negative number. As an example, if price declines, then quantity demanded will increase. This means that the numerator in our formula will be positive and the denominator negative, giving us a negative Ed. For an increase in price, the numerator will be negative but the denominator positive; again yielding a negative Ed. Economists usually ignore the minus sign and simply present the absolute value of the elasticity coefficient to avoid the ambiguity that might otherwise arise. It can be confusing to say that an Ed of -4 is greater than one of -2. This possible confusion is avoided when we say an Ed of 4 reveals greater elasticity than one of 2. This confusion however does not exist with supply because price and quantity supply are positively related.

2 Interpretations of Ed We can interpret the coefficient of price elasticity of demand as follows. Elastic Demand- Demand is elastic if a specific percentage change in price results in a larger percentage change in quantity demanded. Then E d will be greater than 1. Example: suppose that a 2 percent decline in the price of bread results in a 4 percent increase in the quantity demanded. Then demand for bread is elastic and: Ed = 4/2= 2 Inelastic Demand- If a specific percentage change in price produces a smaller percentage change in quantity demanded, demand is inelastic. Then E d will be less than 1. Example: suppose that a 2 percent decline in the price of coffee leads to only a 1 percent increase in quantity demanded. Then demand is inelastic and: Ed = 1/2= 0.5 Unit Elastic- The case separating elastic and inelastic demand occurs where a percentage change in price and resulting percentage change in quantity demanded are the same. Example: suppose that a 2 percent drop in the price of chocolate causes a 2 percent increase in quantity demanded. This special case is termed unit elasticity because Ed is exactly equal to 1 or unity. In this example, Ed = 2/2=1 Extreme Cases- When we say that demand is inelastic, we do not mean that consumers are completely unresponsive to a price changes. In an extreme situation where a price change result in no change whatsoever in the quantity demanded, economists say that demand is perfectly inelastic. The price elasticity coefficient is zero because there is no response to a change in price. Approximate example includes health care. A line parallel to the vertical axis such as in graph (A) below shows perfectly inelastic demand. Conversely, when we say demand is elastic, we do not mean that consumers are completely to a price change. In the extreme case where a small price reduction causes buyers to increase their purchase from zero to all they can obtain, the elasticity coefficient is infinite and economists say demand is perfectly elastic. A line parallel to the horizontal axis such as the one shown in graph (B) indicates perfectly elastic demand an example would be transportation.

3 Graph A Price D Qo Quantity Refinement: Midpoint Formula (Arc) Ed = change in quantity Change in price. sum of quantities/2 sum of prices/2 Determinants of Price Elasticity of Demand We cannot say just what determine the price elasticity of demand in each individual situation. However the following generalizations are often helpful. The number of substitutes: Generally, the larger the number of substitutes a product has, the greater the price elasticity of demand for that product. The Proportion of the consumer s income spent on the product: Other things equal, the higher the price of a good relative to consumers incomes, the greater the price elasticity of demand. A 10% increase in the price of a relatively low-price pencils or chewing gums amounts to a few cents and quantity demanded will probably decline only slightly. Thus, price elasticity for such low-priced items tends to be low. But a 10% increase in the price of relatively high-priced automobiles or housing means additional expenditures of perhaps \$10 to 20 thousand respectively. These price increases are significant fractions of the annual incomes and budgets of most families, and quantity demanded will likely diminish significantly. Price elasticity for such items tends to be high. Luxuries versus Necessities: In general, the more that a good is considered to be a luxury rather than necessities, the greater is the price elasticity of demand. Bread and electricity are

4 generally regarded as necessities; it is difficult to get along without them. A price increase will not significantly reduce the amount of bread consumed or the amount of lighting and power used in a household. On the other hand, travel vacation and jewelry are luxuries, which, by definition can easily be foregone. If the prices of travel vacations and jewelry rise, a consumer need not buy them and will suffer no great hardship without them. Time: Generally, Product demand is more elastic the longer the time period under consideration. Consumers often need time to adjust to change in prices. For example, when the price of a product rises, it takes time to find and experiment with other products to see if they are acceptable. Consumers may not immediately reduce their purchases very much when the price of beef rises by 10 percent, but in time they may shift to chicken or fish. Price Elasticity of Demand and Total Revenue The importance of elasticity for firms relates to the effect of price changes on total revenue and thus on profits (total revenue less total cost). Total Revenue (TR) is the total amount the seller receives from the sale of a product in a particular time period; it is calculated by multiplying the product price (P) by the quantity demanded and sold (Q). That is: TR = P*Q Total revenue and the price elasticity of demand are related. Indeed, perhaps the easiest way to infer whether demand is elastic or inelastic is to employ the total-revenue test, which looks at what happens to total revenue when product price changes. Elastic Demand: if demand is elastic, a decrease in price will increase total revenue. Even though a lesser price is received per unit, enough additional units are sold to more than make up for the lower price. If price is \$8 and Quantity demanded is 1000 units then total revenue would be \$8000. That is TR=8*1000= \$8000 If however price declines from \$8 to \$7 and the quantity demanded increase from 1000 to 2000 units then total revenue would be \$ That is TR =7*2000= Conversely total revenue would decline when demand is elastic and price increases (work backwards from 7 to 8 dollars). Combining these results tells us that demand is elastic if a price change causes total revenue to change in the opposite direction. Inelastic Demand: If demand is inelastic, a price decrease will reduce total revenue. The modest increase in sales will not be sufficient to offset the reduction in price. For example if price is 2

5 dollars and quantity demanded is 7000 units then total revenue would be \$ i.e. TR=2*7000= If however the price declines to 1 \$ and quantity demanded increase to 8000 units then total revenue would be \$8000 that is TR=1*8000=8000. The opposite will happen to total revenue when demand is inelastic and price increase. These results tell us that demand is inelastic if a price change causes total revenue to change in the same direction. Unit Elasticity: In the special case of unit elasticity, an increase or a decrease in price leaves total revenue unchanged. Cross Elasticity of Demand The cross elasticity of demand measures how sensitive consumer purchases of one product (say X) are to a change in the price of some other product (say Y). We calculate the coefficient of cross elasticity of demand Exy just as we do the coefficient of simple price elasticity of, except that we relate the percentage change in the consumption of X to the percentage change in the price of Y: Exy = % change in quantity demanded of X/ % change in the price of Y The cross elasticity (cross price elasticity) concept allows us to quantify and more fully understand substitute and complementary goods, introduce in lecture note 3. Substitute Goods: If cross elasticity of demand is positive, meaning that sales of X move in the same direction as a change in the price of Y, then X and Y are substitutes. An example is Kodak (X) and Fuji film (Y). An increase in the price of Kodak film causes consumers to buy more Fuji film, resulting in a positive cross elasticity. The larger is the positive cross elasticity coefficient, the greater the substitutability between the two products. Complementary Goods: When cross elasticity is negative, we know that X and Y go together or are complements ; an increase in the price of one decreases the demand for the other. For example, an increase in the price of cameras will decrease the amount of film purchased. The larger the negative cross elasticity coefficient, the greater is the complementarity between the two goods. Independent Goods: A zero or near zero cross elasticity suggests that the two products being considered are unrelated or independent goods. An example is nuts and film: We would not expect a change in the price of nuts to have any effect on the purchases of film, and vice versa.

6 Income Elasticity of Demand Income elasticity of demand measures the degree to which consumers respond to a change in their incomes by buying more or less of a particular good. The coefficient of income elasticity of demand Ei is determined with the formula Ei = % change in quantity demanded/ % change in income Normal Goods: For most goods, the income elasticity coefficient Ei is positive, meaning that more of them are demanded as incomes rises. Such goods are called normal goods. Inferior Goods: A negative income elasticity coefficient designates an inferior good. Used clothing, used tires are likely candidates. Consumers decrease their purchases of inferior goods as income rise. HW: Can income elasticity helps us differentiate between luxury and necessity products. Price Elasticity of Supply The concept of elasticity also applies to supply. If producers are relatively responsive to price changes, supply is elastic. If they are relatively insensitive to price changes, supply is inelastic. We measured the degree of price elasticity of supply with the coefficient Es, defined almost like Ed except that we substitute percentage change in quantity supplied for percentage change in quantity demanded : Es = % change in quantity supplied of product X / % change in price of product X When Es is greater than 1 supply is elastic. If Es is less than 1 then supply is inelastic and if Es is equal to 1, supply is unit elastic. Also Es is never negative since price and quantity supplied are directly related. Thus there are no minus signs to drop, as was necessary with elasticity of demand. The main determinant of price elasticity of supply is the amount of time producers have for responding to a change in product price. A firm s response to, say, an increase in the price of Christmas trees depends on its ability to shift resources from the production of other goods (whose prices we assume to be constant) to the production of trees. And shifting resources takes time: the longer the time, the greater the resource shiftability. So we can expect a greater response and therefore greater elasticity of supply, the longer a firm has to adjust to a price change.

7 In analyzing the impact of time on elasticity, economists distinguish among the immediate market period, the short run and the long run. Price elasticity of supply The Market Period The market period is the period that occurs when the time immediately after a change in market price is too short for producers to respond with a change in quantity supplied. Suppose the owner of a small farm brings to the market one truckload of tomatoes which is the entire season s output. The supply curve for the tomatoes is perfectly inelastic (vertical); the farmer will sell the truck load whether the price is high or low. Why? Because the farmer can offer only one truckload of tomatoes even if the price for tomatoes is much higher than anticipated. He or she might want to offer more tomatoes, but tomatoes cannot be produced overnight. Another full growing season is needed to respond to a higher than expected by producing more than one truckload. Similarly, because the product is perishable, the farmer cannot withhold it from the market. If the price is lower than anticipated, he or she will still sell the entire truckload. In our example here, during the market period our farmer s supply of tomatoes is fixed. One truckload is offered no matter how high or low the price is. Price Sm Pm Po D2 D1 Qo Q Price Elasticity of supply The Short Run In the short run, the plant capacity of individual producers and the entire industry is fixed. Even so, firms do have time to use their plant more or less intensively. In the short run, our farmer s plant (land and farm machinery) is fixed. But he does have time in the short run to cultivate tomatoes more intensively by applying more labour or fertilizer and pesticides to the crop. The result is a somewhat greater output in response to a presumed increase in demand; this greater output is reflected in a more elastic supply of tomatoes, as shown by Ss in the graph below. Note now that the increase in demand from D1 to D2 is met with an increase in quantity (from

8 Q0 to Qs) so there is a smaller price adjustment (from P0 to Ps) than would be the case in the market period. The equilibrium price is therefore lower in the short run than in the market period. Price Ss Ps Po D2 D1 Q o Q s Q Price Elasticity of Supply The Long Run The long run is the time period long enough for firms to adjust their plant sizes and for new firms to enter (or exit) the industry. In the tomato industry for example, our farmer has the time to acquire additional land and buy more machinery and equipment. Furthermore, other farmers may, over time, be attracted to tomato farming by the increased demand and higher price. Such adjustments create a larger supply response, as represented by the more elastic supply curve SL in the graph below. The outcome is a smaller price (Po to PL) and a larger output increase (Q0 to QL) in response to the increase in demand from D1 to D2. Price SL PL Po D2 D1 Qo QL Q

9 There is no total revenue test for elasticity of supply. Regardless of the degree of elasticity or inelasticity, price and total revenue always move in the same direction. The notes came from McConnell &Brue, Economics, 15th edition, 2002 You are required to supplement this with additional reading.

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