Amherst College Department of Economics Economics 111 Section 3 Fall 2012 Monday, September 17 Lecture: Elasticity

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1 Amherst College epartment of Economics Economics 111 Section 3 Fall 2012 Monday, September 17 Lecture: Elasticity Market emand and Market Supply Curves Market demand curve: How many cans of beer would consumers purchase (the quantity demanded), if the price of beer were, given that everything else relevant to the demand for beer remains the same? rice of Beer ($/can) * S Market supply curve: How many cans of beer would firms produce (the quantity supplied), if the price of beer were, given that everything else relevant to the supply of beer remains the same? * uantity of Beer (cans) Equilibrium: In equilibrium emand and supply are equal partners in determining the uantity emanded = uantity Supplied equilibrium price and quantity. Why is the Equilibrium rice Important? Market Forces, the Equilibrium rice, and the Actual rice If Actual rice < Equilibrium rice If Actual rice > Equilibrium rice uantity emanded > uantity Supplied uantity Supplied > uantity emanded Shortage exists Surplus exists Actual rice rises Actual rice falls until the equilibrium is reached until the equilibrium is reached surplus S Market forces push the actual price toward its equilibrium level. Assuming that the actual price * is free to move, the actual price will equal the equilibrium price in short order. shortage * Shifts Versus Movements Along the emand and Supply Curves Shifts Movements Along Change in something OTHER Change in the price of beer ITSELF THAN the price of beer ITSELF The slopes of the demand and supply The demand curve for beer The supply curve of beer curves for beer capture the effect can SHIFT ONLY if can SHIFT ONLY if of a change in the BEER RICE itself; something that affects something that affects a change in the price of beer leads demand OTHER THAN supply OTHER THAN to a MOVEMENT ALONG the the BEER RICE changes. the BEER RICE changes. demand and supply curves for beer.

2 2 roject: Advice for the Vermonter The Vermonter is an AMTRAK train that travels from Washington,.C. to St. Albans, VT, with continuing bus service to Montreal, uebec. resently, the price of a ticket from Amherst to St. Albans is $39. The following two individuals are suggesting ways to increase the revenues generated from Vermonter ticket sales. emand for the Vermonter rice ($/ticket) Mr. A: The Vermonter is operating with empty seats. To increase revenues, AMTRAK should fill the empty seats by lowering ticket prices. (tickets) Ms. B: That would be disastrous! Lower ticket prices will lead to lower, not higher, revenues. Your policy would make a bad situation worse. uantity uestion: What additional information do we need to address this question?

3 3 (rice) Elasticity of emand We shall begin with the intuitive notion of the demand elasticity and then make it more rigorous. We know that typically the quantity demanded decreases when the price increases and vice versa; that is, the market demand curve is downward sloping. When a good becomes more expensive we purchase less of it; when a good becomes cheaper, we buy more. How sensitive is the quantity demanded, however? When the price decreases, do we buy just a little more or much more? The price elasticity of demand answers this question; it indicates how sensitive the quantity demanded is to the price. very sensitive to the price, demand is said to be elastic; if the quantity demanded is not very sensitive, inelastic. We simply ask how sensitive is the quantity demanded to the price? very sensitive to the price emand Is Elastic not very sensitive emand Is Inelastic More formally, the price elasticity of demand equals the percent change in quantity demanded caused by a one percent change in the price: rice Elasticity of emand = ercent change in the quantity demanded resulting from a 1 percent change in the price If the price elasticity of demand equals 1, a 1 percent change in the price results in a 1 percent change in the quantity demanded; in this case, demand is said to be unit elastic. (Note that economists are not very creative when it comes to definitions.) Unit elastic is the dividing line between elastic and inelastic demand. If the price elasticity of demand is greater than 1, then demand is elastic, the quantity demanded is very sensitive to the price; more specifically, a 1 percent change in the price results in a more than 1 percent change in the quantity demanded. If the price elasticity of demand is less than 1, demand is inelastic, the quantity demanded is not very sensitive to the price; more specifically, a 1 percent change in the price results in a less than 1 percent change in the quantity demanded. very sensitive to the price not very sensitive emand Is Elastic Unit Elastic emand Is Inelastic rice elasticity of rice elasticity of rice elasticity of demand greater than 1 demand equals 1 demand less than 1 1 percent change in 1 percent change in 1 percent change in price causes the quantity price causes the quantity price causes the quantity demanded to change by demanded to change by demanded to change by more than 1 percent exactly 1 percent less than 1 percent It is important to note that when we say demand is inelastic we do not mean that the quantity demanded is not at all sensitive to the price; instead, we mean that the quantity demanded is not very sensitive to the price. In all but the most extreme cases, the demand curve is downward sloping; consequently, an increase in the price causes a decrease in the quantity demanded. When demand is inelastic, an increase in the price causes only a small decrease in the quantity demanded.

4 4 Elasticity and Total Revenues Collected by Firms The total revenues collected by firms equals the good s price times the number of units consumers buy, the quantity demanded: Total Revenues = rice x uantity emanded uestion: what happens to the total revenues collected when the price of a good rises? Since the demand curve is downward sloping, an increase in the price reduces the quantity demanded; when a good becomes more expensive, we buy less of it. Consequently, we cannot tell in general whether total revenue will rise or fall when the price increases: Total Revenues = rice x uantity emanded rice rises, but quantity demanded falls; the product of the price and quantity demanded could rise, fall, or remain the same. In general, we cannot tell what will occur. We need some additional information to determine what will happen to total revenues. uestion: what information do we need? Answer: demand elasticity. To justify this claim consider the following table: very sensitive to the price not very sensitive emand Is Elastic Unit Elastic emand Is Inelastic rice elasticity of rice elasticity of rice elasticity of demand greater than 1 demand equals 1 demand less than 1 1 percent change in 1 percent change in 1 percent change in price causes the quantity price causes the quantity price causes the quantity demanded to change by demanded to change by demanded to change by more than 1 percent exactly 1 percent less than 1 percent 1% >1% 1% 1% 1% <1% falls constant rises Elastic demand: When the price increases and demand is elastic total expenditures fall. In this case, the quantity demanded is very sensitive to the price. A 1 percent increase in the price results in a more than 1 percent decrease in the quantity demanded. Consequently, total revenues, the product of price and quantity demanded falls. Unit elastic: When the price increases and demand is unit elastic total expenditures are constant. In this case, a 1 percent increase in the price results in a 1 percent decrease in the quantity demanded. Consequently, total revenue, the product of price and quantity demanded, remains constant.

5 5 Inelastic demand: When the price increases and demand is inelastic total expenditures rise. In this case, the quantity demanded is not very sensitive to the price. A 1 percent increase in the price results in a less than 1 percent decrease in the quantity demanded. Consequently, total revenues, the product of price and quantity demanded rises. Ticket rices for the Vermonter The Vermonter is an AMTRAK train that travels from Washington,.C. to St. Albans, VT. with continuing bus service to Montreal, uebec. The following two individuals are consider ways emand for the Vermonter to increase the revenues generated from rice ($/ticket) Vermonter ticket sales. Mr. A: The Vermonter is operating with empty seats. To increase revenues, AMTRAK should fill the empty seats by lowering ticket prices Ms. B: That would be disastrous! Lower ticket prices will lead to lower, not higher, revenues. Your policy would make a bad situation worse. uantity (tickets) To evaluate these statements, recall that the revenues AMTRAK collects from the Vermonter equal the total expenditures made by consumers: Total Revenues = rice x uantity emanded If AMTRAK lowers ticket prices, more consumers will ride the train, the quantity demanded increases. In general, we cannot tell what happens to total revenue, however. It depends on the elasticity of demand. If demand were elastic rises If demand were inelastic falls If demand were elastic, the quantity demanded would be very sensitive to the price. The lower price would result in a large increase in the quantity demand; total expenditures would rise. On the other hand, demand were inelastic, the lower price would result in a small increase in the quantity demanded; total revenues would fall. So, if demand is elastic, Mr. A is correct; if demand is inelastic, Ms. B is correct. If you were in a policy making position at AMTRAK, it would be vital for you to obtain information about the elasticity of demand. It would determine whether you recommend an increase or decrease in ticket prices. This illustration shows that elasticity is not a concept that sadistic economics professors have dreamed up to make life difficult for introductory economics students. It is sometimes key when making real world decisions.

6 6 The Farming aradox Consider the following statements Mr. A: Good farming weather and bountiful harvests are bad for farmers. oor weather and low harvests are good. Ms. B: You can't be serious. Have you gone crazy?" ** S S To evaluate these statements, suppose that farmers experience an unusually bad weather. The bad weather would cause the market supply curve to shift to the left. The price of food would rise from * to ** and the quantity of food would fall from * to **. * ** * What happens to the total revenues collected by farmers? Total Revenues = rice x uantity emanded In general, we cannot tell; the price has increased by the quantity decreased. The answer to the question depends on the elasticity of demand: emand Is Elastic emand Is Inelastic falls rises In this case, we know that the demand for food is inelastic. Consequently, the bad weather will increase the total revenues collected by farmers. This explains the apparent paradox. What influences the price elasticity of demand? We have just seen that it is sometimes important to know if the demand for a good is elastic or inelastic. Therefore, we will now consider what determines a good s elasticity of demand. While many factors are important perhaps the most crucial is the availability of substitutes. To make this point, we shall consider insulin, a good that has no substitutes. If you were a diabetic who needed to use insulin, you would have to take a specific amount of the drug every day. uestion: what would happen to the quantity of insulin demanded if the drug companies suddenly decided to reduce the price of insulin by 50 percent? Answer: nothing. Those individuals who need insulin would not consume any more. They need a prescribed amount. Taking more or less than this amount would probably result in a coma. The demand for insulin is perfectly inelastic; the quantity demanded is constant, unaffected by the price. Beware, however, that goods whose demand is perfectly inelastic are very rare. On the other hand, the demand for many goods is inelastic; that is, for many goods, a change in the price will decrease the quantity demanded, but a small amount. Often, introductory students incorrectly assume that when demand is inelastic, the quantity demand is completely insensitive to the price; be careful not to fall into this trap.

7 7 Next, let us consider luxuries and necessities. By definition, necessities have few substitutes; consequently, the demand for necessities is inelastic. Luxuries, on the other hand, tend to have many substitutes. This winter one might vacation in Tahiti or St. Bart s or Vale or Consequently, the demand for luxuries tends to be elastic. Also, the scope of the good is important. For example, the demand for food in general is inelastic because there are few substitutes for food. On the other hand, the demand for one particular type of food, lima beans for example, would be elastic; there are many substitutes for lima beans: green beans, peas, etc. Example of a ersistent Surplus - Minimum Wage Legislation To investigate the effect of minimum wage legislation, consider the market for low skilled labor. We place the wage rate (the price of labor) on the vertical axis and the quantity of labor on the horizontal axis. Now, let us interpret the market demand curve and supply curve in the context of the labor market. w S The market demand curve for labor answers a long series of hypothetical questions: How much labor would firms hire (the quantity of labor demanded), if the wage were? It is easy to understand why the demand curve for labor is downward sloping. As the wage increases, labor becomes more expensive, and firms response by hiring fewer workers. w* L* L What about the market supply curve? The market supply curve for labor answers a long series of hypothetical questions: How much labor would households provide (the quantity of labor supplied), if the wage were? We have drawn the market supply curve as an upward sloping curve. As the wage increases, households are enticed to work more hours. In equilibrium, the quantity of labor demand equals the quantity of labor supplied. The equilibrium wage rate is w* and the equilibrium quantity of labor is L*. Note that when the wage is w*, there is a job for everyone who wants one. w A minimum wage is a price floor; the wage cannot fall S below the floor. Consequently, minimum wage legislation only affects the labor market whenever the minimum unemployment wage exceeds the equilibrium wage. In this case, the demand curve reveals that firms would hire L Min w Min units of labor. The amount of labor firms hire is reduced from L* to L Min w*. Unemployment results. To understand why, recall that the supply curve tells us how much labor households would wish to provide. When the actual wage is greater than the equilibrium wage, the quantity of L labor demanded is less than the quantity of labor L Min L* supplied; that is, the amount of labor that firms would hire is less than the quantity of labor that households wish to supply:

8 8 uantity of labor demanded < uantity of labor supplied Amount of labor Amount of labor firms are < households wish actually hiring to provide As a consequence of the minimum wage, firms hire less labor and everyone who wants a job will not be fortunate enough to find one. Some people who would like to work at the minimum wage cannot find a job. This is what we mean by unemployment, isn t it? Goal of minimum wage legislation Minimum wage legislation is designed to help the working poor. That is, it is designed to increase the earned income of low skilled workers. How well does the legislation meet the goal? Who is helped by the minimum wage? Low skilled workers who are fortunate enough to find a job are helped. If you have a job, you are better off at the higher minimum wage than would be at the lower equilibrium wage. At the higher wage you would earn more income. Who is hurt by the minimum wage? Firms who hire low skilled workers are hurt because they must pay their low skilled workers the minimum wage that is more than the equilibrium wage. Low skilled workers who are not fortunate enough to find a job are clearly not helped. For lack of a better term, call these individuals frustrated workers. Workers are helped by minimum wage legislation only if they can actually find a job. Frustrated workers are hurt by a minimum because they does not even have the option of deciding whether or not they wish to accept a job - there are no firms willing hire them at the minimum wage. So is the goal met? Well our conclusions are mixed. Some low skilled workers indeed earn more, while others cannot find a job and earn nothing at all. This leads us to the next question: how does the minimum wage affect the earnings of low skilled labor as a group? The answer to this question depends on the elasticity of demand for labor. To understand why, note that total earnings equal the wage times the quantity of labor firms hire, the quantity of labor demanded: Total Earnings = Wage uantity of Labor emanded

9 9 How does minimum wage legislation affect this equation? The wage increases and the quantity of labor demanded by firms decreases. Total Earnings = Wage uantity of Labor emanded In general, we cannot tell what happens to total earnings. It depends on the elasticity of demand for labor: emand Is Elastic emand Is Inelastic w L w L w L falls w L rises What does the wage elasticity of demand equal? Is demand elastic or inelastic? Empirical studies differ: 2 Study Group Wage elasticity Welch and Cunningham (1978) Teens 1.34 Baxen and Martin (1991) Young.51 Anderson (1977) Grant (1979) Hamermesh (1982) Layard (1982) M < F < Lewis (1985) M < F < Most appear to suggest that demand is elastic. Consequently, most suggest that minimum wage legislation does not increase the total earnings of low skilled labor as a group. So, does the legislation accomplish its goal? 2 Hamermesh, aniel Labor emand. rinceton and Chichester, U.K.: rinceton University ress.

10 10 Linear emand Curves: Slope versus Elasticity rice Elasticity of emand = emand Is Elastic ercent change in the quantity demanded resulting from a 1 percent change in the price. emand Is Inelastic rice An increase in the price leads to a large decrease in the quantity; hence, decreases. An increase in the price leads to a small decrease in the quantity; hence, increases. uantity Geometric interpretation of : Area of the rectangle. High rice Low rice rice rice Gain in Loss in Gain in Loss in uantity uantity emand Is emand Is A linear demand curve has an elastic region and an inelastic region: rice Elastic Region Inelastic Region uantity

11 11 Income Elasticity of emand The income elasticity of demand indicates how sensitive the quantity demanded is to income. More formally, the income elasticity of demand equals the percent change in quantity demanded resulting from a 1 percent change in income: Income Elasticity of emand = ercent change in the quantity demanded resulting from a 1 percent change in income The income elasticity for most goods is positive; an increase in income results in a greater quantity demanded. There are some exceptions, however. For example, the quantity of Old Milwaukee Beer an individual purchases typically falls as income rises. As income rises, people typically purchase switch from Old Milwaukee to any brand: Budweser, Coors, etc. The income elasticity of demand for Old Milwaukee is negative; as income rises, the quantity of Old Milwaukee demanded decreases. Old Milwaukee is an example of an inferior goods. Most goods are normal; for a normal good, the quantity demand rises whenever income increases: Normal good Inferior Good An increase in income An increase in income leads to an increase leads to an decrease in quantity demanded. in quantity demanded. Income elasticity of Income elasticity of demand is positive. demand is negative. By convention, when we use the term elasticity of demand without the word price of income preceding it, the word price is understood. In other words, when you see the term elasticity of demand, it is shorthand for the term the price elasticity of demand. (rice) Elasticity of Supply We shall follow the same strategy that we used with the elasticity of supply that we used to introduce the elasticity of demand. We shall begin with the verbal notion of the supply elasticity and then make it more formal. We know that typically the quantity supplied increases when the price increases and vice versa; that is, the market supply curve is upward sloping. How sensitive is the quantity supplied to the price, however. When the price increases, do firms produce just a little more or much more? The price elasticity of supply answers this question; it indicates how sensitive the quantity demanded is to the price. If the quantity supplied is very sensitive to the price, supply is said to be elastic; if the quantity supplied is not very sensitive, inelastic. We simply ask how sensitive is the quantity supplied to the price? If the quantity supplied is If the quantity supplied is very sensitive to the price not very sensitive Supply Is Elastic Supply Is Inelastic More formally, the price elasticity of supply is the percent change in quantity supplied caused by a one percent change in the price: rice Elasticity of Supply = ercent change in the quantity supplied resulting from a 1 percent change in the price

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