Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023 PDF

Chapter 5 The Concept of Elasticity and its Applications©1 Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 21/08/2024 4:56 PM In many applications of the demand and supply model, there is a need to know how much the qu...

Chapter 5 The Concept of Elasticity and its Applications©1 Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 21/08/2024 4:56 PM In many applications of the demand and supply model, there is a need to know how much the quantity demanded of a product has changed in response to a given change in its price. Such an information is used in computing the effect of imposing or increasing a sales tax on the distribution of the tax burden or on government tax revenues. Large firms, such as beer breweries car makers, and phone companies, etc., use the information to estimate the effect of changing the prices of their products on their market share and profits. It is also useful for economists to compute the effects of changes in the economic environment on resource allocation and income distribution. The concept of elasticity summarizes neatly the information about the response of the quantity demanded of a product to a change in its own price or any one of its other determinants. In this chapter, we develop this concept and use it in a few applications of the demand and supply model. Pricing Problem of a Monopolist A monopoly firm is a producer or supplier of a product that has acquired tight control on entry to her industry allowing her/him to bloc or deter the entry of any competitor. The monopoly firm is the only seller of a given product. We call the owners and/or managers of a monopoly firm a monopolist. The buyers or demanders of the product are numerous and too difficult to organize into a countervailing force so that none of them has power to force the monopolist to reduce the price. Thus, the monopolist faces the total demand curve of the market for that product and they are a price maker at all time. Table 1 Demand Schedule and Total Revenue of a Monopolist Price in $ Quantity Demanded Total Revenue Change in Revenue (1) (2) (3) (4) (5) 10 0 0 180 9 20 180 140 A 8 40 320 100 a 7 60 420 60 6 80 480 20 B 5 100 500 -20 b 4 120 480 -60 3 140 420 -100 2 160 320 -140 1 180 180 -180 0 200 0 Columns 2 and 3 of Table 1 give an example of the demand schedule for a monopolist. 1Copyright: Cartago Research and Development, 8/21/24 4:56 PM Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-2 Straight line CD in each of the two panels of figure 1 represent the same corresponding demand curve. By definition Total Economic Profit = Total Revenue - Total Cost. Let us start from combination A in figure 1.a or Situation A. When the managers of the monopoly reduce their price from $8 to $7, sales increase from 40 to 60 units. The increase in sales requires an increase in production, which in turn causes total cost to increase. Whether the increase in sales would increase total economic profit depends on whether total revenue increases more than the increase in total cost. To sell more the monopolist must reduce her price. If the increase in sales more than offsets the decline in price, her total revenue would rise. Otherwise, total revenue could either remain unchanged or decrease. Whether the first case obtains or the second depends on the relative sizes of the increase in the quantity demanded and the fall in the price. This is clear from the definition of total revenue and the fact that for a monopolist, quantity sold = quantity demanded. Total revenue = Price x (Quantity sold at that price) = Price x (Quantity demanded at that price) Let us calculate the change in total revenue when the monopolist reduces the price. The price reduction allows for an increase in sales; but the monopolist must reduce the price on each one of the units previously sold. The increased sales result in an increase in total revenue by (New Price) x (Change in quantity sold). The vertical green bars G in figure 1.a and figure 1.b represent this gain in revenue. The reduction in the price on previously sold units lowers total revenue by an amount equal to (Change in price) x (Quantity sold previously). The horizontal red bars L in figure 1.a and figure 1.b represent this loss in revenue. Thus Change in Total Revenue = (New Price) x (Change in quantity sold) – (Change in price) x (Quantity sold previously) Figure 1 Change In Revenue Of A Monopolist Figure1.a Situation A Figure 1.b Situation B Change in Revenue = G - L < 0 Change in Revenue = G - L >0 Price in $ 11 Price in $ 11 10 C C 10 9 9 A 8 8 a 7 7 L 6 6 5 B 5 4 L b 4 G 3 3 2 2 G 1 D 1 D 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Quantity demanded Quantity demanded Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-3 Since the quantity sold is equal to the quantity demanded, we can write: Change in Total Revenue = (New Price) x (Change in Quantity demanded) – (Change in Price) x (Quantity Demanded previously) (1) In both panels of figure 1, Change in total Revenue = Vertical Bar G - Horizontal Bar L The two panels of figure 1 describe the effect of the change in the price on total revenue starting from two different price levels for the same demand curve. In figure 1.a situation A, the starting price is high. In figure 1.b situation B, the starting price is low. Situation A, Figure 1.a Suppose that the managers of the monopolist firm reduce the price from say $8 to $7. This change corresponds to a movement along demand curve CD of figure 1.a, situation A from point A to point a. Using the data given in Table 1 and equation (1) we get Change in Total Revenue = [$7 x (60 - 40)] – [($8 -$7) x 40] = $100 Column (4) of Table 1 also shows that total revenue increases from $320 to $420. In this case, a price decrease from $8 to $7 raises total revenue by $100. In Figure 1, Situation A, the area of the vertical green bar G is greater than that of horizontal red bar L. Thus, the change in total revenue is positive and total revenue increases. If the increase in total cost is less than this increase in total revenue, the monopolist is better off lowering the price of her product. However, this is not always the case; total revenue may actually fall if the monopolist reduces the price of her product. Situation B, Figure 1.b Suppose that the managers of the monopoly firm reduce the price of their product from say $5 to $4. This change corresponds to a movement along the demand curve CD of figure 1.b, situation B from point B to point b. Equation (1) and Table 1 imply that Change in Total Revenue = [$4 x (120 - 100)] - [($5 -$4) x 100]= -$20 Column (4) of Table 1 also shows that total revenue decreases from $500 to $480. In this case, a price decrease from $5 to $4 reduces total revenue by $20. In Figure 1.b, Situation B, the area of vertical green bar G is smaller than that of horizontal red bar L. Thus, the change in total revenue is negative and total revenue falls. Regardless of the increase in total cost, total economic profits would fall if the monopolist reduces her price. To increase her total economic profit in this case, the monopolist should raise her price since in this case total revenue would increase and total cost would fall. Concept of Price Elasticity of a Market Demand Curve The difference between situations A and B of figure 1.a and figure 1.b is the following. In situation B of Figure 1, the effect of the increase in sales on total revenue is smaller than the effect of the price decrease on the total revenue obtained from the quantity previously sold. (New Price) x (Change in quantity demanded) < (Change in price) x (Quantity demanded previously) The opposite is true in situation A of Figure 1. In this situation, total revenue increases when price decreases because: Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-4 (New Price) x (Change in quantity demanded) > (Change in price) x (Quantity demanded previously) Let us analyze first the case of Situation A of figure 1. Dividing both sides of this last inequality by the quantity [(New Price) x (Quantity demanded previously)], we can write after dropping the words “new” and “previously” Total revenue increases when price falls if Change i n Quantity demanded Change in Price > Quantity demanded Price After multiplying both sides of this inequality by 100, we can identify its left hand side as the % change in quantity demanded and its right hand side as the % change in price. Thus Total revenue increases when the managers reduce the price if % Change in quantity demanded > % Change in price That is, total revenue increases when the managers reduce the price if % Change in Quantity demanded > 1 (2) % Change in Price We call the left hand side of inequality (2) the price elasticity of demand or E p. % Change in Quantity demanded Ep = (3) % Change in Price It follows that Total revenue increases when price falls if E p > 1, or Total revenue decreases when price increases if E p > 1. Similarly in Situation B figure 1.b, using a similar argument to that developed for situation A figure 1.a, we can show that Total revenue falls when a monopolist lowers the price of her product, if E p < 1 It follows that the managers of a monopoly firm will continue to increase the price of their product as long as the price elasticity of the demand curve for their product is less than one. In situation A, % Change in price = 100 x ($8-$7)/$7) = 14.2$8% % Change in quantity demanded = 100 *((60 - 40)/60) = 33.33%. Clearly, % change in quantity demanded > % change in price: Thus in situation A of figure 1, E p = 33.33/14.28 = 2.33 > 1 In situation B, % Change in price = 100 x (($5-$4)/$4) = 25% Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-5 % Change in quantity demanded = 100 x ((120 - 100)/120) = 16.66%. Clearly, % change in quantity demanded < % change in price. Thus in situation B of figure 1, E p = 16.66/25 =0.66 < 1 We conclude that If the price elasticity of the demand curve for the product of a monopoly firm is less than one, the monopoly firm’s total Revenue increases if the firm’s managers raise the price of the product If the price elasticity of the demand curve for the product of a monopoly firm is greater than one, the monopoly firm’s total Revenue increases if the firm’s managers lower the price of the product It follows that knowing the price elasticity of the demand curve for their product, the managers of a monopoly firm can tell if lowering the price will increase or reduce total revenue by estimating the elasticity of the demand curve of their product and comparing it to 1. It is easy to understand why the managers of the airline companies, colluding together worldwide by forming alliances, have raised their prices continuously since the end of the pandemic in 2022. Thus, the concept of elasticity is an important piece of information for managers or owners of monopoly firms. For example, when managers at Acadia University raised substantially student fees in the middle of the nineteen nineties, they should have calculated the price elasticity of the demand curve for higher education at Acadia University before raising the fees. They probably did not. Terminology and Shapes of Demand Curves and Price Elasticity When the price elasticity of a demand curve is greater than one, the demand curve is elastic. When the price elasticity of a demand curve is less than one, the demand curve is inelastic. When the price elasticity of a demand curve is equal to one, the demand curve is unit elastic. Changing the price will not affect total revenue if the demand curve is unit elastic. Usually, an elastic demand curve is close in shape to a horizontal line and an inelastic demand curve is close in shape to a vertical line. Figure 2 Perfectly Elastic and Inelastic Demand and Supply Curves Figure 2.a Demand Curves Figure 2.b Supply Curves 60 Price 60 Price Vertical Demand Curve B Vertical Supply Curve B F 50 50 40 Horizontal Demand Curve 40 Horizontal Market Supply Curve C D C D 30 30 20 20 10 10 O A A 0 0 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 Quantity demamded Quantity demamded Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-6 The elasticity of the vertical line demand curve AB in figure 2.a is zero because consumers demand the same amount OA regardless of the product price. The % change in quantity demanded is zero for any % change in price. Thus, E p = 0. In contrast, the elasticity of the horizontal line demand curve CD in figure 2.a is very large, that is infinite, because if the market price of the product rises even slightly above OC = $30, the quantity demanded falls to zero. In the opposite case, if the market price of the product falls even slightly below OC = $30, the quantity demanded is equal to an infinite number. If the market price In fact, the demand curve is actually curve FCD as in figure 2.a. It is composed of two segments FC and CD. For a very small percentage increase in the price there is a large drop in the quantity demanded. Thus, E p is very high. It is equal to infinity. However, except for the two extreme cases of demand curves that are vertical or horizontal lines in shape, the shape of a demand curve is usually a misleading indicator of its price elasticity. Indeed, one can change the units on the horizontal and vertical axis to make the shape of a demand curve look, as one wishes it to be, very close to a vertical line or very close to a horizontal line. For instance, as our computations based on the data given in Table 1 show, the demand curve in Figure 1 is both elastic and inelastic, of course, in different sections. One should remember that the slope of a curve is not its elasticity. Method of Calculation of Percentage Changes When we calculated the % change in price for figure 1.a situation A, we divided the change in price by the new price. There is no compelling reason to use the new price rather than the old price. However, if we use the old price we get a different answer. A better approximation to the percentage change in price is to use the average of the two prices. Similarly, it is advisable to use the average of the old and new quantities demanded to calculate the percentage change in quantity demanded. Thus, we compute the % change in quantity demanded and % change in price using the following formulas: Change in quantity demanded % Change in quantity demanded = 100 x New Quantity demanded + Old Quantity demanded 2 Change in Price % Change in Price = 1 00 x New Price + Old Price 2 For example in figure 1.a situation A, 100 x (60 - 40) The percentage change in quantity demanded is = 40% 60 + 40 2 100 x ($8 - $7) The percentage change in price is = 13.3%. $8 + $7 2 40 It follows that the price elasticity of the demand curve at point A of figure 1.a at A is equal to = 3. 13.3 Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-7 Other Elasticities of a Demand Curve When average income changes it is also important to know the degree of responsiveness or elasticity of the quantity demanded. If the good is a normal good, the quantity demanded increases as income rises. Monopolists and economists are usually interested in estimating the exact amount of this increase. We can get a good approximation using the income elasticity of demand. We define the income elasticity of demand Ei as: % Change in quantity demanded Ei = (5) % Change in Average Income If average income rises by 5% and E i = 1.5, then the quantity demanded would rise by % Change in quantity demanded = (% Change in average income) x E i = 5% * 1.5 = 7.5%. Price elasticity of a supply curve Similarly, we can also define the price elasticity of a supply curve as: % Change in quantity Supplied (6) Esp = % Change in Price There are two special kinds of supply curves, a vertical supply curve and a horizontal supply curve as shown in figure 2.(b). A vertical supply curve such as straight line AB in figure 2.b has zero price elasticity since the quantity supplied is a constant regardless of the price of the product. Thus, regardless of the percentage change in the price of the corresponding product, the percentage change of the quantity supplied is zero. Applying equation (6) we conclude that the price elasticity of a vertical supply curve is zero. The supply curve is perfectly inelastic. When the marginal cost is constant at any quantity produced and supplied, the market supply curve is a horizontal straight line at a price equal to the constant marginal cost such as supply curve CD in figure 2.b where the marginal cost is equal to $30. This supply curve is most likely a market supply curve rather than the supply curve of an individual producer or supplier. The price elasticity of a horizontal supply curve is infinitely large. That is because any slight increase in the price of a product with a constant marginal cost will attract a large number of potential suppliers and a large response from the current suppliers. Thus for a small percentage increase in the price of the corresponding product, the percentage change in the total quantity supplied to the market is infinitely large. Similarly, for any small decrease in the price of the corresponding product, the quantity supplied drops to zero. Actually, this kind of supply curve has two sections a vertical section OC at zero quantity and a horizontal section CD. Applying equation (6) with a large numerator for a tiny denominator, we conclude that the price elasticity of a horizontal supply curve is infinite. The supply curve is perfectly elastic. Determinants of the Price Elasticity of Demand If the demand curve for education at Acadia is inelastic, the university can reduce its costs by raising tuition. The revenues from fees will rise. The number of students will decrease by little. Thus, the total government grant to Acadia University, which is proportional to the number of students, will decrease by little and total costs fall. Everything else equal, if the increase in total revenue from raising the fees were greater than the fall in total grants, the university would be able to reduce its deficit. However, if the demand curve is elastic, the university is ill advised to raise the fees. Yet, the university managers Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-8 did raise the fee substantially in the second half of the nineteen nineties without paying attention to the determinants of the elasticity of the demand curve for education at Acadia or elsewhere. What makes a demand curve elastic or inelastic? A few factors control the elasticity of demand; we call them the determinants of the price elasticity of demand. These are: Availability of Strong Substitutes We decompose the effect of an increase in the price of a product A on its quantity demanded in two parts. The first part is the substitution effect. The second part is the income effect. Everything else equal, let the price of product A increase. Then, The purchasing power of the average income of consumers or average real income decreases. This gives rise to the real income effect. The average real income decreases because the actual money income in dollars and the price of every other product remain unchanged. Everything else equal, every consumer cannot buy anymore the same number of units of every product after the increase in the price of the product as she bought before the product’s price increase. It is reasonable that a consumer would reduce her/his purchases of every product to remain within her/his budget, as the actual consumer’s income did not increase. It is in this sense that, everything else equal, the increase in the price of a product causes the purchasing power of every consumer’s income to decrease. (This is also true if the prices of all products increase at the same time by the same percentage as a consequence of inflation). We say the consumer’s real income decreases when the price of any product he/she consumes increases. The fall in the average real income would reduce the quantity demanded of every normal product, including the quantity demanded of product A, if the latter is a normal product, and the corresponding willingness to pay for an additional unit of product A decreases. This is the real income effect of an increase in the price of product A on its quantity demanded if it is a normal product. We say the real income effect of the increase of the price of a normal product is negative The product becomes relatively more expensive as compared to its substitutes whose prices did not change. This gives rise to the substitution effect. The relative increase in the price of product A reduces the product’s quantity demanded further because consumers would attempt to replace part or all of their consumption of product A by cheaper substitutes if there are such substitutes. The extent of this substitution depends on the degree of substitution between product A and other substitutes. Suppose that product B is a substitute of product A. If product B is a perfect substitute for product A, an increase in the price of product A entices consumers to substitute product B for product A. In this case, the quantity demanded of product A decreases to zero. If product B is a strong but not a perfect substitute, consumers would shift a substantial proportion of their expenditures away from product A to product B. Finally, if all other products are very poor substitutes or no substitutes at all (for example product A is food in general) then the quantity demanded of product A on the account of substitution of other products will barely decrease. This is the substitution effect of an increase in the price of a product A on its quantity demanded. The substitution effect is always negative. The total effect is the sum of the substitution effect and the real income effect. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-9 The total effect of an increase in the price of a normal product on its quantity demanded is negative and the quantity demanded will decrease but its strength depends on strength of the substitution effect Thus, the price elasticity of the demand curve of a normal product would be large and much greater than one if the product is normal and has a strong substitute. In this case, its demand curve is elastic. If only poor substitutes to the product are available, consumers have no choice. The substitution effect would be weak and the price elasticity of its demand curve is less than one. The demand curve for the product is inelastic. Necessity or Luxury If product A is a necessity, it has no strong substitutes. For example, food in general is a necessity and thus its demand curve is inelastic. Usually, a luxury good has strong substitutes and their demand curve is elastic. Degree of Precision in the Definition of the Product Food is a general term. It includes meat, bread, chicken, vegetables and so on. While food is a necessity, meat is not. Consumers could substitute fish, chicken meat, beans, or potatoes for meat. Thus, meat has strong substitutes, the price elasticity of its demand curve is greater than one, and its demand curve is elastic. Its demand curve is more elastic than that of food. The more precise is the definition of a product, the more substitutes it would have and thus the more elastic is its demand curve. Importance of the Product in Consumers Budgets When the expenditures on a product represent a large proportion of the budget, the income effect of a change in its price is large. The response of the quantity demanded is also substantial. A one percent increase in the price of cars will have a larger effect on consumers’ budgets than a 1% increase in the price of a shirt. Consumers would reduce the quantity demanded of cars by a larger percentage than the quantity demanded of shirts. Thus, the price elasticity of the demand curve for cars will be larger than the price elasticity of the demand curve for shirts. Time Elapsed since the Price Change A product A may have strong substitutes. However, when the price of product A increases the shift from product A to one of its substitutes may not be easy in the short run and sometimes quite impossible. The quantity demanded of product A would not change much in the short run. When oil prices increased in the early nineteen seventies (1973), the quantity consumed of oil did not change much. To reduce oil, motorists in North America needed to switch away from large cars to small cars or to shift to public transportation, which was not available in many North American cities. It takes time and resources to replace existing relatively new large cars by smaller ones because the former are expensive to discard and it takes a lot of time to build an appropriate public transportation infrastructure. Similarly, to switch from heating with oil to heating with electricity or gas requires a change in the buildings heating systems. This change takes time and resources. Accordingly, it is only in the long run that such switches are possible and cost effective. In the long run, the quantity demanded of oil would decrease by much more than in the short run in response to an increase in the price of oil. The price elasticity of the demand curve for oil is small in the short and much higher in the long run. The above argument shows that in general the short run price elasticity of the demand curve of almost any product is significantly smaller than its long run price elasticity. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-10 Who Bears the Tax Burden? A framework Most governments impose sales taxes on products sold in the markets of their respective countries. Usually, the government charges sellers with collecting the sales taxes. In Canada the sales tax is called the Harmonized Sales Tax or HST. The Canadian government and every seller in Canada like to post on the products labels only the prices of products excluding the sales tax. When the consumer pays for his purchase at the cashier register, the seller tacks on the sales tax by adding it to the announced price (i.e. the price excluding the sales tax). The Canadian politicians claim ostensibly that this makes people aware of the amount of taxes they pay. One wonders why the government does not require the seller to post the actual other costs of transportation, raw material, labour, etc… they incurred so that the consumer is better informed? Be it as it may, it appears as if the consumers pay the entirety of those taxes. While this is true in the long run and for the case of markets that operate under perfect competition, it is not true in the short run and for all markets, We shall see in this section and the following one that In many cases, the imposition of a sales tax raises the equilibrium price of the product by less than the amount of the tax because the quantity demanded and supplied at equilibrium falls. This means that in the short run, consumers as demanders do not shoulder the whole burden of the tax and producers would share in the burden. In some cases the imposition of a sales tax causes an inefficient allocation of resources and in other cases, contrary to what many economists and textbook authors claim, they prevent a loss of efficiency in the allocations of resources. To understand better how the imposition of a sales tax affects economic activity and who pays for it, we need to know the government’s reason for imposing it. Most people who do not want to pay taxes and most economists assert that a sales tax causes efficiency losses and thus they are a burden. Although a tariff on imports is a sales tax, some people think, depending on their special interest, that a tariff on imports enhances economic efficiency and a sales tax does not. All those people argue that they are entitled to tax evasion and tax loopholes that allow them to pay no taxes. An efficient allocation of resources requires equality between marginal social cost and marginal social benefit. The marginal social cost is rarely equal to the private marginal cost. Many economists point out that when it comes to pollution, a sales tax, called a carbon tax, is not anymore a cause of efficiency loss to the contrary they help us to achieve economic efficiency. They see the carbon tax as a paradox since they think that in general a sales tax causes an efficiency loss. We shall see in a later chapter devoted to the study of natural resources that we can use sales taxes to achieve economic efficiency but their use does not give rise to a paradox or a sui generis case justification. The carbon tax is a clear indication that the marginal social cost is greater than the private cost. So it is the case for most economic activities that involve specialization and exchange through a market. Markets need a physical infrastructure and an appropriate environment to function. The infrastructure and environment include security, justice, health, roads and so on. The building and the maintenance of the required infrastructure and environment devolve to the government as a representative of society and give rise to a recurrent cost. The corresponding unit cost must be included in the marginal social cost. In the absence of a sales tax to pay for those recurrent costs, the private marginal cost does not include the unit cost associated with the building and maintenance of the appropriate infrastructure. The idea that the marginal social marginal is higher than the private cost that does not include an appropriate sales tax to pay for the recurrent government expenditures to maintain and Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-11 build an appropriate infrastructure suggests that we distinguish, as we shall do, two kinds of a sales tax: An unproductive sales tax and a productive sales tax: An unproductive sales tax is a sales tax that is used by government officials and politicians to pay for unproductive government expenditures. A productive sales tax is a sales tax that serves to pay for recurrent cost of the building and maintenance of an appropriate infrastructure that helps markets function better. When the sales tax is unproductive, it makes sense to ask who bears the sales tax and how does it cause a loss of efficiency. The answer to the first question depends on the relative sizes of the price elasticity of the demand curve and that of the price elasticity of the supply curve. When the sales tax is productive, it makes no sense to ask who bears the sales tax but it makes sense to ask how does it save the economy from incurring a loss of efficiency. The answer to the first question is obvious and in this case the price elasticity of the demand curve and that of the supply curve do not matter. We start with the analysis of the effects of the imposition of an unproductive sales tax. Demand Curve Elasticity and Tax Burden Sharing of an unproductive Sales Tax When the government imposes a sales tax to pay for extravagant expenses or for other unproductive government expenditures, such as subsidies granted to special interest groups to win votes including managers of private companies, it makes sense to ask who bears a sales tax: the consumers on the demand side or the producers and suppliers on the supply side. Elastic Demand curve In figure 3, demand curve AB is price elastic and its price elasticity at point B is 10 , the supply curve before the imposition of the sales tax is CB. Let the government charge the supplier or the producer to collect the sales tax. The sales tax is then an additional cost to the seller or supplier. Thus, when the government imposes a sales tax say of $4, the private marginal cost at every quantity supplied increases by $4. Consequently, as indicated in figure 3, the supply curve shifts upward by $4 from CB to AD. The equilibrium point moves from B to A in figure 3. The equilibrium price including the sales tax increases from $8 to $9 or by one dollar. Accordingly, as distance AE in figure 3 shows, consumers pay one dollar more, which represents 25% of the $4 dollar sales tax. Their share of the tax burden is thus 25%. The quantity demanded falls from 80 units to 20 units. 1 The percentage change in price is 11.8% = 100x and the percentage change in quantity 8.5 60 demanded is 120% = 100 x. Thus, the price elasticity of the demand curve is 10.17. This (80 + 20) 2 is a high price elasticity of the demand curve and consumers pay a relatively small share of the tax. At the new equilibrium, the producers or sellers must pay to the government a sales tax of $4 for each of the 20 units they sell at the new equilibrium out of the equilibrium price of $9 that they receive for each one of the 20 units of their product that they sell at the new equilibrium. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-12 The price that producers or sellers receive net of the sales tax at the new equilibrium is thus $5. This net price is equal to the height at 20 units of the supply curve before the imposition of the sales tax, which is also equal to the marginal cost not including the sales tax. Thus, the marginal cost not including the sales tax and the price net of the sales tax fall by $3 from $8 at the old equilibrium quantity of 80 units to $5 at the new equilibrium quantity of 20 units. Figure 3 Elastic Demand Curve and Tax Burden Price 14 Supply Curve after Supply Curve before 13 imposi tion of Tax imposi tion of Tax 12 D 11 Sal es Tax 10 = $4 A $1 =Consumer's Tax 9 Burden per unit 8 E B $3 = Suppli er's Tax 7 Burden per unit 6 5 C 4 Demand Curve 3 High Ep 2 1 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 Quantity At the old equilibrium price, a producer or supplier used to receive a price of $8 for each one of the 80 units sold at equilibrium before the imposition of the tax, including the first 20 units. After the imposition of the tax, he/she collects a total of $9 per unit from the consumers on each of the 20 units sold at equilibrium, out of which he/she pays the $4 sales tax to the government and he/she is left with $5 equal to her/his marginal cost of $5 at the quantity supplied of 20 units. In Canada, a storeowner shows on the label attached to the product a price of $5. When the customer pays for the purchase, the storeowner charges the price of $5 plus the sales tax of $4 for a total of $9, which is the equilibrium price. It looks like the consumer is paying the whole sales tax. In fact this is correct only when the demand curve is perfectly inelastic or the supply curve is perfectly elastic. After the government imposes the sales tax, a producer or supplier now receives on each of the first 20 units sold $3 less as indicated by segment CE in figure 3 since before the imposition of the sales tax he/she receive a price of $8 on each of those 20 units.. Her/his total economic profit per unit decreases by $3 (=$8 - $5) on each one of the 20 units that he/she sells at the new equilibrium. The producer or supplier’s share of the tax burden is equal to $3/$4 = 75%. Her/his total economic profit decreases by much more. In summary, the price elasticity of the consumers demand curve is 10.17, much greater than one, the consumers’ share of the tax burden is 25%, and the supplier’s share of the tax burden in the form of a reduction of per unit economic profit is 75%. We conclude Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-13 When the price elasticity of the demand curve is high (much higher than one), producers or suppliers bear most of the tax burden and demanders or consumers bear little of the tax burden. We note that in this case, the sales tax is used to pay for unproductive government expenditures. The imposition of the sales tax Does not change the marginal social cost of production at any quantity produced and supplied, which is equal to the corresponding height of the supply curve CB before the imposition of the sales tax. Does not change the marginal social benefit as given by demand curve AB From the social point of view, the marginal social benefit for each one of the 60 units between the new equilibrium quantity of 20 units and the old equilibrium quantity of 80 units is greater than the corresponding marginal social cost. Therefore every one of these 60 units is worth producing and consuming as it results in a positive marginal net social benefit. After the government imposes the sales tax none of the 60 units between 20 and 80 units is produced and consumed anymore. After the imposition of the sales tax, society loses the total sum of the excesses of the marginal social benefit of each one of the 60 units over its corresponding marginal social cost. This sum is equal to the area of triangle ABC in figure 3, which is equal to $120. Area of triangle ABC is the Deadweight Loss associated with an unproductive sales tax. Before the imposition of an unproductive sales tax, the market produced an efficient allocation of resources at equilibrium point B in figure 3, since at B the marginal social benefit is equal to the marginal social cost. After the imposition of an unproductive sales tax, the market produced an inefficient allocation of resources at equilibrium point A in figure 3 since at A the marginal social benefit is equal to $9 in excess of $4 over the corresponding marginal social cost of $5. At the new equilibrium A the total net social benefit is lower than its maximum value achieved at B by an amount equal to the Deadweight Loss given by triangle ABC. Nobody benefits from the Deadweight Loss. We also note that this Deadweight Loss is equal to the sum of a $30 loss of consumer surplus, which is equal to the area of triangle ABE in figure 3 and a $90 loss of total economic profit, which is equal to the area of triangle BCE in figure 3. The government officials collect a total sales tax of $80 = ($1x20 units + $3x 20) Inelastic Demand curve Figure 4 reproduces figure 3 except that the price elasticity of the demand curve is now equal to zero. In figure 4, The demand curve AB is vertical. Its price elasticity is zero since the quantity demanded does not change when the price changes. The supply curve, before the imposition of the sales tax is CB, the same as in figure 3 The equilibrium price and quantity demanded and quantity supp-lied before the imposition of the sales tax are respectively $8 and 80 units the same respectively as in figure 3. The major difference between the two situations in figure 3 and in figure 4 is the price elasticity of the demand curve. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-14 As in figure 3, let the government impose an unproductive per unit sales tax of $4 and charge the producers or suppliers to collect the tax on its behalf. The sales tax is an additional cost to a seller or supplier. After the government imposes the sales tax, the total marginal cost of an additional unit at every quantity supplied, including the per unit sales tax, increases by $4. In figure 4, the supply curve shifts upward by $4 from supply curve CD to supply curve AF and the equilibrium point moves from B to A, the equilibrium price increases from $8 to $12, while the corresponding quantity demanded and supplied remain unchanged and equal to 80 units. Demanders or consumers pay the corresponding equilibrium price. At the equilibrium after the imposition of the sales tax, they pay $4 more than before the imposition of the sales tax. This is equal to the entire per unit sales tax on each unit they now purchase. Their share of the sales tax burden is 100%. The demanders or consumers buy and consume in the equilibrium before and after the imposition of the sales tax the same quantity of 80 units of the product because the price elasticity of the demand curve is zero. It follows that the equilibrium quantity supplied is also unchanged and remains equal to 80 units the same before and after the imposition of the sales tax. Figure 4 Inelastic Demand Curve and the Tax Burden Price 14 Supply Curve after 13 Sales Tax = $4 imposition of an A unproductive sales Tax 12 11 $4 =Consumer's Sales 10 D F Tax Burden per unit 9 8 E B 7 Supply Curve before 6 imposition of an 5 unproductive sales Tax C 4 3 Perfecctly inelastic Demand 2 Curve Ep= 0 1 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 Quantity Thus, the marginal cost not including the sales tax at the equilibrium quantity is the same and equal to $8 before and after the imposition of the sales tax. The producers or suppliers receive on each unit of the 80 units equilibrium quantity supplied after the imposition of the sales tax a price net of the sales tax equal to $8. This net price is equal to the difference between the equilibrium price of $12 that consumers pay after the imposition of the sales tax and the per unit sales tax of $4. Therefore, the marginal economic profit per unit supplied of a producer is unchanged and the total economic profit of all supplies taken together is unchanged equal to $160. Their total economic profit is equal to the area of triangle CBE in figure 4. This is the same total economic profit as they received before the imposition of the sales tax. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-15 The share of the suppliers or producers of the product in the sales tax burden is zero. We conclude that When the demand curve is perfectly inelastic, consumers or demanders bear the entire tax burden; sellers or suppliers bear none of it. In general, For the same price elasticity of the supply curve, the smaller is the price elasticity of the demand curve the greater (smaller) is the demanders or consumers (producers or suppliers) share of the burden of an unproductive sales tax. If the demand curve is perfectly inelastic, there is no Deadweight Loss In the case of an unproductive sales tax there is a Deadweight Loss when the demand curve is not perfectly inelastic. The relative shares in this Deadweight Loss are related in the same way to the price elasticity of the demand curve. If the supply curve is perfectly elastic, the imposition of an unproductive sales tax on a product Will cause a Deadweight Loss and Consumers will bear the whole burden of the tax. Suppliers or producers will bear none of it. Most li9lely necessities such as food have a perfectly inelastic demand curve and low income people are make up a substantial proportion of the electorate. It follows that politicians and government officials are fond of their decision to exempt food from sales taxes but they do not exempt them form the other costs of production of food. Productive Sales Taxes Promote Efficiency Contrary to what most economists and other people like to think, not all sales taxes cause a dead weith los or an efficiency loss. We now show that the imposition of a productive sales tax on the basis of economic principles prevents a deadweight loss of efficiency loss. In figure 5, straight line AB is a market demand curve for a product and the horizontal straight line CB at a price of $6 is its long run market supply curve in the absence of a productive sales tax and reflects only the private marginal cost We must now distinguish between Marginal Social Cost and Private Marginal Cost.. As we shall discover in a later chapter, the market supply curve CB is perfectly elastic because in the long run when perfect information prevails and there is free entry and exit, the industry’s private marginal cost is constant. As in figure 5, we assume that the industry’s long run private marginal cost is equal to $6 as horizontal line CD shows. Assume that perfect competition prevails in the market for this product. The equilibrium occurs at point B in figure 5 with an equilibrium price equal to $6 and equilibrium quantity demanded and supplied equal to 200 units. In the absence of an appropriate productive sales tax, the private marginal cost does not include the additional unit cost of $2, associated with building and maintaining the appropriate infrastructure necessary for this product market to operate properly. Then, the marginal social cost is equal to $8 = $6 + $2. Horizontal straight line FG in figure 5 at a constant marginal social cost of $8 represents correctly the marginal social cost curve. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-16 It follows that the height of horizontal straight line CB, which represents the industry’s private marginal cost of $6, underestimates the marginal social cost. At the equilibrium quantity demanded and supplied of 200 units, the marginal social benefit is equal to the private marginal cost of $6, which is lower than the marginal social cost, which is equal to $8 Thus, at the equilibrium quantity demanded and supplied of 200 units under perfect competition, the marginal social benefit is lower than the marginal social cost. The perfect competition equilibrium is not efficient. According to figure 5, at any quantity between 0 and 80 units, the marginal social benefit of an additional unit, as given by the height of demand curve AB at that quantity is greater than the marginal social cost of $8. Therefore, the additional unit should be produced and consumed and the total net social benefit increases. At 80 units in figure 5, the marginal social benefit is equal to the marginal social cost. At any quantity greater than 80 units in figure 5, the marginal social benefit is less than the marginal social cost. Producing more than 80 units would lower the total net social benefit. At 80 units in figure 5, where the demand curve or the marginal social benefit curve AB intersects the marginal social cost curve FG, the marginal social benefit is equal to the marginal social cost and the total net social benefit is at its maximum, as represented by the area of triangle AEF in figure 5. Figure 5 A Productive Sales Tax Removes an Efficiency Loss If we accept the current view that any sales taxes is a burden and a source of inefficiency and we rely on perfect competition in the allocation of resources, the market will settle at equilibrium point B in figure 5. This equilibrium involves an inefficient allocation of resources and overproduction of the product. We know that producing and consuming units between 80 and 200 units in figure 5 would result in a lower total net social benefit than at 80 units. The production of those units would result in Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-17 a Deadweight Loss equal to the area of triangle BEG in figure 5. The Deadweight Loss is equal to $2 x (200 - 80) $120 = = $120. 2 There is no free lunch. Indeed, history shows that countries whose governments borrows to build infrastructure and does not charge for it through the imposition of a tax or a user fee ended up colonized, oppressed, and poor. Let government impose a tax of $2 equal to the marginal cost of building and maintaining the infrastructure. If politicians do not use the tax proceeds for frivolous other activities that cater to their own interests then the private marginal cost becomes equal to the marginal social cost. The marginal social cost curve FG in figure 5 becomes the private marginal cost curve and the correct long run supply curve. Perfect competition regains its powers to achieve an efficient allocation of resources at the intersection point E of the correct long run supply curve FE and demand curve AB. Society avoids a Deadweight Loss and the imposition of the correct sales tax per unit of the product helps the economy achieve an efficient allocation of resources. The government must use the total collected tax to improve roads and services and/or interest on debt incurred to build the productive infrastructure.. There is no more quibbling about who pays for the tax. The sales tax represents a cost of production and in the long run there is no economic profit under perfect competition. The long run supply curve is flat and its price elasticity is infinite. Efficiency requires that consumers must pay for the full unit cost of a product they wish to consume. Producers earn a zero economic profit and they pay no tax. The difference between the total revenue from the sales of product at the higher efficient equilibrium price and the total costs other than the sales tax is equal to the total revenue of the government equal to area CDEF in figure 5 = $2 x 80 = $160, enough to pay for the cost of building and maintaining the infrastructure and the provision of the environment necessary for the market to function properly under perfect competition. If the price elasticity of the supply curve is infinite, consumers pay the entire sales tax. Sales Taxes on Imports or a Tariff Tariffs are sales taxes on imported products from other countries in addition to the national sales tax. Tariffs discriminate against foreign produced products. They have proved to be damaging to the standards of living of the average person and they are associated with the advent of World War II. We have seen in the chapter on international trade (chapter 4) that, under perfect competition and if there is no bullying or manipulation by powerful countries, free trade improves the standard of living both of advanced and less advanced countries alike. One way a country’s government could manipulate markets that operate under perfect competition is to impose a tariff. Like an unproductive sales tax, a tariff on imports causes a Deadweight Loss, an inequitable distribution of income, and an inefficient allocation of resources. In the case of a tariff, both the people living in the exporting country and the people living in the country whose government imposes a tariff lose in the short and the long run. When the country imposing the tariff is large its citizens may gain before the other country retaliates by imposing its own tariffs on its imports from the large country. The best recent example of a tariff is the recent move by a large developed country to impose a 25% tariff on the imports of steel, aluminium, and a 10% tariff on cars and other imported products, in retaliation and purportedly for national security reasons. The extent of the Deadweight Loss and the distribution of the burden of the tariff between the people of the country whose government imposes the tariff and the people of the other exporting country depend in part on the price elasticities of the demand curve and the supply curve. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-18 In the long run, the price elasticity of the market supply curve is much greater than its elasticity in the short run. Accordingly, we consider two cases: A supply curve that has a finite elasticity and a perfectly elastic supply curve. Case A: Elastic Supply Curve: Short Run In figure 6, suppose that straight line AB is the market demand curve for an imported product in a given country and straight line CB is its market supply curve by foreign producers in the absence of tariffs. The market supply curve CB is upward sloping it is also the marginal social benefit curve. Assume that perfect competition prevails in the market for this product. The equilibrium occurs at point B in figure 6 with an equilibrium price equal to $6 and equilibrium quantity demanded and supplied equal to 200 units. The country imports 200 units of the product. At equilibrium point B in figure 6, the marginal social cost is equal to the marginal social benefit equal to $6. Thus, at equilibrium point B, there is an efficient allocation of resources. As Columns (1), (2) and (3) of Table 2 below show, at this equilibrium without a tariff, The consumer surplus of the consumers of the product importing country is equal to area of triangle AHB in figure 6 equal to $333. The producer surplus or economic profit of the producers of the product exporting country is equal to area of triangle HBC in figure 6 equal to $333. Figure 6 A Tariff and Efficiency loss or Deadweight Loss Maximum total net social benefit = area of triangle ABC in figure 6 = $666 = Consumer Surplus + Producer Surplus = $333 + $333 Table 2 Decomposition of the Maximum Total Net Social Benefit No Tariff $2 Tariff Loss (1) (2) (3) (4) (5) (6) ($9.33 - $6) x 200 ($9.33 - $7) x 140 Consumer surplus = $333 = $163 - $170 2 2 Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-19 Producer surplus = ($6 - $2.66) x 200 ($5 - $2.66) x 140 = $333 = $163 - $170 Total economic profit 2 2 Total government 0 $0 ($2 x 140) = $280 $280 revenue from tariff Maximum total net ($9.33 - $2.66) x 200 $666 (($9.33 - $2.66) + $2) x 140 = $606 -$60 social benefit = 2 2 0 $2 x (200 - 140 ) Deadweight loss = $60 2 Now, suppose that the government of the product importing country imposes a $2 tariff on every unit imported that producers or suppliers must collect on its behalf. Then, the private marginal cost on every unit he/she exports to the country imposing the tariff of every foreign producer or supplier must increase by the same amount as the tariff of $2. The supply curve of the imported product shifts upward by $2 from CB to FE in figure 6. Clearly, the marginal social cost is not affected and straight line CB in figure 6 remains the marginal social cost curve while straight line FE in figure 6 represents now the private marginal cost and it represents also the new market supply curve after the imposition of the tariff. Perfect competition in the market for this product after the imposition of the tariff results in a new equilibrium given by the intersection point E in figure 6 of the same market demand curve AB and the new market supply curve FE, The equilibrium quantity falls from 200 units to 140 units and the equilibrium price increases from $6 to $7. Since the marginal social benefit curve AB and the marginal social cost curve CB do not change, the new equilibrium under the tariff is not efficient. Indeed, at the equilibrium quantity of 140 units, the marginal social benefit exceeds the marginal social cost by $2 since at 140 units, The marginal social benefit as given by the height of demand curve AB is equal to $7and The marginal social cost as given by the height of the marginal social cost curve CB is equal to $5. Figure 6 A Tariff and Efficiency loss or Deadweight Loss Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-20 The area of trapezoid ACDE in figure 6, which is reproduced above for convenience, is equal to the maximum total net social benefit after the government of the product importing country imposes the $2 tariff on every unit imported and consumed. This area is equal to the sum of the excesses of the marginal social benefit (height of demand curve AB) over the marginal social cost (height of straight line CB) for every unit produced and consumed between zero and the new equilibrium quantity demanded and supplied of 140 units at point E in figure 6. As columns (1), (4) and (5) of Table 2 show, at the equilibrium point E with a $2 tariff in figure 6, The consumer surplus of the consumers of the product importing country is equal to the area of triangle AEJ equal to $163. The producer surplus or total economic profit of the producers of the product exporting country is equal to the area of triangle CDK equal to $163. Total Tariff Revenue of Government imposing the tariff = area of rectangle DEJK = $280 Maximum total net social benefit = area of trapezoid ACDE = $606 = Consumer Surplus + Producer Surplus + Total Tariff Revenue = $163 + $163 + $ 280 Deadweight Loss associated with the imposition of the tariff = area of Triangle DEB= $60 As column 6 of Table 2 shows, the maximum total net social benefit is $60 ($666– $606) smaller after the government of the product importing country imposes the tariff than it was before the imposition of the tariff. The area of triangle DEB in figure 6 represents this loss in the maximum total net social benefit. Clearly, the imposition of the tariff on the imported product causes an efficiency loss equal to the Deadweight Loss corresponding to the failure to produce and consume units from 140 to 200, for which the marginal social benefit is greater than the marginal social cost. The increase in the equilibrium price of the product by $1 from $6 to $7 as the equilibrium moves from point B to point E in figure 6 means that the government grabbed a portion, equal to the area of rectangle EGHK in figure 6 equal to $140 = ($1x140), of the much larger consumer surplus $333 that consumers enjoyed in the absence of the tariff. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-21 Consumers of the country whose government imposes the tariff lose another chunk of the consumer surplus, they enjoyed before the imposition of the tax. This chunk is equal to the area of triangle BEG in figure 6 equal to half of the Deadweight Loss. This second chunk is part of the consumer surplus that nobody gets because of the imposition of the tariff. It is equal to the sum of the excesses of the marginal social benefit over the no tariff equilibrium price of $6 over the units between 140 and 200. In addition, because of the higher equilibrium price of $7 after the imposition of the tariff, some of the consumers are priced out of the market. These consumers would be the lower income consumers whose willingness to pay is lower because they have a lower income. In addition to causing a Deadweight Loss, the imposition of the tariff by the government of a country increases income inequality in that country by hurting the poorest section of the country’s population. The foreign producers, sellers or exporters of the product receive now a net price of $5 (= equilibrium price of $7 after imposition of the tariff - $2 tariff) on a lower number of 140 units they can export after the imposition of the tariff. Before the tariff was imposed, foreign producers or suppliers received an equilibrium price of $6 on the 140 units. Their total economic profit on those units shrunk by an amount equal to $140 (= ($6 - $5) x 140 units). This amount is equal to the area of rectangle DGHK in figure 6. The government that imposed the tariff appropriates this amount. The foreign producers or suppliers also lose a chunk of their total economic profit equal to the other half of the Deadweight Loss given by the area of triangle BDG in figure 6. We conclude that in the case of an upward sloping market supply curve, the burden of paying for the tariff is shared between the consumers of the country whose government imposed the tariff and the foreign producers or sellers of the product. The government of the country imposing the tariff may claim success as it extracted part of the total economic profit that used to be earned by foreign producers or suppliers of the product. Case B: Perfectly Elastic Supply Curve: Long Run The situation is significantly different when the supply curve of the imported product is perfectly elastic as it is in the long run for many manufactured products. In figure 7, straight line AB is the market demand curve for an imported product in a given country and the horizontal straight line CB at a price of $6 is now its market supply curve by foreign producers or sellers in the absence of tariffs. Market supply curve CB is perfectly elastic because in the long run, when perfect information prevails and there is free entry and exit, the marginal social cost is constant, equal to the minimum long run average cost, as we shall show in a later chapter. In the case of figure 7, we assume that the minimum long run average cost and marginal cost are equal to $6. In figure 7, the equilibrium before the imposition of the tariff occurs at point B with an equilibrium price equal to $6 and equilibrium quantity demanded and supplied equal to 200 units. Figure 7 A Tariff and Deadweight Loss: an Infinitely Elastic Supply Curve Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-22 The country imports 200 units of the product. At equilibrium point B without a tariff, The marginal social cost is equal to the marginal social benefit, equal to $6, We have an efficient allocation of resources. The consumer surplus of the consumers of the product importing country is equal to area of triangle ABC equal to $333. The producer surplus or economic profit of the producers or suppliers of the exporting country’s product is equal to zero. Maximum total net social benefit = area of triangle ABC in figure 7 = $333 = Consumer Surplus + Producer Surplus = $333 + $0 = $333 Now, suppose that the government of the product importing country imposes a $2 tariff tax on every unit imported that suppliers must collect on its behalf. Then, the marginal private cost of every foreign producer or supplier must increase by the same amount as the tariff from $6 to $8 and the marginal private cost curve of the foreign producer or supplier of the product along with the market supply curve shifts upward from CB to FH in figure 7. Clearly, the marginal social cost is not affected and straight line CB in figure 7 remains the marginal social cost curve while straight line FE in figure 7 represents now the marginal private cost and it represents also the new market supply curve after the imposition of the tariff. Perfect competition in the market for this product results in a new equilibrium given by the intersection point E in figure 7 of the same market demand curve AB and the new market supply curve FE, The equilibrium quantity falls from 200 units to 80 units and the equilibrium price increases from $6 to $8.The importing country imports fall from 200 units to 80 units. Since the marginal social benefit and the marginal social cost curves do not change, it follows that the area of trapezoid AEGC in figure 7 is equal to the maximum total net social benefit after the government of the product importing country imposes the $2 tariff on every unit imported and consumed. This maximum is equal to the sum of the excesses of the marginal social benefit (height of straight line AB) over the marginal social cost (height of straight line CB) for every unit produced Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-23 and consumed between zero and the new equilibrium quantity demanded and supplied of 80 units at point E in figure 7. Table 3 Decomposition of the Maximum Total Net Social Benefit No Tariff $2 Tariff Loss (1) (2) (3) (4) (5) (6) Consumer surplus ($9.33 - $6) x 200 ($9.33 - $8) x 80 - $280 = $333 = $53.33 2 2 Producer surplus = ($6 - $6) x 200 $0 ($6 - $6) x 80 $0 0 = = Total economic profit 2 2 Total government = $0 ($2 x 80) = $160 +$160 revenue from tariff Maximum total net ($9.33 - $2.66) x 200 $333 (($9.33 - $6) + 2)x 80 $213.3 -$120 social benefit = 2 2 Deadweight loss 0 $2 x (200 - 80) $120 $120 = 2 As columns (1), (4) and (5) in Table 3 show, the maximum total net social benefit after the imposition (($9.33 - $6) + $2) x 80 of the $2 tariff = Area of trapezoid AEGC = = $213.3 2 Thus, the maximum total net social benefit after the imposition of the tariff is $120 (= $333.33– $213.3) lower after the imposition of the tariff than it was before the imposition of the tariff. This difference is equal to the Deadweight Loss and as columns (1), (4) and (5) of Table 3 show, Deadweight Loss = area of triangle EGB = $120. Columns (1), (4) and (5) in Table 3 give the details of the computations after the government of the product importing country imposes the $2 tariff. Clearly, the imposition of the tariff on the imported product causes an efficiency loss equal to the Deadweight Loss corresponding to the failure in the new equilibrium to produce the units from 80 to 200 units for which the marginal social benefit is greater than the marginal social cost. The increase in the equilibrium price of the product by $2 from $6 to $8 as the equilibrium moves from point B to point E in figure 7 means, as Table 3 shows, that the total revenue of the government imposing the tariff is equal to the area of rectangle CFEG equal to $160 = ($2x80). The tariff imposing government has grabbed a portion equal to $160 of the much larger consumer surplus given by area ABC that consumers enjoyed before the imposition of the tariff on imports. The foreign producers exporters of the product receive the same net price as before of $6 (= equilibrium price of $8 after imposition of the tariff - $2 tariff or tax) on a lower number 80 of units they export after the imposition of the tariff or tax. Before the tariff or tax was imposed foreign producers or suppliers received an equilibrium price of $6 on the 80 units. Their total economic profit on those units is still zero as the net price they receive is the same $6 and it is equal to their marginal private cost. In this case of a long run market supply curve with infinite price elasticity, the burden of paying for the tariff is borne entirely by the consumers of the country whose government imposed the tariff. Furthermore, the government imposing the tariff may claim success in reducing imports but it is Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-24 wrong for it to claim that its country as a whole has gained since the government extracted nothing from the profits that used to be earned by foreign exporters. It only bled its own citizens and caused more income inequality as now a larger number of low-income people will not be able to consume the units 81 to 200 of the product. There are some benefits to its country from restraining free trade by the government that imposes a tariff on its imports. Those benefits consist in the protection of local producers with high marginal cost. These benefits may turn out to be ephemeral if a later government of the country or the current government itself removes the tariff to avoid retaliation by the government of the foreign country whose producers would suffer from the imposition of the tariff, to restore efficiency, or to reverse the increase in income inequality. Such possibilities of reversal of policy increase uncertainty in economic activity and wipe out the benefits of a temporary tariff. Conclusions The price elasticity of a demand curve is the percentage change in the quantity demanded in response to a one percent change in price. Managers of firms who have a substantial control over the price of their own product are interested in increasing their firm’s market share since their total compensation (wages and fringe benefits) depends on their firm’s market share and on its total revenue, both of which depend on the price and the quantity demanded of the firm’s product. Knowledge of the price elasticity of the demand curve for their firm’s product helps predict the impact of a price change on such firm’s market share, total revenue, and profit. If the price elasticity of the demand curve for the product of a company whose managers hold a monopoly over the production and/or sales of the product is higher than one, then an increase in the price of the product may result in a substantial fall in the quantity demanded of the product, a fall in the company’s market share, a fall in her total revenue, and possibly a fall in the total economic profit as well as the total compensation of the managers. In this case, lowering the price or improving the quality of the product might be a better alternative. A demand curve is elastic if its price elasticity is greater than one. It is inelastic if its price elasticity is smaller than one. It is unit elastic if its price elasticity is equal to one. A horizontal demand curve is perfectly elastic and its price elasticity is infinite. A vertical demand curve is perfectly inelastic and its price elasticity is zero. The price elasticity of a supply curve is the percentage change in the quantity supplied in response to a one-percentage change in price. The income elasticity of a demand curve is equal to the ratio of the percentage change in the quantity demanded and the percentage change in the average income of the demanders. There are two kinds of a sales tax, an unproductive sales tax and a productive sales tax. An unproductive sales tax is a sales tax that is used by government officials and politicians to pay for unproductive government expenditures. A productive sales tax is a sales tax that serves to finance the building and maintenance of the economy’s infrastructure and superstructure, which help markets function better under perfect competition and the members of society improve their productivity. Everything else equal, when the demand curve for a product is elastic, the sellers or suppliers of the product bear most of an increase in an unproductive sales tax. When the demand curve for a product is inelastic, the demanders or consumers bear most of an increase of an unproductive sales tax. Chapter 5 The Concept of Elasticity and its Applications, Chapter 5 Elasticity and its applications Introductory Microeconomics June 2023, 8/21/2024 4:56 PM 5-25 A tariff on imports is a discriminatory sales tax against other countries producers. Like it is the case for an unproductive sales tax, a tariff on imports causes a Deadweight Loss, a misallocation of resources, and it hurts the low-income people when imposed on imports of products heavily consumed by them. A tariff destroys free trade and gives rise to trade wars since most other countries will retaliate. The imposition of a tariff on imports amounts to a beggar thy neighbour policy. A Deadweight Loss is a loss of a portion of society’s total net social benefit that benefits nobody. A productive sales tax removes a Deadweight Loss and leads to an efficient allocation of resources. It is part of the social marginal cost. As it should be, in the long run, demanders or consumers must bear the entire burden of a productive sales tax. Producers or suppliers bear none. End