Web Supplement to Chapter 2


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1 Web upplement to Chapter 2 UPPLY AN EMAN: TAXE 21 Taxes upply and demand analysis is a very useful tool for analyzing the effects of various taxes In this Web supplement, we consider a constant tax per unit of output How will the equilibrium price and quantity of a product be affected if a tax of T $10/unit is levied on each unit sold by the producer? There are two equivalent ways to approach this question The first is to suppose that the tax is levied on the seller In Figure 21, the line denotes the original supply schedule At a price of P 0 $25/unit, sellers were willing to supply Q 0 units of output When a tax T 10 is levied on sellers, the market price would have to be P 0 10 $35/unit for them to get the same net payment that they used to receive when the price was P 0 $25/unit At a price of $35/unit, then, suppliers will offer the same amount of output they used to offer at a price of $25/unit The resulting aftertax supply schedule is the original supply schedule shifted upward by T 10 In Figure 22, represents the demand curve facing the sellers who have been taxed T $10 per unit of output The effect of the tax is to cause the equilibrium quantity to fall from Q * to Q* 1 The price paid by the buyer rises from P * to P* 1, and the price, net of the tax, received by the seller falls to P* 1 10 Note in Figure 22 that even though the seller pays a tax of T on each product purchased, the total amount the seller receives per unit lies less than T below the old equilibrium price Note also that even though the tax is collected from the seller, its effect is to increase the price paid by buyers The burden of the tax is thus divided between the buyer and the seller Algebraically, the seller s share of the tax, denoted t s, is the reduction in the price the seller receives, divided by the tax: t s P* 1P* 1 T2 T (21) 21 TAXE 21
2 FIGURE 21 A Tax of T $10/Unit Levied on the eller hifts the upply chedule Upward by T Units The original supply schedule tells us what price suppliers must charge in order to cover their costs at any given level of output From the seller s perspective, a tax of T $10/unit is the same as a unitcost increase of $10 o the new supply curve lies $10/unit above the old one 35 = P 0 + T 25 = P 0 ' Q 0 T = 10 ' FIGURE 22 Equilibrium Prices and Quantities When a Tax of T $10/Unit Is Levied on the eller The tax causes a reduction in equilibrium quantity from Q* to Q* 1 The new price paid by the buyer rises from P* to P* 1 The new price received by the seller falls from P* to P* 1 10 P* 1 P* P* 1 10 ' ' T = 10 Q* 1 Q* imilarly, the buyer s share of the tax, t b, is the increase in price (including tax) divided by the tax: EXERCIE 21 Verify that t s t b 1 t b P* 1 P* T (22) In general, t b and t s depend on the shapes of the supply and demand schedules If, for example, supply is highly unresponsive to changes in price, t b will be close to zero, and t s will be close to 1 Conversely, if demand is highly unresponsive to price, t b will be close to 1, and t s will be close to zero These claims amount to a statement that a tax tends to fall most heavily on the side of the market that can least escape it If buyers have no substitute products to which they are prepared to turn, the lion s share of the 22 Web upplement to Chapter 2: UPPLY AN EMAN: TAXE
3 tax will be passed on to them by suppliers But if suppliers have no alternative other than to go on supplying a product, most of the burden of a tax will fall on them As long as the supply curve is positively sloped and the demand curve is negatively sloped, however, both t s and t b will be positive The second way of analyzing the effect of a tax of T $10 per unit of output is to imagine that the tax is collected directly from the buyer and to analyze how that would affect the demand curve for the product In Figure 23, the demand curve before the imposition of the tax is denoted by the line At a price of P 1, buyers would demand a quantity of Q 1 After the imposition of the tax, the total amount that buyers have to pay if the product price is P 1 will be P 1 10 Accordingly, the quantity the buyers demand falls from Q 1 to Q 2 In like fashion, we can calculate the quantity demanded at any other price after imposition of the tax The resulting aftertax demand curve will be the line in Figure 23 It is simply the original demand curve translated downward by $10/unit If line in Figure 24 denotes the supply schedule for this market, we can easily trace the effects of the tax on the equilibrium price and quantity The equilibrium quantity falls FIGURE 23 The Effect of a Tax of T $10/Unit Levied on the Buyer Before the tax, buyers would buy Q 1 units at a price of P 1 After the tax, a price of P 1 becomes P 1 10, which means buyers will buy only Q 2 The effect of the tax is to shift the demand curve downward by $10/unit P ' P 1 T = 10 Q 2 Q 1 ' FIGURE 24 Equilibrium Prices and Quantities After Imposition of a Tax of T $10/Unit Paid by the Buyer The tax causes a reduction in equilibrium quantity from Q* to Q* 2 The new price paid by the buyer rises from P* to P* 2 10 The new price received by the seller falls from P* to P* 2 ' P* P* P* 2 Q* 2 Q* T = 10 ' 21 TAXE 23
4 from Q * to Q* 2, and the equilibrium price falls from P * to P* 2 The total price paid by the buyer after imposition of the tax rises to P* 2 10 Is the effect of a tax on the seller any different from the effect of a tax levied on the buyer? Not at all To illustrate, suppose the supply and demand curves for a market are given by P Q s and P 10 Q d, respectively, and consider first the effect of a tax of $2 per unit of output imposed on the seller Figure 25( a ) shows the original supply and demand curves and the new aftertax supply curve, The original equilibrium price and quantity are both equal to 5 The new equilibrium price to the buyer (inclusive of tax) and quantity are $6 per unit and 4 units, respectively The price received by sellers, net of the tax, is $4 per unit Now, consider a tax of $2 per unit of output imposed on the buyers Figure 25( b ) shows the original supply and demand curves and the new aftertax demand curve, Note that the effects on price and quantity are exactly the same as in the case of the tax levied on sellers shown in panel ( a ) FIGURE 25 Price Price A Tax on the Buyer Leads to the ame Outcome as a Tax on the eller The price received by sellers (net of the tax), the price paid by buyers (including tax), and the equilibrium quantity will all be the same when the tax is collected from sellers (panel [a]) as when it is collected from buyers (panel [b]) ' ' T = (a) 10 8 ' Quantity (b) T = 2 ' 8 Quantity 10 EXERCIE 22 Consider a market whose supply and demand curves are given by P 4 Q s and P 12 2 Q d, respectively How will the equilibrium price and quantity in this market be affected if a tax of $6 per unit of output is imposed on sellers? If the same tax is imposed on buyers? When tax revenues have to be raised, political leaders may find it expedient to propose a sales tax on corporations because they can best afford to pay it But careful analysis of the effects of a sales tax shows that its burden will be the same whether it is imposed on buyers or sellers The legal incidence of the tax (whether it is imposed on buyers or on sellers) has no effect on the economic incidence of the tax (the respective shares of the tax burden borne by buyers and sellers) Economically speaking, the entity from which the tax is actually collected is a matter of complete indifference A word of caution: When we say that the economic burden of the tax does not depend on the party from whom the tax is directly collected, this does not mean that buyers and sellers always share the burden of taxes equally Their respective shares may, as noted, be highly unequal The independence of legal incidence and economic incidence simply means that the burden will be shared in the same way no matter where the tax is placed 24 Web upplement to Chapter 2: UPPLY AN EMAN: TAXE
5 QUETION FOR REVIEW wwwmcgrawhillca/olc/frank 21 The steeper the demand curve for some good relative to the supply curve for that good, the greater the proportion of a tax on that good that will fall on buyers True or false? Explain, using a diagram 22 uppose you are an elected government member and need to collect revenue by taxing a product For political reasons, you want the burden of the tax to fall mostly on consumers, not firms (who have been substantial contributors to your campaign fund) What should you look for when picking a product to tax? PROBLEM 21 The government, as a revenuegenerating measure, imposes a tax of $2/kg on the retail price of gumdrops It collects the tax from gumdrop sellers The original supply and demand schedules for gumdrops are as shown in the following diagram how, in the same diagram, how the shortrun equilibrium price and quantity of gumdrops will be affected by the tax Label all important points clearly How much tax revenue does the government receive? Price ($/kg) Quantity (tonnes/yr) 22 In the market for gumdrops described in Problem 21 (with no tax), suppose that a price floor of $4/kg results in sales of only 2 tonnes/year If the price floor was removed, describe a transaction that would make some buyers and sellers better off without harming others 23 uppose the gumdrop market in Problem 21, with a tax of $2/kg, experiences growth in the demand for gumdrops because of newfound medical uses The new demand curve is P 8 Q, where P is in $/kg and Q is in tonnes Find the change in government tax revenue due to the heightened demand for gumdrops 24 uppose instead that the gumdrop market in Problem 22, with no tax but a price floor at $4/kg, suffers a reduction in supply The new supply curve is P 2 Q a How does excess supply change due to the reduction in supply? b Is the price floor still binding (does it cause price to be above its equilibrium level)? 25 The market for Vs has supply and demand curves given by P 2 Q s and P 42 Q d, respectively, where P is in $/V and Q s and Q d are in Vs Construct and label a diagram a (i) How many units will be traded at a price of $35? (ii) At a price of $14? (iii) Which participants will be dissatisfied at these prices? b What quantity of Vs at what price will be sold in equilibrium? c What is the total revenue from V sales? Where is it shown on your diagram? PROBLEM 25
6 wwwmcgrawhillca/olc/frank 26 uppose that in the market described in Problem 25, the government levies a tax of $9 on each V sold, collected from sellers a What quantity of Vs will be sold in equilibrium? b (i) What price do buyers pay? (ii) How much do they spend in total? c (i) What aftertax price do sellers now receive? (ii) What is their total aftertax revenue? d How much money goes to the government? e how the above results graphically 27 For the tax described in Problem 26, (a) what fraction of the tax do the sellers bear and (b) what fraction of the tax do the buyers bear? *28 The Frug, a subcompact car, is produced only in the small country of Leutonia The Canadian government, concerned by high levels of Frug imports, negotiates a voluntary import quota on Frugs with Leutonian Frug exporters ome Canadian economic advisers recommend using an import tax (or tariff) instead If the tariff (at $T per Frug) was set to produce the same reduction in imports as the quota, a How will the prices paid for Frugs by Canadian consumers compare under the two policies? b How much revenue will Frug exporters receive? c How much import tariff revenue will the Canadian government receive under each policy? how your results in a diagram *29 Because of concerns that barbecuing meat using charcoal may cause cancer, the government decides to impose a 100 percent tax at the retail level on charcoal briquettes uppose the daily demand for charcoal was P 120 2Q and the supply was P 30 Q, where P is in dollars and Q is the number of 10kg bags of charcoal sold daily a Give the beforetax charcoal price and quantity exchanged b Give the aftertax charcoal price to buyers, the quantity exchanged, and total tax revenues c How is the tax divided among sellers and buyers? 210 In the Gizmo market, supply is given by the equation P 4 Q, while demand is given by P 20, where P is price in dollars per unit and Q is quantity in units per week a Find the equilibrium price and quantity (using both algebra and a graph) b If sellers must pay a tax of T $4 per unit, what happens to the quantity exchanged, the price buyers pay, and the price sellers receive (net of the tax)? c How is the burden of the tax distributed across buyers and sellers and why? 211 Repeat Problem 210, but instead suppose the buyer pays the tax, demand is P 28 Q, and supply is P uppose the supply of a good is given by the equation P Q and demand is fixed at Q 12 units per week, with P in dollars per unit a Find the equilibrium price and quantity b uppose the government levies a tax equal to $4 per unit on sellers of the good Find the equilibrium quantity, price paid by buyers, and price received by the sellers (net of taxes) c How is the tax burden distributed and why? *Problems marked with an asterisk are more difficult 26 Web upplement to Chapter 2: UPPLY AN EMAN: TAXE
7 ANWER TO INUPPLEMENT EXERCIE wwwmcgrawhillca/olc/frank 21 t s t b [(P * P* 1 T ) ( P* 1 P * )]/T T /T The original price and quantity are given by P * $8/unit and Q * 2 units, respectively The supply curve with the tax is given by P 6 4 Q s Letting P and Q denote the new equilibrium values of price and quantity, we now have 6 4 Q 12 2 Q, which yields Q 1 unit P $10/unit, where P is the price paid by buyers P 6 $4/unit is the price received by sellers Alternatively, the demand curve with a tax of $6/unit levied on buyers is given by P 6 2Q d, and we have 4 Q 6 2Q, which again yields Q 1 unit P $4/unit, where P is the price received by sellers P T P 6 $10/unit is the price paid by buyers, including the tax ANWER TO INUPPLEMENT EXERCIE 27
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