Econ. 410Spring 2008Tauchen/BiglaiserPractice Problems Answers -- Applications of the Competitive ModelIn addition to these practice and homework problems, be sure that you have worked through the examples in the text for the effects of per unit taxes, per unit subsidies, minimum prices and maximum prices. With linear demand and supply curves, the surplus areas are combinations of triangles and rectangles, so it is straightforward (but tedious and somewhat repetitive) to compute numerical values for the surpluses. In the problems below you need not provide a numerical answer unless specifically asked. 1. The following questions are based on the graph on page 409.a. Determine the per unit tax that would result in an equilibrium quantity of 600 units. Answer:$2 per packb. What price do consumers pay for each pack? What price do sellers receive for each pack? Answer: $3, $1c. Complete the chart below.Competitive Outcome Outcome with Per Unit TaxCS F+E+G E+FPS C+L+B BGovernment Surplus E+CTotal Surplus F+E+C+B+G+L F+E+C+A 2. Good X is produced in a competitive market and the graph below shows the market supply and demand curves.a. A per unit tax of $40 is levied on the good and the tax revenues are collected from the purchasers of the product. i. Determine the equilibrium quantity, the total price paid by consumers, and the net price received by firms.ii. Determine the consumer surplus, the producer surplus, tax revenue, and total surplus. You may find it easier to work with a graph that includes only the initial demand and supply curves in order to determine the consumer and producer surplus. b. Compare the total surplus with the tax to the total surplus for the case in which the tax revenues are collected from the seller.c. Suppose now that the tax is levied in a manner analogous to the Social Security system with a$20 tax levied on the sellers and a $20 tax levied on the purchasers. Compare the consumer, producer, and total surplus for this tax system with the tax system from part a.Answer: The graph shows thesupply and demand curvescorresponding to each of theinstitutional arrangements forlevying the tax. Purchasers pay $40 to the taxagent: The demand curve shiftsdown by $40. (We use the initialsupply curve) The equilibriumquantity is 20. The market price is$20. The total cost to consumers is$60 for each unit and the pricereceived by firms is $20.Sellers pay $40 to the tax agent:The supply curve shifts up by $40.(We use the initial demand curve.)The market price is $60. The totalcost to consumers is $60 for eachunit and the net price received byfirms is $20.A tax of $20 per unit is levied onconsumers and a tax of $20 per uniton firms: The market price is$40. The total cost to consumersis $60 for each unit and the netprice received by firms is $20.The simplest approach is touse the initial demand and supplycurves to show the consumersurplus and the producer surplusand to show the tax revenues. Asnoted above, consumers pay $60for each unit, firms receive $20 foreach unit sold and the governmentreceives $40. The consumer andproducer surplus and thegovernment tax receipts are thesame for each of the institutionalarrangements for levying the tax.3. Use the graph on page 388 of Besanko and Breaeutigam for this question. a. Determine the numerical values of consumer surplus, producer surplus, and total surplus at the competitive equilibrium. Answer: See the first column of Figure 10.2.b. A tax of $6 per unit is placed on the good. Determine the new consumer surplus, producer surplus, tax revenue, and total surplus.Answer: With a tax of $6 per unit, consumers pay $12 for each unit and sellers receive $6 for each unit. The equilibrium quantity is 4 million units per year. Consumer Surplus The area of YTR is $16 million (per year). Producer Surplus The area of the triangle bounded by W,Z, and $6 on the verticalaxis is $8 million (per year).Tax Revenue The area of the rectangle bounded by R, T, W and $6 on the vertical axis is $24 million. Total Surplus $48 million (per year)4. The equilibrium price and quantity in the competitive market for good X are $10 and 100 units. a. Construct two examples. In each example the equilibrium price is $10 and the equilibrium quantity is 100. In one example, the demand schedule is very price inelastic and in the other the demand schedule is very price elastic.b. In both markets, a per unit tax of $5 is imposed. Determine the change in consumer surplus and total surplus as a result of the tax. Compare the changes for the two cases. As a result of the tax, the consumer surplus changes from the area A+B to the area A.As a result of the tax, the consumer surplus changes from the area F+G to the area F.The reduction in quantity is much smaller for the product with inelastic demand than for the product with elastic demand.The deadweight loss of taxation is the area ABC. The deadweight loss is marked as DWL.c. Are your results an argument for taxing insulin rather than movie tickets? Explain.Answer: In addressing this issue, we must consider the income distribution. As mentioned above, the tax on the product with inelastic demand results in a smaller reduction in quantity than the tax on the product with elastic demand – or in other words, there is less distortion in the quantity. If we are able to redistribute income in some other manner (for example through the federal earned income tax credit) , then we can consider only the effects of the tax on the surpluses in the market in deciding which good to tax. 5. The equilibrium price and quantity in the competitive market for good X are $10 and 100 units.a. Construct two examples. In both examples the equilibrium price is $10 and the equilibrium quantity is 100. In one example, the supply schedule is very price inelastic and in the other the demand schedule is very price elastic. b. In each market, a per unit tax is imposed. Determine the change in producer surplus and total surplus as a result of the tax. Compare the changes for the two cases.The deadweight loss of taxation is ABC in the two cases above. 6. For the example in Section 10.13 of the text, the government sets a quota of 4 million units per year. In the set-up of the problem in the text, the market price is the price such that consumers demand 4 million units so that there is no excess demand for the good. The text assumes that the most efficient (lowest cost) firms are allowed to produce the good.