Unformatted text preview: PADP 8670 Fertig Fall 2011 UGA Homework 4 Due September 19, 2011 1. The diagram shows the demand and supply for passenger rail service between two cities. Initially the price per ticket is $4 and 1000 trips are made per week. An excise tax of $2 is placed on each ticket, which raises supply to S' and reduces the number of rail trips to 800. a. Identify the area on the diagram that represents the tax revenue collected. b. What does consumer surplus mean? Identify the area on the diagram that represents the consumer surplus received by rail passengers after the tax has been imposed. c. Identify the area on the diagram that represents the deadweight loss (or equivalently the "efficiency cost") of the tax. Explain the meaning of this concept. P $6 S' $4 S D 800 1000 Tickets per week 2. There are forty consumers in an economy who purchase a drug to relieve the pain of arthritis. They think that the only effective drug is Namebrand. However, the same drug can be bought by its chemical name acethistestamine, or ace for short. The drug costs $2 to produce no matter what it is called; any quantity demanded can be supplied at that price. The company producing Namebrand exploits consumer ignorance by charging $6 for each unit; that is, the consumers buy Namebrand at $6 per unit, not realizing that ace is a perfect substitute available for only $2. The aggregate demand curve of the 40 uninformed consumers is Q=400 40P. a. What would be the value to consumers of knowing that ace and Namebrand are identical? b. How much is deadweight loss due to the consumers' lack of perfect information? 3. Suppose that you have $5000 in income to spend on two goods, durable goods (D) and all other goods (O). The price of both D and O is $1. Your utility function is U=D0.3O0.7. Your demand for D is D = (0.3*M)/PD and your demand for O is O = (0.7*M)/PO. Calculate the compensating variation needed to maintain your initial utility level if a tax of $1 is imposed on D. The following are the steps necessary to do this calculation. Show all of your work. a. Find the initial utility. To do this, plug the prices into the demand equations to figure out the quantity of D and O currently chosen. Then plug these quantities into the utility function and calculate the utility at this bundle. b. Derive the expenditure function. To do this, plug the demand functions for D and O into the utility function. Rearrange the equation using the property of exponents that XaXb=Xa+b to collect M by itself. Then, solve the equation for M as a function of U, PD, and PO. This is the expenditure function. c. Calculate the compensating variation. To figure out how much money you would need to get back to your initial utility if the price of D increased from $1 to $2, plug in the initial U, PO, and the new PD into your expenditure function. The difference between the new value of M and the original M ($5000) is the compensating variation. ...
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