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# EconS 330, Fall 2012 Homework #2: Due on September 26th Instructor: Ana Espinola, [email protected] O ce hours: Tuesdays 9:00am-10:00am, or by...

Question #8 - 12 Points
Subsidy for inÂ‡uenza vaccination in developed countries is often provided to the elderly in order to encourage
them to receive a Â‡u shot. Assume that the marginal cost of producing the vaccine is MC = 10+q and the
external marginal beneÂ…t (MBE) and private marginal beneÂ…t (MBP ) from the Â‡u shot are represented by
the following functions: MBE = 40ô€€€:25q and MBP = 120ô€€€:75q. Please answer the following questions:
a. Identify the MBS (Social Marginal BeneÂ…t function) and the optimal quantity Â“XÂ”. (4 Points)
b. Assuming that the optimal quantity is produced. How much are consumers willing to pay Â“Y Â”? Identify
the optimal subsidy and government cost from the subsidy. (4 Points)
c. Calculate the Consumer and Producer Surplus after the subsidy. (4 Points)
EconS 330, Fall 2012 Homework #2: Due on September 26th Instructor: Ana Espinola, [email protected] O¢ ce hours: Tuesdays 9:00am-10:00am, or by appointment 1 Question #1 - 15 Points You have been assigned to determine the Dynamic E¢ cient allocation of cooper (Depletable resource). Please take into account that the consumption of current generations should not a/ect the consumption of future generations. Assume that the inverse demand function for Cooper is P = 110 & q and the marginal cost of supplying it is \$15 per ton. a. If 85 tons are to be allocated between two periods, in a dynamic e¢ cient allocation how much would be allocated to the &rst period and how much to the second period when the interest rate is 15% ? (5 Points) b. What would be the e¢ cient price and the marginal user cost MUC in the two periods? (5 Points) c. Identify the net bene&ts in both periods and in the case that they are di/erent, argue how future generations could be compensated for this di/erence. (5 Points) 2 Question #2 - 15 Points Assume the same demand conditions as stated in Problem 1, but let the discount rate be 10% . The marginal cost of extraction in period 1 is \$25 and in period 2 is \$15 (technological change). How much would be produced in each period in an e¢ cient allocation? What would be the marginal user cost in each period? Would the static and dynamic e¢ ciency criteria yield the same answers for this problem? Why? (15 Points) 3 Question #3 - 15 Points A &rm in a perfect competitive industry has patented a new process for making widgets. The New process lowers the &rm±s average cost, meaning that this &rm alone (although still a price taker) can earn real economics pro&ts in the long run. a. If the market price is \$20 per widget and the &rm±s marginal cost is given by MC = 0 : 4 q , where q is the daily widget production for &rm, how many widgets will the &rm produce? (5 Points) b. Suppose a government study has found that the &rm±s new process is polluting the air and estimates the social marginal cost of widget production by this &rm to be MC S = 0 : 5 q . if the market price is still \$20 , what is the socially optimal level of production for the &rm? What should be the rate of a government-imposed excise tax to bring about this optimal level of production? (10 Points) 4 Question #4 - 10 Points The microeconomic theory of fertility provides an opportunity to determine how public policies that were designed for quite di/erent purposes could a/ect fertility rates. Europe±s working-age population is shrinking as fertility rates decline. In a &t of gloom, one German minister recently warned of the country &turning the light out± if its birth rate did not pick up. E/orts to encourage couples to breed have a turbulent history. In Italy for instance Mussolini heavily taxed single men in his Battle for Births and in Germany Hitler awarded medals to women with large families in his quest for a superior German race. Explained how these two policies a/ected the Marginal bene&t and Marginal Cost of children, and as result the total number of children. Please use a graph to answer this question. 1
5 Question #5 - 15 Points Consider an increasing marginal-cost depletable resource with no e/ective substitute. a. Describe in general terms how the user cost for this resource in the earlier time periods would depend on whether the demand curve for that resource was stable or shifting outward over time. (10 Points) b. How would the allocation of that resource over time be a/ected? (5 Points) 6 Question #6 - 10 Points Some education is funded by property taxes, whereas other forms of education are funded by charging tuition. Suppose that within a community, more money is needed for education. Assuming that they raise the same amount of revenue, would the rising cost of education have the same e/ect on the desired number of children regardless of whether the system was funded by property taxes or tuition? Using the microeconomic theory of fertility, trace the expected impacts. Draw a graph to answer this question. 7 Question #7 - 8 Points A &rm can produce steel with or without a &lter on its smokestack. If it produces without a &lter, the external cost on the community are \$500 ; 000 per year. If it produces with a &lter, there are no external costs on the community, and the &rm will incur an annual &xed cost of \$300 ; 000 for the &lter. a. Use the Coase Theorem to explain how costless bargaining will lead to a socially e¢ cient outcome, regardless of whether the property rights are owned by the community or the producer. (4 Points) b. How would you answer to part (a) change if the extra yearly &xed cost of the &lter where \$600 ; 000 ? (2 Points) c. Explain the main problems associated with the Coase Theorem. (2 Points) 8 Question #8 - 12 Points Subsidy for in±uenza vaccination in developed countries is often provided to the elderly in order to encourage them to receive a ±u shot. Assume that the marginal cost of producing the vaccine is MC = 10 + q and the external marginal bene&t (MBE) and private marginal bene&t ( MB P ) from the ±u shot are represented by the following functions: MB E = 40 & : 25 q and MB P = 120 & : 75 q . Please answer the following questions: a. Identify the MB S (Social Marginal Bene&t function) and the optimal quantity ² X ³. (4 Points) b. Assuming that the optimal quantity is produced. How much are consumers willing to pay ² Y ³? Identify the optimal subsidy and government cost from the subsidy. (4 Points) c. Calculate the Consumer and Producer Surplus after the subsidy. (4 Points) MB P MC MB E MB S X 160 85 160 57.1 77.15 Y Z 40 W P Vaccines Q Vaccines (2) (1) Figure 1 2

a.
Marginal social benefit function (MBS) = MBE+MBP = 160-q ……….. (1)
Social optimum occurs at a point where social marginal benefit (MBS) equals marginal cost (MC)
So marginal...

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