econimcs 36574

(3) Appalled by the answer to the previous questions, you set your scientists to work again. They concoct another breakthrough technology that raises medical expenditures without having any effect on death rates. A truly remarkable achievement. Now you have lower death rates and higher medical expenditures. The new yearly medical expenditures per person are: Age Expenditures Young SC Old $1,500 Very Old $6,000 Will the Medisure trust fund ever go bankrupt now? If so, when? (4) Suppose the breakthroughs never happened so that the original death rates and schedule of yearly medical expenditures per person holds. Since your scientists are apparently no help, you decide that the right way to save Medisure is to raise the retirement age from old to very old. Now the old work and are taxed $1,000 per person, just like the young, while consuming $0 of Medisure health care (hopefully, they have other sources of insurance). Everything else stays the same. Will the Medisure trust fund ever go bankrupt now? If so, when? (5) People (especially the old) hate your decision to raise the retirement age and they force you to lower it again. As a firm leader, you consider raising taxes to $2,000 per year on each of the young. While this is bound to be unpopular in the short run, if you save Medisure, it might establish your legacy. Will the Medisure trust fund ever go bankrupt now? If so, when? (6) Well, increasing taxes proved more unpopular than you could have imagined, and you were forced to lower them again to $1,000 per year on each of the young. Ever resourceful, you hit upon another strategy - invest the trust fund in the stock market instead of those horrible Treasury bonds that earn no interest. You are confident that with the right investments, you can earn 10% per year on the trust fund. Will the Medisure trust fund ever go bankrupt now? If so, when? (7) Alas, the stock market venture didn't work out quite as well as you might have liked - you earn 0% interest on the trust fund. You are truly desperate now, so you do the unthinkable. You allow 200 extra young workers to immigrate to your island and force them to pay the Medisure tax (thus making 300 young workers in total). To mitigate the political impact, you force them to leave your island before they become old and start using health care. Will the Medisure trust fund ever go bankrupt now? If so, when?1. Decide whether each of the following three statements is True, False, or Uncertain, and give a brief but clear explanation why. (Note: these questions provide practice for the True, False, Uncertain section on the midterm and final exam) a. Some consumers strongly prefer Pepsi and some strongly prefer Coke. Therefore there is no single market for colas. b. Suppose that a tax on gasoline is imposed to encourage fuel efficiency. Over the following few years, the share of the tax paid by consumers will gradually fall. C. The mayor of Boston and other housing advocates are in favor of re-imposing rent controls on apartment units. (Rent control keeps apartment rents below their free-market levels, a practice that was abolished in 1994.) Suppose that the supply of apartment units is completely price- inelastic. Then once rent controls are imposed, there will be no deadweight loss to society. 2. The market for high definition television sets (HDTV's) in the U.S. can be expressed by the following demand and supply equations: Qd =7500-2400P, Qs = 600P. Where Q is the number of HDTV's, and the price P is in thousands of dollars. a. Calculate the equilibrium price and quantity that will prevail in a free market. b. Calculate the elasticities of demand and supply at the equilibrium. c. Calculate the consumer surplus and producer surplus at the equilibrium. d. Suppose that the U.S. government provides a subsidy of $300 per television in an effort to accelerate the adoption of HDTV. What will be the new equilibrium price paid by consumers and quantity bought? Is there a net welfare loss to society under the subsidy program? If not, why not? If so, what is the size of the net welfare loss? 2 3. At present, the price of a football in the U.S. is $15, and 5 million are sold annually. Market research has shown that the demand curves are linear, and that price elasticity of market demand is -4.0 and the price elasticity of supply is +2.0. a. Calculate the demand and supply curves for footballs for the U.S. b. The U.S. government proposes a $3 tax on every football sold in the country. How much revenue will the tax raise, and how will the tax affect consumer surplus and producer surplus? 4. A client has provided you with data on the price of cars, the price of gasoline, the quantity of new cars sold in each of a number of countries. In addition you observe Gross Domestic Product per capita (GDP is a measure of national income and 'per capita' means per person.) Using the techniques that you will soon learn in DMD, you use the data to estimate the following log-linear market demand equation for new cars: In Que =5-2.4 In po - 1.2 In p + 0.5 In (GDP per capita) a. What is the estimated elasticity of demand for new cars with respect to the price of cars? What is the estimated elasticity of demand for new cars with respect to the price of gasoline? c. What is the estimated elasticity of demand for new cars with respect to GDP per capita? d. Use the equation to calculate the estimated elasticity of demand with respect to GDP per capita when 1,000,000 new cars are shipped each year, GDP is 1.3 trillion U.S. dollars, and 250 million people live in the country.2. Managers at a machine tool manufacturer, McTools Inc., have estimated the following learning curve for the production of a new air conditioner where labor input is measured in minutes. Let N denote cumulative lot number and S mean lot size. Then In (labor input per air conditioner in N" lot) = 8.0 - 0.9 In (N) -0.4 In (S) 2 a) Suppose managers at McTools Inc., decide to increase the lot size by 5%, what happens (approximately) to the labor input per air conditioner? b) If the air conditioners are manufactured 100 in each lot, how much labor is required to produce the first lot? c) Suppose 1000 air conditioners are produced in four lots, each of size 250. Compute the labor input required for each lot and then the total labor input required for 1000 air conditioners and the overall average labor input per air conditioner. It may help to create a table in Excel like the following: Cumulative Lot Lot Size, S Labor Input in N" lot Number, N 1 250 2 250 3 250 4 250 Total Labor Input required to produce 1000 air conditioners = Average Labor Input per air conditioner (over the full 1000) = I) What would the overall average labor input per air conditioner be if you organized production of 1000 air conditioners into one lot of size 1000? Two lots of size 500? Which of these three production plans (4 lots of 250, 2 lots of 500 or I lot of 1000) provides the lowest overall average labor input cost when producing 1000 air conditioners? 3. Suppose your firm is thinking about producing televisions next period. The price of a TV is $100 and the marginal cost is $80 for each TV produced up to a capacity of 10,000 units. However, in order to produce next period, a fixed development cost of $185,000 must be paid this period. Be sure to show your calculations: a) With a discount rate of 0.05 would you take on the project? What if your discount rate were 0.1? Now suppose that you expect to produce 10,000 units in each of the next three periods. In order for the development to last for the next three years, the fixed development cost this period increases to $450,000. With a discount rate of 0.05, would you take on the project? With a discount rate of 0. 1? Now return to the setting of part a, except that the price is not known this period. Instead, at the before starting production next period you will learn that the price is either $100 with probability 0.9 or $70 with probability 0.1. Calculate the expected present value of the project with a discount rate of 0.05. Would you take on the project in this environment? For the situation in part c, how much would you be willing to pay for market research that allows you to determine the price ($100 or $70) prior to your decision to invest $185,000 in developing the product?2. You are the advisor of Unity Car, a company that provides partially assembled automobile components to Packard, a major automobile manufacturer. They have just received a rush order from Packard, offering to pay $160 per unit for the first 500 units, and $120 per unit thereafter. In your initial interviews of the management and the workers of Unity Car, you have collected the following information: The cost structure of our plant involves fixed costs of $30,000 per month, plus variable costs for assembly Unity Car's variable costs are the following: Units Variable Cost 100 5,000 200 15,000 300 24,000 400 33,000 500 43,000 600 54,000 700 67,000 800 83,000 900 103,000 1,000 128,000 Assume that Unity Car can only produce in multiples of 100. The Top Management of Unity Car is divided about whether to accept the offer. These are some arguments mentioned by them: Unity Car should turn the order down because Packard is not paying enough Producing 500 units, the average costs would be lower than the pricing offered by Packard, but this wouldn't be true at 600 units. Therefore, Unity Car should agree to produce 500 units. There is a possibility to negotiate a price of $160 for each unit. In that case, Unity Car would produce 1000 units, since Average Costs for that production level would be $158. 3 What would be your recommendations to the company? Remember to explain how many units Unity Car should produce (assuming that you can only produce a multiple of 100 and that the rush order is Unity Car's only production) and at what profits/loss. In your answer, comment on each of the statements using your knowledge of the firm's cost schedules. 3. You have the following information about the three electricity generation plants in Cleanland. Source Capacity Marginal Cost (in GW-hour) (C$/GW-hour) 1. Coal 4. 1,310 2. Gas 2.7 1,86 3. Oil 2.0 1,730 C$=Cleanland dollars) Due to the regulation prevailing in this country, the price that the consumers pay for electricity is equal to the marginal cost during the peak hours. The peak hours demand for electricity varies depending on the season. Cleanland has two seasons: Dry and Wet. A recent estimation of the peak demand is the following: Dry Q=14.25 -0.005-P Wet: Q= 18.3-0.005-P (quantities expressed in GW-h and prices in CS/GW-h) a. Draw a graph showing the supply-demand equilibrium for each season. What would be the price paid by consumers in each season? What would be the surplus of each plant? What would be the consumer surplus? b. Assume that the government imposes a tax on the oil used as an input for electricity generation. This tax raises the marginal cost of this plant by 20%. How will this measure affect the producers and consumers? How do you think that the different producers and the consumers will react to this tax? 4. "Daily Bugle", the oldest newspaper in Historicville, owns a building called "The Blue House". This building was declared a historic monument in 1965 and, therefore, any alteration of its external or internal form was expressly prohibited. Due to the historic link between the paper and the building, the only economic activity that was allowed inside the building was the operations of the "Daily Bugle". Last year a new mayor was elected. The new administration reinterpreted the historic monuments regulation in the following way: "although we will protect our cultural heritage, we will allow any development that, without changing the external layout of our historic monuments, allows the current owner to adapt its property to new economic activities". a. Does the mayor's decision change the user cost of capital of "Daily Bugle"? b. Historic preservation activists worry that the Bugle may leave its traditional home. They issue a statement where they argue:(c) Federal Block Grant Suppose instead that the federal government provides l\\.'Iaine with a blocl: grant of equivalent size to the federal grant calculated in (b). l. \""hat is Maine's eEective price per unit of improving education quality under this proposal? 2. How would you expect the quality provided to change under this proposal, relative to no federal intervention? Should this be an income effect. a substitution effect. or a combination of both? Provide intuition for how each price effect impacts the provided level of quality for the education program. 3. Present the state's revised problem graphically. as above. labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. 4. Solve mathematically for the revised level ofquality provided for the education prograrri and the total size of the grant. 5. The size of the federal grant under this proposal is (by construction) the same as in [b]. Explain any dierence between the number of education quality units provided here vs. under the grant in (b). In particulan which is larger. and why? (d) Federal Conditional Block Grant Suppose instead that the federal government provides Maine with a conditional block grant of equivalent size to the federal grant calculated in (b), whereby the grant is provided to the state with a mandate that the grant be spent only on improving the quality of Maine's education program. 1. How does this problem dier from the unconditional grant in part (c)? For what parameter values will the level of provided education be the same as in (c). and for which values will it differ? 2. Present the state's revised problerri relative to no federal government intervention graphically, labeling the original and revised budget constraints as well as the original and revised number of education quality units purchased. Draw two sets of graphs one for the set of parameter values where the provided education is the same as in (c) and one where provided education differs from that in (c). 3. Solve mathematically for the revised level of quality provided for the education pro- gram. 4. Assuming validity of the behavioral "ypaper elfect,' how would you expect the real world response to (d) to compare to the theoretical response assessed above? {e} Optimal Program If the federal government is specically concerned with perceived under-provision of educa- tion quality in Maine, which intervention assessed above is most eEective? Alternatively. if the federal govemment is only concerned with the overall welfare of Maine. which interven- tion assessed above is most effective. Provide intuition for similarities or differences in your responses. Question 2 The remote island nation of \"'heredat has two types of citizens; earls and plebs. \"rheredat is a small, beautiful island composed of a bunch of villages connected to each other by dirt walking paths. Due to rough seas and dangerous shoals around the island, the citizens use these paths as their sole method for transportation in the country. Unfortunately, \"'rheredat is plagued by the virurlike weed accumula, which if left alone quickly over-grows the walking paths and makes walking along the paths dangerous. especially at night. (c) Federal Block Grant Suppose instead that the federal government provides l\\.'Iaine with a blocl: grant of equivalent size to the federal grant calculated in (b). l. \""hat is Maine's eEective price per unit of improving education quality under this proposal? 2. How would you expect the quality provided to change under this proposal, relative to no federal intervention? Should this be an income effect. a substitution effect. or a combination of both? Provide intuition for how each price effect impacts the provided level of quality for the education program. 3. Present the state's revised problem graphically. as above. labeling the original and revised budget constraints as well as the original and revised level of quality provided for the education program and relevant indifference curves. 4. Solve mathematically for the revised level ofquality provided for the education prograrri and the total size of the grant. 5. The size of the federal grant under this proposal is (by construction) the same as in [b]. Explain any dierence between the number of education quality units provided here vs. under the grant in (b). In particulan which is larger. and why? (d) Federal Conditional Block Grant Suppose instead that the federal government provides Maine with a conditional block grant of equivalent size to the federal grant calculated in (b), whereby the grant is provided to the state with a mandate that the grant be spent only on improving the quality of Maine's education program. 1. How does this problem dier from the unconditional grant in part (c)? For what parameter values will the level of provided education be the same as in (c). and for which values will it differ? 2. Present the state's revised problerri relative to no federal government intervention graphically, labeling the original and revised budget constraints as well as the original and revised number of education quality units purchased. Draw two sets of graphs one for the set of parameter values where the provided education is the same as in (c) and one where provided education differs from that in (c). 3. Solve mathematically for the revised level of quality provided for the education pro- gram. 4. Assuming validity of the behavioral "ypaper elfect,' how would you expect the real world response to (d) to compare to the theoretical response assessed above? {e} Optimal Program If the federal government is specically concerned with perceived under-provision of educa- tion quality in Maine, which intervention assessed above is most eEective? Alternatively. if the federal govemment is only concerned with the overall welfare of Maine. which interven- tion assessed above is most effective. Provide intuition for similarities or differences in your responses. Question 2 The remote island nation of \"'heredat has two types of citizens; earls and plebs. \"rheredat is a small, beautiful island composed of a bunch of villages connected to each other by dirt walking paths. Due to rough seas and dangerous shoals around the island, the citizens use these paths as their sole method for transportation in the country. Unfortunately, \"'rheredat is plagued by the virurlike weed accumula, which if left alone quickly over-grows the walking paths and makes walking along the paths dangerous. especially at night. 1 Tax Distortions This question establishes some basic mathematical ways for thinking about taxation and its re- lationship to the marginal rate of substitution between goods. Consider individuals that have preferences over two goods, cy, 5, and leisure, L. Let pup, be the (before-tax) prices of goods c and a. Let w be the (before-tax) wage. The agent has an endowment of non-labor wealth of m. As usual, we assume that u is continuously differentiable in (c, ce, L). Let in (ci, ce, 2) denote the marginal utility of c, we (ca, (2, L) denote the marginal utility of ca, and up (ci, cr, [) denote the marginal utility of leisure. 1. Write the agent's budget constraint assuming no taxes and that the individual is endowed with I unit of leisure so that I + 2 = 1, where I is the amount of time spent working for a winge- 2. Derive the first-under conditions for the agents maximization problem by placing a lagrange multiplies, A, on the budget constraint. Derive two equations that combined with the budget constraint characterize the solution to the maximization problem, (ci ci, [). One condition should be for the marginal rate of substitution between ci and cy and another for the MRS between co and L. Explain the intuition of both equations. Note: you do not (and cannot in general) solve for the solution explicitly; however, you should notice that you have 3 equations and 3 unknowns, so that given any well-specified function a one could solve the system off equations. Also, note that one could also write a condition for the MRS between or and L; however this would be redundant given the other two equations) Now, suppose that the government levies a lump-sum tor of + on all individuals, so that their net non-labor wealth is now m - T (Assume for simplicity that this for is used to finance things for which individuals have no utility). . Set up the new budget constraint (assuming the agents never receive the money paid to the government and the money is used to finance things for which individuals have no utility). Derive the first order conditions and provide the analogous two conditions for the marginal rates of substitutions (for c vs cy and for cy vs 2). Explain the intuition of both equations. Is the MRS distorted? (i.e. are they different than they would be in the absence of taxation?) Why or why not? Now, suppose that instead of the lump-sum for, the government institutes a fax on ci of 71, so that individuals must now pay pit ri per unit of c. 4. Set up the new budget constraint (assuming the agents never receive the money paid to the government and the money is used to finance things for which individuals have no utility). Derive the first order conditions and provide the analogous two conditions for the marginal rates of substitutions (for c vs cy and for c vs 2). Explain the intuition of both equations. Is the MRS distorted? (i.e. are they different than they would be in the absence of taxation?) Why or why not? Now, suppose that, in addition to the tax on c, the government institutes a for on ce of f2 and on labor earnings, Tu