代做ECON4043 The 2nd Assignment of Public Finance代做留学生Matlab编程

The 2nd Assignment of Public Finance (ECON4043)

Question 1 [32 marks total]

Assume that there are two roommates who spend all of their income on groceries (X) and a  Netflix subscription (Y). When one of the roommates pays for the Netflix subscription, the  other one also enjoys the access to movies and series. Thus, Y is a public good. For simplicity, assume that the unit price of each good is $1 and each individual has the following utility  function:

U(X,Y) = ln(X) + ln(Y)

(Hint: the total level of Y consumed by each roommate is Y1+ Y2 where Y1 is the Netflix contribution of roommate-1 and Y2  is the Netflix contribution of roommate-2)

a.    [12 marks] Find the socially optimal aggregate level of Y (or Y1+ Y2) under the following two cases:

Case 1: Each roommate has an income of $100.

Case 2: One roommate has $150 of income whereas the other one has $50.

b.    [12 marks] For each case above, now find the level of Y, the aggregate level of Netflix contribution, if each individual will pay for Y1  and Y2  separately. How many more/less units of Netflix contribution will the two neighbors provide than is socially optimal?

c.    [8 marks] Under case 1, assume that the government taxes each individual by $16.67 and  with this revenue, pays for the Netflix subscription itself by 33.34 units. Find the level of  Y each individual will provide under this scenario. Can the socially optimal level of Y be achieved? What is the extent of crowding-out? In other words, how many more/less units  of Netflix contribution will the two roommates provide with this government intervention compared to the case without the intervention?

Question 2 [26 marks total]

Suppose that Guangdong provincial government plans to construct a new bridge between Zhuhai city and Shenzhen city. The construction needs 200,000 tons of cements, 50,000 tons of steel, and 600,000 labor days. Suppose that the cements will be purchased from an Oligopoly firm, HaiLuo Corporation, at a price of RMB 2,500 per ton, with a cost of RMB 2,200 per ton. Steel will be purchased from MaAnShan Steel Corporation with a price of RMB 5,000 per ton, which is lower than the market price of RMB 5,200 per ton charged by all other steel companies. The construction workers  hired in the project will receive the average wage for construction workers all over the country - RMB 300 per day, which is lower than the average wage of high-skilled workers (RMB 400 per day) but higher than the average wage of low-skilled workers (RMB 200 per day). Workers with certain skills will not work in other types of jobs with different skills. After the bridge is built, the maintenance expenses will be RMB 4,000,000 per year for its life time, which lasts for 100 years.

Meanwhile, the average housing price at each end of the bridge will increase by RMB500,000 since the average commuting time of each person living in these two areas will fall by 1 hour per day. Suppose that there are a total of 2,000 households living in these two areas, that there is one commuter per household, that the average commuter works 5 days a week and 50 weeks a year for a total of 40 years. In addition to these households, the bridge can also save the same amount of time each year for other 5,000 commuters, whose value of time (say, per hour) is assumed to be the same as the commuters in the households above. Moreover, the new bridge can save 10 lives each year (the average number of persons killed among those commuting between the two cities before the new bridge is built). Suppose that each person’s life value is measured by the PDV of his/her life-time wages, and he/she is supposed to work 8 hours a day, 5 days a week and 50 weeks a year for a total of 40 years. Assume the hourly wage is the same as the hourly value of time of the commuters above.  Suppose that the benefits of reduced commuting time and saved lives apply to current and future citizens during the bridge’s life time. We use a discount rate of r = 4% whenever we need to discount the future value to the present value. Throughout this question, denote all your answers for value in million RMB (except for hourly wage), and round them to integers.

a.   [3 marks] What is the material cost of the bridge?

b.   [2 marks] What is the labor cost of the bridge?

c.   [2 marks] What is the PDV of the maintenance cost of the bridge?

d.   [2 marks] What is the total cost of the bridge over its life time?

e.   [6 marks] Use the revealed preference approach to estimate the average value of an hour for a commuter based on the information provided.

f.    [2 marks] What is the total benefit of time saving from this bridge PER year?

g.   [5 marks] What is the total benefit of life saving from this bridge PER year?

h.   [3 marks] What is the total benefit of this bridge over its life time?

i.    [1 mark] Is it worthwhile to construct this bridge?

Question 3 [42 marks total]

Part A: Suppose there is an imaginary country which  is composed of only three towns, namely Town X, Town Y and Town Z. The expenditure on national security of this country needs to be jointly borne by these three towns. The marginal benefits of national security for these three towns are shown in the following table.

a.   [5 marks] Calculate the country-wide social marginal benefits of national security for this country. What is the optimal condition for national security provision? Explain why.

b.   [5 marks]  Suppose that the marginal cost of providing national security is constant and lies within the range of greater than $400,000 and less than $500,000. Use a diagram to illustrate and explain the optimal condition of providing national security to these three towns.

c.   [9 marks] In the table shown above and part b), do the contributions made by these three towns suffice to fund the provision of four units of national security on an annual basis? Explain why. Is Tiebout model a appropriate model for predicting the optimal provision of national security in this country? Explain why.

Part B: Assume there are only two towns in a hypothetical country: Town ABC and Town XYZ. Town ABC has 10 residents, while Town XYZ has 20 residents. The demand for public facilities by each resident in Town ABC is described by the equation Q = 200 –P, while the demand for public facilities by each resident in Town XYZ is determined by 2Q = 500 –5P. Suppose that the marginal cost of constructing public facilities for these two towns is $1200 per unit. Due to the restrictions of strict zoning between these two towns, residents in one town are not permitted to move to another town to become its residents or to live there for a long time(Round the answer to 2 decimals ifit’s necessary).

d.   [8  marks]  Given the conditions given above, calculate the optimal provision level  of public facilities in these two towns. Explain your calculation approach. Which town has the higher per capita and overall level of public facilities provision under the optimal condition?

e.   [10 marks] If the government of this country promotes the equalization policy for the per capita provision level of public facilities in these two towns, how should the government levy taxes on or provide subsidies to the residents of these two towns? Calculate the optimal levels of public facilities in these two towns after the tax or subsidy policies are implemented. How big should a tax be levied on each citizen in one town under the optimal levels?

f.    [5 marks] The Tiebout model predicts that people living in a local community might move to another community or place  (voting  with their feet). In part d), suppose  that  five residents move from Town XYZ to Town ABC, while their demand for public facilities still remains unchanged. Ignoring the relocation costs of these five people, calculate the per capita and overall optimal provision level of public facilities in these two towns.