ECON 44821: Public Economics - Quantity Approach and Price Approach - Report Writing Economics Assignment Help

Assignment Task:

Problem I. True or False

Please provide a brief, precise argument for each case. 

1. Quantity approach is as good as price approach to solve the externality problem. 

2. Coasian solutions are more likely to resolve the problem of externality when the problem is local and there are less parties involved. 

3. Cable TV is an example of non-rival but excludable products. 

4. Free rider would not be a problem if people had convex utility functions. 

Problem II. Road Damage (15 points)

One hundred com muters need to use a strip of highway to get to work. They all drive alone and prefer to drive in big cars- it gives them more prestige and makes them feel safer. Bigger cars cost more per mile to operate, however, since their gas mileage is lower. Worse yet, bigger cars cause greater permanent damage to roads. 

The weight of the car is w. Suppose that the benefits from driving are 12w, while the costs are 3w2. The damage to roads is 2w3. Assume that individuals have utility functions of the form U = x, where x are the net benefits from driving a car of a given size. 

1. What car weight will be chosen by drivers? (5 pts) 

2. What is the optimal car weight? If this differs from (1), why does it? (5 pts) 

3. Can you design a toll system that causes drivers to choose the optimal car weight? If so, how would such a system work? (e.g. how might the toll depend on the car)? (5 pts) 

Problem III. Firefighters (20 points)

The town of Springfield has two residents: Homer and Bart. The town currently fund its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over 

private goods (X) and total firefighters (M), of the form U = 6 log(X) + 2 log(M). The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons: M = MH + MB. Homer and Bart each have an income of $100, and the price of both the private good and a firefighter is $1. Thus, they are each limited to providing between 0 and 100 firefighters.(Hint: Read the mathematics appendix of chapter 7 ) 

1. How many firefighters are hired if the government does not intervene? How many are paid for by Homer? By Bart? (10 pts) 

2. What is the socially optimal number of firefighters? If your answer differs from (1), why? (10 pts) 

Problem IV. Snowplowing in Minneapolis

Minneapolis residents obtain util ity from consuming the private good, c, and from total snowplowing service, G, in the city, u(c, G) = cαG1−α. There are N residents living in Minneapolis. Price of the private good is normalized to 1. Individuals are identical and each has income of I. 

Suppose that snowplowing is provided privately and G =PNi=1 gi, where giis the amount of snowplowing service purchased by person i at price p. 

1. Find the private optimal level of snowplowing service, G∗. (5 pts) 

2. Find the social optimal level of snowplowing service, Gˆ. (5 pts) 

3. Show that the private provision results in underprovision. (5 pts) 

4. Design a system of public provision and show that it leads to social optimum. In other words describe how snowplowing public service is financed and show that the equilibrium subject to the snowplowing finance matches the social optimum. (10 pts) 

5. Now suppose individuals have different incomes, Ii 6= Ij . Would the public provision you designed still match the social optimum? Explain. (5 pts) 

6. Now suppose that snowplowing is provided privately and publicly simultaneously. Show that public provision crowds out the private provision. (10 pts) 

Problem V. Shared Driveway

Recall the textbook example where two neigh bors share a driveway. Suppose each person gets utility on the private consumption good, c, and the driveway, D = d1 + d2, such that ui(ci, D) = ln(ci) + γiln(D). Price of snowplow ing/repairing services is p in terms of the consumption good. Each person has income Ii. Let δi ≡ pdi/Ii denote the income share of driveway expenditures for person i. 

First, assume that γ1 = γ2 = γ and I1 = I2 = I. 

1. Find the social optimal income share of driveway services, ˆδ. (5pts) 

2. Find the private optimal income share of driveway services, δ∗. (5 pts) 3. Compare δ∗ and ˆδ. Explain intuitively why they are different. (5 pts) 

4. Now suppose there is some extent of altruism. I.e. ui(ci, D) = ln(ci) + γ ln(D) + ˆγ ln(D). Find the private optimal income share with altruism δA. Compare δA and ˆδ. What happens if ˆγ = γ. (10 pts) 

5. Now, consider the case with warm glow where each person cares about his contribution to the driveway rather than his consumption of driveway. Specifically, ui(ci, di) = ln(ci) + γ ln(di). Find the private optimal income share with warm glow, δW . Compare δW and ˆδ. Explain intuitively. (10 pts) 

6. Now suppose I1 > I2. Specifically, I1 = MI2 but γ1 = γ2 = γ. Find the social and private optimal level of income share: ˆδ1 and δ∗1. What happens if M → ∞. Explain intuitively. (10 pts) 

7. Now suppose I1 = I2 but γ1 = M γ2. Find the social and private optimal level of income share: ˆδ1 and δ∗1. What happens if M → ∞. Explain intuitively. (10 pts) 

Problem VI. Childcare (30 points)

For this problem, you are encouraged to read two articles: one from NBER and another one from Brookings. Then write an essay (2-3 paragraphs) and discuss the following issues: 

1. Whether childcare is a public good. 

2. Whether private equilibrium matches the social optimum. 

3. If not what are the proper solutions? Discuss both the private sector solution and the public sector solution. 

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