## Net social benefits

An analyst is trying to determine the net social benefits generated by the city’s public swimming pool. At the current admission price of $1.00, 1,000 individuals visit the pool annually. The total cost of the pool is $1,000 annually, and these costs are fixed and do not depend on how many people visit the pool.

Assume a review of economic studies has found that a typical price elasticity of demand for similar community pools is -0.3333. Use this information to calculate net benefits of allowing free admission.

If admission becomes free, the city will increase income taxes slightly to cover the expenses of running the pool. Describe briefly how the issue of marginal excess tax burden would brelevant to determining the efficiency of this free admission policy.

Describe briefly how this question illustrates the use of the “benefits transfer” method.

Consider the market for electricity. Assume that inverse supply is given by P=10+Q, private demand is given by P=20-Q, and every unit produced generates an external cost equal to $2 (i.e total external costs = 2Q, and marginal external costs equal $2). Because the private actors in this market do not suffer any consequences of generating these external costs, they do not factor them into their decisions. (This question is worth a total of 5 points, and each part below is worth one point.)

a. Plot the demand curve, the private marginal cost curve, and the social marginal cost curve (where social marginal costs equal private plus external marginal costs.)

b. What is the equilibrium quantity and price in this market in the absence of government intervention?

c. The outcome you described in part b. does not maximize social welfare. In words, why not?

d. Describe the socially efficient (optimal) quantity of electricity. If a policy maker proposes to impose an excise tax on sellers in this market, what amount of tax is needed to bring about the social optimum?

e. Redraw the figure from part a and identify the areas of gains and losses to consumers, producers government and 3rd parties of the efficient tax, identified in part d.; in addition, create a social accounting ledger showing the gains and losses (in dollars) to the four groups.

Compare and contrast the role of taxation as an efficiency enhancing or harming policy with regard to the way taxation is used as a tool to finance pool expenses in question 2 above, versus its use as a tool to reduce electricity consumption in question 3 above.

An analyst assesses two alternatives: (1) a ring levee with a 20-year life and (2) floodwalls with a 60-year life, both designed to prevent river flood damage to neighboring residential properties. Suppose the NPV for the 20-year ring levee is $2.5 million and the NPV for the 60-year floodwall is $5 million, both discounted at 5%. Calculate the EANB for each project.

A government data processing center has been plagued in recent years by complaints from employees of back pain. Consultants have estimated that upgrading office furniture at a net cost of $40,000 would reduce the incidence and severity of back injuries, allowing the center to avoid medical care that currently costs $10,000 each year. The furniture would have a useful life of five years, after which it would have zero salvage value. Assume the avoided costs occur at the end of each year. In its investment decisions, the center uses a nominal discount rate of 8 percent and an assumed general inflation rate of 4 percent.

a. Using summation notation, write an expression for the NPV, expressed in real dollars

b Using summation notation, write an expression for the NPV, expressed in nominal dollars

c. Using summation notation, write an expression for the NPV, expressed in real dollars, assuming the cost of medical care will rise 3 percent faster than other prices.

d. Using summation notation, write an expression for the NPV, expressed in nominal dollars, assuming the cost of medical care will rise 3 percent faster than other prices.

e. Use a spreadsheet to calculate answers for parts a-d. Upload your spreadsheet along with your answers.

Inflation problems. Search the Internet for the latest Economic Report of the President and find, “Table B-3: Quantity and price indexes for gross domestic product, and percent changes, 1967-2017.” use the GDP implicit price deflator to answer these questions.

a. Provide the Internet address to prove you found the table.

b. An analyst locates a study that estimates the average beachgoer was willing to pay $2.25 per hour in 2017 to visit a renourished beach. What is the value of this in 2009 dollars?

c.A study reports that the real operating expenses for a sewage treatment plant were $40,000 in 2010 prices. What is the value of this expense in 2017 prices?

Suppose a government is considering building a bullet train to connect the main population centers in its territory. Construction of the high-speed rail system would require acquiring land from current property owners for the right-of-way, as well as construction of the tracks and purchases of train sets. The land acquisition costs depend on political factors, and the government expects land acquisition costs to range from $10 billion to $20 billion, with $15 billion likely. Construction of the tracks and purchases of the train are expected to cost $20 billion. The land acquisition costs, as well as the construction and train set expenses, are expected to occur today. Beginning one year from today, the bullet train would start operation. Operating expenses for personnel, maintenance, supplies, etc. are estimated at $1 billion annually. The benefits of the bullet train (which are treated as the gross willingness-to-pay of riders) are assumed to accrue at the beginning of each year. Depending on the level of eventual ridership, the bullet train benefit estimates range from $1 billion to $11 billion, with $4 billion likely. Assume construction would start tomorrow, take one year to complete, the bullet train operates for twenty years thereafter, and the real discount rate is 4%. Although the land occupied by the tracks and stations would have some value after twenty years, assume for the purposes of this analysis that the salvage value of the system is zero at the end of the project life.

a. Calculate a base case estimate of the net present value of the bullet train system. (Hint: Use the formula for the annuity factor, and the fact that 1.04^20 = 2.2.)

b. Given the uncertainty surrounding the land acquisition costs and rider benefits, calculate best case and worst case NPV estimates.

c. A more complete picture of the uncertainty surrounding this project can be provided with a Monte Carlo analysis. Briefly describe how one conducts such an analysis.

d. Implement a Monte Carlo analysis, where relocation costs and medical benefits vary uniformly from their low and high estimates. Also, allow the discount rate to vary uniformly from 3% to 7%. Calculate 1,000 estimates of NPV. Create a histogram that displays the distribution of NPV while varying these three values. Upload the spreadsheet file that contains your work, and paste the histogram in your answers.