Homework Assignment July 2016
Instructions: You can collaborate with other students in preparing your answers, but each student must write up his or her answer independently. Answers should be submitted on paper, and be typed rather than hand-written. If you have difficulty typing equations you can leave space and add them neatly by hand after printing. Likewise if you include diagrams you can add them neatly by hand after printing. The assignment is due at the start of class August 4.
Each of a model town's 200 residents has a marginal benefit function for the town's public good (a park) as follows:
MB = 100 - 0.5A, where A is the number of acres in the town park. Also given:
Marginal social cost (MSC) per acre per year = $10,000.
(a) Explaining briefly the meaning of efficient public good consumption, solve for the efficient park size A*. If the model town uses a head tax what is the equilibrium park size A'?
(b) In this part of the question the provincial government passes a law designating the model town's park a natural heritage site. The law, which the town must obey, says that the number of acres in the park [equilibrium A' from part (a)] cannot be changed up or down. At the same time the provincial government passes another law requiring the model town to replace the head tax with a property tax.
The model town has 150 small houses, each of them valued at $400,000 while the head tax was in effect. It also has 50 big houses, which of them valued at $800,000 while the head tax was in effect.
There are many other towns nearby, each with 200 residents all of whom have MB = 100 - 0.5A; these other towns all have MSC = $10,000. The provincial government allows these other towns, which have been using a head tax, to continue using a head tax - only the model town has to change to the property tax. These other towns have many small houses valued at $400,000 each and many big houses valued at $800,000 each.
The original house values in the model town ($400,000 and $800,000) are not used to calculate tax bills. Instead the model town manager is able to correctly predict the prices that will be paid for houses when they go on the market, and uses these predicted prices to calculate tax bills from day one.
These predicted prices are Vs for small houses, Vb for big houses. For example the tax bill for a big house will be rVb per year where r is the property tax rate. A key point that the manager considers when predicting prices is that buyers have a choice between buying houses in the model town or buying houses in any of the other towns nearby. To answer part (b) you must calculate Vb, Vs, and r. Briefly explain the calculation steps you take in reaching your answers.
Note: as an intermediate step you may need to determine the present value of future payments. If so, you can assume a discount rate of 5 percent, and use the formula PV 2 (present value) = $X / 0.05, when $X will be paid each year starting in one year. Another point to note: correct answers for some variables may not be exact dollar amounts; in these cases you can round your answer to 2 places after the decimal.