Econ 323
Comprehensive Problem Set (CPS) Block 3.
This problem set will be made up of three blocks. Block 1 and 2 are published previously. This block corresponds to material between MT2 and MT3.
The CPS is optional. All three blocks are required to complete the CPS.
If a student elects to do it, the CPS score may replace one of the three midterm exams. The CPS can replace a low midterm score, or if a student has not taken one of the exams for some reason, it can fill in for the missing test. It is fine if a student wishes to opt-out of MT3 and use the CPS to fill in the gap.
As described in the syllabus and in class, the CPS is intended to be incrementally more challenging than the “standard” practice problems or exam problems we do routinely. You can think of it as a “stretch” assignment. All questions will have a small novelty or two that the student needs to work out on their own. The problems should then seem harder than our “standard” work.
Answer each of the following two questions.
1. (50 points)We will imagine there being two markets for computers: Home computers and Business computers. The curves in these markets are linear, but I will not tell you what those formulas are [you don’t need to know them to answer the questions]. However, I will tell you that at the equilibrium, the elasticity of demand for home computers is -2.5, the elasticity of demand for business computers is -.90, and the elasticity of supply for computers for both purposes is 1.
a. (10) A per-unit tax of $200 is imposed on the suppliers of computers. How much does the buyer price increase in each market? You can and should do this without knowing anything about the pre-tax equilibrium, if you use the elasticity formulas we covered in lecture.
b. (10) Suppose the untaxed market equilibrium price and quantity in the home computer market are $850 and 10 million, respectively. In the business market, the untaxed market equilibrium price and quantity are $1200 and 15 million, respectively. What is the total revenue from the tax?
c. (10) What is the deadweight loss of the $200 tax?
d. (10) Comment on the relative sizes of the DWL in the two markets. Why are they different?
e. (10) Imagine that you could tax the consumer and business markets separately. That is, a different tax for each market. Call these taxes th and tb.What would these taxes be if you wanted to generate the same level of revenue as part b, while minimizing the DWL? [To answer this part, it will greatly help if you use the formula for the marginal deadweight loss shown briefly in class. Since the derivation of that required some calculus and I don’t want you to have to derive it on your own, I’ll write it down right here for you to use:
2. (50 points) As described in lecture, the government can incentivize certain types of behaviors by allowing spending on those behaviors to be deducted from income. One example of this is the Mortgage Interest Tax Deduction (MITD). During a year, homeowners can subtract any spending on the interest payments from their mortgages from their income, lowering their income and their tax bill. In this problem we will explore this deduction in some detail, and how it may impact decisions on how much to borrow to purchase a house.
This problem requires a fair bit of set up. I will walk you through it
Take a look at the following mortgage calculator linked below to help answer the following.
https://www.bankrate.com/calculators/mortgages/amortization-calculator.aspx
Suppose the value of a property is $500k (this number is not necessarily the loan amount, and will change for different parts of the problem), the interest rate is 5% (approximately the correct interest rate as of this writing), and the length of the loan (the “loan term”) is 30 years. Set the loan start date for January. Leave any other values at the default settings. In the center of the web page of the calculator, you can choose to view “Chart” or “Schedule.” The Chart is nice, but you’ll need the Schedule because that has the numbers.
Throughout the problem, the marginal tax rate for the borrower is 33%.
Assume the individual has $500k cash on hand, and any of this money that remains after taking the mortgage/making mortgage payments is invested at the interest rate 3%. The earnings of the investments can be taxed each year at the marginal rate. The value of the property also grows at rate 3% per year. This means that as the borrower repays the loan and starts building principal, the value of that principal goes up at the same rate as other investments. However, the increased value of the property is not taxed, as the borrower doesn’t actually receive that increased value until or if they sell the property in the future. Finally, assume that the year’s mortgage payment is paid to the bank from cash on hand at the START of the year. This turns out to be important if we want to make comparisons. Homeowners are able to deduct the amount of interest paid on their mortgage when calculating taxes.
NOTE: There are 4 sets of calculations you will make before you are finished. I recommend you set up your answers in an excel spreadsheet. It will make the calculations much easier and faster.
i. (10) Suppose there is no MITD, and the homeowner borrows the full value of the property ($500k). According to the mortgage calculator, for the first year:
a) How large is the annual mortgage payment? How much interest has been paid on the mortgage?
b) How much principal has been paid off by the borrower?
c) The amount of the annual mortgage payment from part a) was paid at the beginning of the year. That reduces the cash available to invest. How much cash gets invested? What is the pre-tax value of the cash investment at the end of the year? How much tax is owed on this investment? What is the after-tax value of the investment after one year?
d) Add up the values of all the investor’s assets at the end of year one. How has this value changed over the year?
ii. (10) Suppose there is a MITD, the homeowner borrows the full value of the property. Repeat a-d from part i.
iii. (10) Not surprisingly, you hopefully saw in ii that the deduction is a boon to the homebuyer. Now, suppose the buyer makes a down payment of 20%, or $100k. Assume the MITD is not available. She invests the remaining cash at 3%. Repeat a-d from part i. in this case.
iv. (10) Once again, suppose the buyer makes a down payment of 20%. Assume the MITD is available. Repeat a-d.
v. (10) Comment on/compare your results for the different cases.