(1) Urban Labor Market (3 pts + 7 pts)

In a city, labor supply is given by w=10+0.1Ls, where w denotes the wage. Labor demand is given by w= 100-0.5Ld.

(a) Calculate the equilibrium labor quantity and the corresponding wage

(b) Now assume the city imposes an environmental tax of $5 per unit of labor on firms. As a result, companies will now lower their willingness to pay for labor by $5 per worker. The city uses the money to beautify the local park, which attracts many workers to the city. An economic consultant firm finds out the labor supply curve will shift because workers will be happy with a wage that is $12 lower than before the improvement (at any quantity at quantity of labor). Calculate the new equilibrium wage and the new number of jobs. Will the number of jobs increase or decrease compared to (a)?

(2) NPV (10 pts)

Assume you will get 40 rental payments paid over 40 years at the beginning of each year. Initially the rent equals R=$40; but it will grow at a rate of g=1% per year. The NPV of this income stream equals $162.87. What is your discount rate? Provide your answer as a percentage with two decimals, e.g.,  1.23% (or 0.0123). Show your work.

(3) NPV (10 pts and 5 pts)

Assume you will receive constant rental payments over a time period of 66 years. For the first 33 years, you will receive a rent of $33 at the beginning of each year. For the next 33 years thereafter, you will receive $33 at the end of each year.

(a) Employing the equation for identical payments over a limited time period, show how you would alter this equation applied to this problem. Show the abstract equation using R for rent and i for the discount rate. Only for T, plug in the appropriate numbers.

(b) Now fill in the numbers and assume your discount rate is 2.5%. Calculate the resulting net present value of this income stream.

(4) Mortgage Rates and House Prices (15 pts)

On the internet, go to Freddy Mac and look up the 30-year mortgage rates http://www.freddiemac.com/pmms/pmms30.htm. Download the data.

(you can download an Excel file of the 30-year mortgage rate data at the very bottom.)

a) (3 pts) When did mortgage rates reach their historical high (year and month); how high was it?

When did mortgage rates reach their historical low (year and month); how low was it?

What is the current 30-year mortgage rate (Oct 2022)?

b) (12 pts) Now go to the Federal Reserve’s data website FRED and download the “S&P/Case-Shiller 20-City Composite Home Price Index“ https://fred.stlouisfed.org/series/SPCS20RSA

Drawing on these two data series, create a scatterplot with the 30-year mortgage rates on the x-axis and the composite home price index on the y- axis. Disregard the “points” in the Freddie Mac data.”1 (Since the Case-Shiller Index only covers the period from Jan 2000 to Aug 2022, you will have x-y pairs for this time period only)

In Excel, run a simple linear regression

Home Price Index = b0 + b1*MortgageRate

and show it in your scatterplot (use the Trendline function in Excel). In your Excel file, show all data and the chart

Below is an example with imaginary data.