Urban Economics Quiz: Labor Market Equilibrium & NPV Challenges
School
New York University**We aren't endorsed by this school
Course
ECON-UA 227
Subject
Economics
Date
Dec 12, 2024
Pages
4
Uploaded by SargentWillpowerSardine39
Urban Economics, Fall 2024, Quiz #2 Due Friday, Nov 15, 11.59am (one minute before NOON) online on Brightspace no late problem sets, one single file submission only Word, Excel, or PDF formats only (1) Urban Labor Market(3 pts + 7 pts) In a city, labor supply is given by w=20+0.1Ls, where w denotes the wage. Labor demand is given by w= 160-0.5Ld. (a) Calculate the equilibrium labor quantity and the corresponding wage. (3 pts) (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 that 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 of labor). Calculate the new equilibrium wage and the new number of jobs. Will the number of jobs increase or decrease compared to (a)? (7 pts) (a) Set equal 20+0.1L = 160-0.5L èL = 233.33, w=43.33 (b) Lower the demand curve by 5 and lower the supply curve by 12. 155-0.5L = 8 +0.1L àL=245, w=32.50 (2) NPV (10 pts) Assume you will get 60 rental payments paid over 60 years at the beginning of each year. Initially the rent equals R=$10; but it will grow at a rate of g=1% per year. The NPV of this income stream equals $800. What is your discount rate? Provide your answer as percentage with two decimals, e.g., 1.23% (or 0.0123). Show your work. Note, when including g --- you can do this as in Gordon’s Model --- as (i-g). (10 pts) There are two possible answers. For both make sure you use “at the beginning of each year.” That is, in both cases, there must be an undiscounted R up front and T=59 Also, since time is limited, you cannot not GORDON’s Model. That is, using
࠵?࠵?࠵?=࠵?࠵?− ࠵?is incorrect. a) This is the answer we expected; simply use (i-g) instead of (i) Plug into Excel ài = 0.0731% b) Use Plug into Excel ài = 0.034% (3) NPV (15 pts) Assume you will receive constant rental payments over a time period of 88 years. For the first 44 years, you will receive a rent of $44 at the beginning of each year. For the next 44 years thereafter, you will receive $88 at the end of each year. In addition, due to illness, you will not get paid in the 66thyear. Employing the equation for identical payments over a limited time period, show how you would alter this equation applied to this problem. Plug in the numbers given in the question. Assume your discount rate is 2%. Calculate the resulting net present value of this income stream.
࠵?࠵?࠵?= ࠵?+࠵?࠵?+1−1(1+ ࠵?)!"/+࠵?࠵?+1−1(1+ ࠵?)##/−࠵?࠵?+1−1(1+ ࠵?)!!/−࠵?(1+ ࠵?)$$࠵?࠵?࠵?= 44+440.02+1−1(1+ 0.02)!"/+880.02+1−1(1+ 0.02)##/−880.02+1−1(1+ 0.02)!!/−88(1+ 0.02)$$࠵?࠵?࠵?= 2351.9955≈2352(4) NPV(5 + 5 pts) Assume you will get 111 payments of $20 annually at the end of each year. What is the difference to a payment scheme were you get the payments at the beginning of each year? The discount rate iequals i=10% a) calculate the difference for g=0 b) calculate the difference for g=1% (a) end of year payments, g=0, use this equation: ࠵?࠵?࠵?=200.1+1−1(1+ 0.1)%%%/beginning of year payments, g=0, use these equation: ࠵?࠵?࠵?= 20+200.1+1−1(1+ 0.1)%%&/NPV end of year = 199.9949 NPV beginning of year = 219.9944 difference: 19.9995 à20.00 (b ) end of year payments, g=1%, use this equation ࠵?࠵?࠵?=200.1− 0.01+1−1(1+ 0.1− 0.01)%%%/
࠵?࠵?࠵?= 20+200.1− 0.01+1−1(1+ 0.1− 0.01)%%&/NPV end of year = 222.2066 NPV beginning of year = 242.2052 difference: 19.9986 à20.00 There is an alternative method for g=1%. Here are the equations for payments received at the end of each year and at the beginning of each year, respectively. ࠵?࠵?࠵?=20(0.1− 0.01)91−:1+ 0.011+ 0.1;%%%<࠵?࠵?࠵?= 20+20(0.1− 0.01)91−:1+ 0.011+ 0.1;%%&<NPV end of year = 222.2052 NPV beginning of year = 242.2036 difference: 19.9985 à20.00