2. The value of an apartment to prospective tenants depends upon the level of ma
ID: 1148902 • Letter: 2
Question
2. The value of an apartment to prospective tenants depends upon the level of maintenance: V-600+400VM), where V is the maximum monthly rental an individual would pay for an apartment that receives M dollars of maintenance per month. An apartment will last forever provided M240. The interest rate is 1% per month. a. (6 points) What amount of monthly maintenance will a profit-maximizing owner provide? What rent will the owner charge (assuming she can make a take-it-or-leave-it offer to prospective tenants, which means she will ask them to pay their entire valuation V (or perhaps V minus epsilon) b. (3 points) What is the market value of the apartment? (What is the present value of the stream of profits that can be generated from the apartment?) A rent control program is enacted which limits the rent for this apartment to $1000/month, and requires the owner to provide at least $100/month of maintenance. The existing tenant is entitled to retain her lease forever. c. (6 points) What amount of maintenance will the owner provide? (Assume that the owner is law-abiding.) What is the deadweight loss (in present value terms) associated with the permanent rent-control program? Why is there any dead-weight loss at all in this situation? Please explain.Explanation / Answer
Profit Function for Owner is
Profit(M)=V-M=600+40sqrt(M)-M
We need to find FOC when Profit changes with change in unit of M
d(Profit(M))/dM=40*(1/2)(1/sqrt(M))-1=0
20/sqrt(M)=1
M=400 (Optimum Level of Maintenance)
Profit =600+40(sqrt(M))-M=600+40*20-M=1400-M=1000
This is Rent provided is 1400 per month
Market Value of an Apartment = PV of Future Cashflows
as said in this quetion if M>40 then apartment will last for infinitely.
Hence to find PV of rent which has infinite cash flows cna be found with the formula (Cash Flow/Interest Rate)
PV=(1000/0.01)=100,000
Value of Apartment is $100,000
The rent cant exceed $1000 due to rent control program
1000=600+40sqrt(M)
Profit =V-M=1000-100=900
M=100 at which an owner can provide but each dollar increase beyond $100 will create dead weight loss to Owner
He will be having a profit of 900 each month over 1000 each month previously
Hence PV of Deadweight loss is 100/0.01=$10000
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