Background: The value of an apartment to prospective tenants depends upon the level of maintenance: V=600+40(√M), 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 M>=40. The interest rate is 1% per month.

BUT... 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. 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. Thank you!

(The former question was... 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). This may help inform this question. No additional information provided).