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The value of an apartment to prospective tenants depends upon the level of maint

ID: 1149227 • Letter: T

Question

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.

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).

Thank you very much!

Explanation / Answer

Answer:

An owner will have optimum rent if following condition is maximised by equalising FOC to zero

Profit function for owner is V-M

PROFIT=@=600+40×sqrt (M)-M

Differentiating above equation to find optimum rent and maintainance level.

d@/dM=20/sqrt(M)-1=0

M=400 (Optimum maintenance level)

V=600+40×sqrt(400)=1400 (optimum level of rent)