(a) A landlord may not demand or receive a security deposit for an unfurnished dwelling unit in an amount or value in excess of one month's periodic rent. If the rental agreement provides for the tenant to use furniture owned by the landlord, the landlord may demand and receive a security deposit not to exceed 1½ months' rent, and if the rental agreement permits the tenant to keep or maintain pets in the dwelling unit, the landlord may demand and receive an additional security deposit not to exceed ½ of one month's rent. A municipal housing authority created under the provisions of K.S.A. 17-2337 et seq., and amendments thereto, which is wholly or partially subsidized by aid from the federal government, pursuant to a rental agreement in which rent is determined solely by the personal income of the tenant, may demand and receive a security deposit in accordance with a schedule established by the housing authority, which is based on the bedroom unit size of the dwelling unit. Any such municipal housing authority which establishes such a schedule shall provide a deferred payment plan whereby the tenant may pay the deposit in reasonable increments over a period of time.