In connection with any housing project located wholly or partly within the area in which it is authorized to act, any state public body may contract with a housing authority or the Federal Government with respect to the sum which it may agree to pay during any period to the state public body for the improvements, services, and facilities to be furnished by it for the benefit of the housing project. The amount of the payments shall not exceed the estimated cost to the state public body of the improvements, services, or facilities to be furnished. The absence of a contract for such payments does not relieve any state public body from the duty to furnish for the benefit of the housing project the customary improvements and the services and facilities it usually furnishes without a service fee.