A housing authority shall have the power, within its area of operation:
(1) To investigate into living, dwelling, and housing conditions and into the means and methods of improving these conditions;
(2) To determine where slum areas exist or where there is a shortage of decent, safe, and sanitary dwelling accommodations for persons of low income;
(3) To make studies and recommendations relating to the problem of clearing, replanning, and reconstructing of slum areas and the problem of providing dwelling accommodations for persons of low income; and
(4) To cooperate with the city, the county, and the state, or any political subdivision therof, in action taken in connection with these problems; and
(5) To engage in research, studies, and experimentation on the subject of housing.