What was the purpose of setting up the public works administration and the works progress administration?

To provide employment through federal deficit spending was the primary goal of both The Public Works Administration and the  Works Progress Administration is the right answer.  

The Public Works Administration was founded by the "National Industrial Recovery Act on June 16, 1933". It was intended to fund big bucks on big schemes.

Created on April 8, 1935, Work Progress Administration  was created to grant aid for the unemployed by providing employment and income for millions of Americans during the Great Depression.

disequilibrium means that either supply is greater than the demand for an available good, or that the demand for a product outstrips the available supply. it implies that the price for a is either too low creating large demand, or too high creating a large surplus of supply.