Given the utility function U(c, 1) = 2ca (1-1) 1.5 the budge constraint as p. c = w(1-1) 1.5 The production function is given as y=zn 0.5 Let p=1, and a and z as parameters in the model. c is the consumption, I is the leisure, n is the labor input. w is the wage. In the labor market equilibrium, n=1-1. a) Find the household labor supply function. b) Find the optimal labor demand.