Consider a one period model of an economy with a representative consumer. The consumer's utility function is U(C, l) = (1/2) C + a P\1 1 The firm's production function is Y = 2 K3 NE, where Yis output, K is capital, 2 is total factor productivity, and N is labor. (f) What is the equation for the firm's profit function? (g) Write down the firm's optimization problem. (h) Maximize profits to get the firm's optimal labor demand function. That is, solve for labor demand as a function of given exogenous variables and parameters). (i) How is the labor demand function, Nd, change when (a) w increases? (b) 2 increases? (c) K increases? Given the solutions you have from the consumer and firm optimization problems, solve for equilibrium in the economy. (j) Solve for equilibrium wage, w (k) How does the equilibrium wage change when 2 increases? Draw the graph of the labor market and show the effect of an increase in z. (I) How does the equilibrium wage change when or increases? Draw the graph of the labor market and show the effect of an increase in a