1. Suppose that the production function of an economy is given by Y = VN. The (representative) firm hires workers (N) at a wage rate w. Assume that the firm maximizes profits by choosing how much to produce and how many workers (hours) to hire. (Remember that the profit function is Y - WN.) The representative consumer has preferences given by the utility function U( ) = log (c) + log (1), with a marginal rate of substitution given by c/, where c is consumption and / is the leisure time. The endowment of time of an individual is 24, which has to be allocated between labor and leisure. (Recall that N + ( = 24.) a. Derive an expression for the labor demand function. b. Derive an expression for the labor supply function. c. Compute the equilibrium wage rate and the equilibrium quantity of labor employed. d. Consider a technical improvement of the production process that determines a new production function Y = 2vW. Compute the new equilibrium quantity of labor and wage rate. e. Draw a graph of the labor market to describe parts c and d