Question 1. Consider an economy in which the representative consumer preferences are described by U(C, 1) = 0.9 log C + 0.1 log l. The total number of hours available to the representative consumer is h = 1, and the real market wage is w. The representative firm produces the final consumption good using the technology function Y=zNd, where Nd is the labor demand, and z = 2. Assume the government sets the level of its spending to G = 0.75, which has to be financed through a proportional tax t. a) Write down the consumer's optimization problem and find the optimal consumption bundles. b) Write down the firm's profit maximization problem and the equilibrium wage w*. c) Find the Competitive equilibrium allocation (t*,l*, N*,Y*). d) Find the Pareto Optimal allocation by solving the social planner's problem. e) What do you conclude?