For the CEOP model from chapter 5, assume that the First Fundamental Theorem holds such that the model can be solved as the benevolent social planner's (BSP) problem. The consumer's utility function is: U(C, 1) = In (C) + * In (2) and the firm's production function is: zF(K, N) = z(ak + N), where , a and 8 are all positive constants. (a) What is Lagrangian that the BSP will solve? (3 points) (b) Solve the BSP's problem and find the optimal consumption (C), employment (N), output (Y), leisure (I) and the real wage (w) in a competitive equilibrium. As always, show your work to get credit. (14 points) (c) Sketch this equilibrium on a graph with consumption on the vertical axis and leisure on the horizontal axis. You can just label the optimums that you computed for (b) with an asterisk, for example, C*, N*, etc. You don't need to label wage on the graph