Consider the closed economy, one period model with the following utility and production functions: U(C,l) = ßln C + Inl = and Y = In(z) + alnK + (1 – a)N = - = = where Y= output, z = total factor productivity, K = capital, N= labor, C = consumption, and 1 = leisure; a & ß are positive constants; and 0 < a < 1. At the competitive equilibrium, the government must satisfy its budget constraint (where G is government spending and T = lump-sum taxes); the representative firm optimizes; the representative consumer optimizes; and the labor market clears (h = total number of hours available for work or leisure). (a) Compute the competitive equilibrium values of consumption (C) and leisure (1). (6 points) (b) What is the equilibrium real wage? (2 points) (c) Graph the equilibrium from (a) on a graph with consumption on the vertical axis and leisure on the horizontal axis. Be sure to label the optimal C, 1, Y, and N. (6 points) (d) On the graph from (c), illustrate what happens to this competitive equilibrium when government spending decreases. Note: you don't have to compute anything; just illustrate and label the new values as C1, 11, N1, and Yį. Be sure to distinguish your 'new'curves from the original ones with accurate labelling.