1. The static general equilibrium model. Based on the static general equilibrium model discussed in class and Williamson (2014), determine if the following propositions are true or false. If true, prove it mathematically or graphically (including a brief explanation). If false, provide a counterexample or a rigorous argument. (a) According to the firm's problem and the income approach, the sum of after-tax profits and labor income is equal to GDP. (b) If the representative consumer minimizes total spending measured as C+wl subject to a certain level of utility U = U(C,l), where U is a constant, then we obtain the standard optimality condition: MRS l,C = w. (c) If the government introduces transfers (TR > 0) and give them to the representative consumer such that the new budget constraint is C = wN + (1 ) T + TR, then the labor supply decreases. (d) If the technology is Y = zN and the government imposes a proportional tax on labor income such that C = (1)wN+T, then the competitive equilibrium (CE) is not Pareto optimum (CE is not the social planner's optimal bundle)