1. Answer this question with diagrams. Consider a variant of the static G.E. model in which the representa- tive consumer has preferences given by U(C,1), where U() is a standard, quasi-concave utility function. The representative firm's production func- tion, F(K, Nd) is a standard, concave production function. Suppose that the capital input is fixed. The government differs from the model in the notes. Like the notes, sup- pose that the government has to finance an exogenous level of government spending given by G. For simplicity, assume that these government expendi- tures are useless. Unlike the notes, we suppose that the government finances its expenditures by taxing firms. The government does this by levying a proportional tax, where the tax rate is denote by T, on employment. That is, the firm pays t units of output to the government for every unit of labour the firm hires. (a) Formally define a competitive equilibrium in this economy. Make sure to include an expression for the government's budget constraint in your definitions. [3 points] (b) Depict the competitive equilibrium in a diagram. [3 points] Note: Make sure that the key part of your diagram is large enough that I can evaluate whether you have or have not depicted an equilibrium correctly. (c) Show that your diagram in part (b) satisfies your definition in part (a). Don't worry about depicting the fact that the government balances its budget for this question. [3 points) (d) Show whether the equilibrium in part (b) is or is not efficient. Explain. [3 points]