et's use this problem set question to think about how to integrate government activity into our static general equilibrium model of an economy with production. Specifically, suppose that the government needs to finance an exogenous level of spending gt. (a) Suppose that the government finances gt through a lump sum tax T on households. Define a competitive equilibrium for this economy. Make sure to include a government budget constraint, and be careful about what to include about equilibrium variables in your equilibrium allocations. (b) Now suppose that the government finances gt through a proportional tax c on house- hold consumption. Define a competitive equilibrium for this economy. (c) Now suppose that the government finances gt through a proportional tax n on firm's wage bill (i.e., this is like a payroll tax, in which a firm pays n to the government for each unit of salary it pays to its workers). Define a competitive equilibrium for this economy. (d) Write down the planner's problem for an economy with government spending gt, and solve for this problem's optimality conditions