Problem 5. Consider a variant of the static G.E. model in which the representative household's preferences and the representative firm's production function satisfy our usual Econ 306 assumptions. The government differs from the model in the notes. First off, let G = T = 0. Instead, the government provides a proportional labour income subsidy to household. That is, for every unit of labour income earned by the household, the government will grant the household a subsidy of s units of output. The government finances this subsidy by levying a lump sum tax on firms. Denote the tax on firms by 7. Treat the subsidy rate s as the exogenous variable. (a) Formally define a competitive equilibrium in this economy. Make sure to include an expression for the government's budget constraint as well as expressions for the market clearing conditions in your definition. [3 points] (b) Write down the household's optimization problem. Depict the solution to the household's problem in a diagram. Explain the solution and contrast this to the solution to the household's problem in the baseline model. [3 points] (c) Depict the competitive equilibrium in a diagram. 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. [3 points] (d) Show that your diagram in part (c) satisfies your definition in part (a). Don't worry about depicting the fact that the government balances its budget for this question. [3 points] (e) Formally evaluate the following claim "This policy will make the house- hold better off (relative to the case where there is no subsidy) because the subsidy to wages will enable the household to increase consumption and the tax is non-distortionary." Explain. Comment: By "formally evaluate" I mean that you should give me some formal analysis, in this case in form of appropriate diagrams, in addition to your written explanation. [3 points] 3