Define competitive equilibrium in this economy

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Reference no: EM133985919

Consider a variant of the static G.E. model in which the representative consumer has preferences given by U (C, l), where U (·) is a standard, quasiconcave utility function. The representative firm's production function, F ( ¯K, N d) is a standard, concave production function. Suppose that the capital input is fixed.

The government differs from the model in the notes. First off, let G = T =0. Now suppose that the government wants to increase the total amount of output produced in this economy. , it pays firms a subsidy of rate's for each unit of output the firm pays to its workers. The government finances this subsidy by taxing households using a lump sum tax. The government balances its budget. The subsidy rate is s > 0, and the lump sum tax is given by τ . Treat the subsidy rate as an exogenous variable and the tax level as endogenous.

(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 definitions.

(b) Write down the firm's optimization problem. Depict the solution to the firms's problem in a diagram. Explain the solution and contrast this to the solution to the firm's problem in the baseline model.

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.

(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.

(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 labour will enable the firm to pay higher wages to the household, which will allow it to increase consumption."
Comment: By "formally evaluate" I mean that you should give me some formal analysis, in this case in form of appropriate diagrams, rather than just discussion.

Reference no: EM133985919

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