Reference no: EM132405678

Consider a version of the general equilibrium model seen in class. The government is different than in class. The government raises revenue by imposing a labour income tax on households, where t is the tax rate. The government uses this revenue to finance an exogenously given level of spending, G. The government balances its budget.

A representative consumer has preferences over consumption and labour that satisfy the usual assumptions. A representative rm produces output using labour and an exogenously given amount of capital. The government's expenditures, G, are a public good which serves as an input in the production process. Thus the rm's production function is given by Y = zF( K ;N;G), where all marginal products are positive and diminishing, and F() is constant returns to scale and strictly concave.

Households and firms interact on competitive markets for goods and labour.

(a) Dene a competitive equilibrium in this economy.

(b) Formally write the representative consumer's problem. Generate the first order condition(s).

(c) Formally write the representative rm's problem. Generate the first order condition(s).

(d) Interpret the representative firm's first order condition(s).

(e) Generate the system of equations that characterizes a competitive equilibrium.

(f) Show that the competitive equilibrium allocation is not efficient. Explain.