Answer this question using calculus. Please answer the questions yourself.

5. Answer this question using calculus. Consider a version of the one period general equilibrium model with pro duction in which the government produces a public good, G. The public good is something like infrastructure. It enters as an input into the production function of the rm. That is, Y = zF (K , N , G). The government nances its spending via a proportional tax on labour income. (a) Formally dene a competitive equilibrium in this economy. [3 points] (b) Write down the household's problem, and generate rst order conditions. [3 points] (c) Generate equations that characterize the equilibrium allocation and prices. [3 points] (d) Write down the government's optimization problem. [3 points] (e) Will the government optimally choose to provide the same level of the public good as would a social planner? Explain. (You can answer this problem in words only.) [3 points]