Problem 4. Answer this question using calculus. Consider a version of the one period general equilibrium model with pro- duction, as seen in class. The main deviation from the model seen in class is that the government produces a public good, G, that generates utility for households. The gov- ernment finances its spending via a lump sum tax on households. Treat G as exogenously given, unless otherwise specified. (a) Formally define a competitive equilibrium in this economy. Make sure to write out the government's balanced budget constraint as part of your equilibrium definition. [3 points] (b) Write down the household's problem, and generate first order conditions. [3 points] (c) Write down the representative firm's problem, and generate first order conditions. Generate the system of equations that characterizes the equi- librium allocation and prices. [3 points] (d) Show whether the decentralized equilibrium is efficient or not. Does your answer rely on the fact that G is exogenous? Explain. [3 points]