please help with 5b and 5d, thanks!

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 Jething like national parks. It enters as an input into the utility flmctiou of the household. That isI the utility function is given by U(C, I? G}, where all of the marginal utilities are positive. The government nances its spending via a proportional sales tax. [a] Formally dene a competitive equilibrilmi in this economy. (b) Generate equations that characterize the equilibrium allocation and prices. (c) 1".iifrite down the government's optimization problem. [d] 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.)