please help me with this question with an explanation, thank you!

Consider a version of the two period general equilibrium model with pro duction, as seen in the notes. Suppose that there is a negative pollution externaljty that takes the same form as the externality in section 7.2 of the chapter 4 notes. That is, let P denote the aggregate level of pollution. The household gets utility from three goods: consumption, leisure, and clean air. This formula tion allows us to maintain the assumption that the household's preferenoes are monotonic and convex. The household's per period utility function be comes \"(Chin Pt), where n1(-),u2(-), and u;;[-} are all positive due to the fact that conslnnption, leisure, and clean air are all goods, not bads. Pollu tion enters the utility f1n1ction with a negative sign, because an increase in pollution decreases the cleanliness of the air that the household breathes. Answer the following questions about the household's problem. (Note: you are not asked to characterize the entire equilibrilnn for this question.) (a) Write down the household's problem, and generate rst order conditions. (b) Interpret the household's rst order conditions. You only need to in terpret the intertemporal and intratemporal conditions once each. (c) Explain why the rational expectations asslnnption is needed in order to solve household's