Can you please help me solve the following question (especially f,g, and h)? I have solved a, b, c, and e. I skipped d because I don't think it's necessary to solve f,g, and h. I started f, but I'm not sure how to continue the question.

The first image is the question and the second image is my answers.

I al max U( ci) = B( ct) sit . U = 0 Post - Pe Ci 1 - X b) citc ? = Ette, V6= 0,1, 2 ,.... C)ACE is 1. A sequence of prices ERS 3 and 2. A sequence of consumption ( co] for each consumer i such that 1. Given [ BE ), Sci) solves consumer i's problem, Hi= 1, 2 max U ( ci) = 2 BB ( C ) " at. Epicis poet 1 - 8 2. Market clears in each period 22= + ez i , VE = 0 , 1, 2 ... 2 ) max , V ( ci)t 2 V (c 2 ) s.t cite? = enter,ve Li, +2: utility weights f ) = 2 R ( ci ) + hil = poles - ci) ] ? 1- 8 g ) ? h ) ?1. Pure exchange economy: The economy has two agents and infinite time horizon. There is one consumption good in the economy. Utility of agents are: U( c') = [ B(a )- 1 - y where y is a risk aversion parameter. Notice that the consumer has Constant Relative Risk Aversion (CRRA) utility function. Each consumer is endowed with a sequence of consumption goods {et}=0,1,2,.... (a) Write down consumers' problems "b) Write down the market clearing condition c) Define Competitive Equilibrium (d) Define Pareto Efficiency (e) Define Social Planner's problem (f) Characterize the competitive equilibrium defined in (c). (That is, write down first order conditions and other equations necessary to solve the equilibrium.) g) Characterize Social Planner's solution (Write down first order conditions and other equations necessary to solve the problem) (h) Now, endowment is given as follows: Time : 0, 1, 2, 3, ... Consumer 1 (el) : 2, 3, 2, 3, ... (2) Consumer 2 (e?) : 3, 2, 3, 2, ... (3) That is, el = 2 for t : even and et = 3 for t : odd. Analogously, e? = 3 for t : even and e? = 2 for t : odd. In this environment, answer the followings: i. Solve for the Competitive Equilibrium defined in (c) ii. Solve for the Social Planner's problem defined in (e) iii. State First Welfare Theorem. Does the theorem hold? Verify it. iv. State Second Welfare Theorem. Does the theorem hold? Verify it