please answer the question

1. Consider the Melitz model of trade. [5 marks each = 20 marks] (a) For the case of exactly TWO varieties, the utility maximization problem is given by l p p 3 giggle + 92] subject to P191 +P2f12 = R Form the Lagrangian, solve the optimization problem and verify that demand is given W: R (l _ _ P w -0 where each variable is dened exactly like in the Melitz [2003) model. Describe what the aggregate Price index P stands for. (b) Given that prot maximization for each rm producing variety to is given by: 1 13(50) = E where (,0 is rm productivity, show that (J-1() r 11' (p or to (c) Hence, use the ZCP condition ((9') = 0 to show that average prot in the industry is: w=d$r4n and is hence independent of labor supply L. (d) Verify that who}