Can you please help solve these questions. I am stuck, especially part d,e,f,g

Questions 1. Consider a single country (call it country 1) which produces two prod- ucts, product A and product B. The country is inhabited by L; identical workers and two specific factors, one for each product. Let the quantity of the specific factor in country 1 for product A be A; and the quantity for the specific factor in country 1 for product B be B;. Suppose the production function for the production of product A can be written as: QAl = (LAl)a(Al)l_a: where () 4; is the quantity produced of product A in country 1, L 4; is the number of workers employed in the production of product A, and a (0, 1). Similarly, suppose the production function for the production of product B can be written as: Qp1 = (LBl)B(Bl)l_'@, where (Jp; is the quantity produced of product B in country 1, Lpg, is the number of workers employed in the production of product B, and g (0,1). (a) Suppose that a representative agent for country 1 has preferences U (C41, Cp1), where C 4 is the quantity consumed of product A and Cg; is the quan- tity consumed of product B. i. List the exogenous model parameters. ii. List the endogenous model outcomes. iii. Define the equilibrium. (b) Using the labor market clearing condition (i.e. that L1 = L + Lp1), write down an equation for the production possibility frontier (i.e. a function for the maximum amount of () 4; that can be produced for a given quantity of Qp; produced). (c) Find the marginal product of labor in the production of product A (i.e. ggji) and the marginal product of labor in the production of product L0 B (i.e. a%i) (d) Calculate the equilibrium relationship between the relative price % and the allocation of labor between the two products. (Hint: use the equilibrium condition that workers maximize their income). (e) Suppose that Uy(Ca1,Cp1) = ylogCyuy + (1 v)logCpy, where v (0,1). Calculate the equilibrium relationship between the relative price % and the quantity consumed of the two products. (Hint: use the equilibrium condition that the representative agent maximizes her util- ity subject to the income earned in the country). (f) Combining your previous two answers, write all the endogenous model outcomes as functions only of the exogenous model parameters. (g) Suppose that workers and owners of each specific factor all have identi- cal preferences to the representative agent. Write down expressions for the welfare of workers and owners of each specific factor as a function only of the exogenous model parameters. 2