Take the following model of two countries, country 1 and country 2, tgat live for two periods, period 1 and period 2. Each have preferences over traded and non-traded goods expressed as...

Take the following model of two countries, country 1 and country 2, that live for two periods, period 1 and period 2. Each have preferences over traded and non-traded goods expressed as U = alog(C: 1,7) + (1 - a) log(C1,0) +B (a log(C 2,7) + (1 - a) log(Ci,2,0)) where i = 1,2 for country 1 and 2. The budget constraints for the countries are C.1.2 + P.C.1. + B1 = y 1.7 + P1.NY1N C.27 + P2.C.2. - (1+r)B,1 = Y27 + P2,Y 2, a) Derive the optimal consumption of traded goods for each country i as a function of the output of traded goods and the world interest rate. Then show how the equilibrium price of non-traded goods is determined in each period of each country b) Noting that output of traded goods must equal consumption of traded goods in the world economy, compute the equilibrium world interest rate c) Show the impact of (i) a rise in the output of period 1 traded goods in country 1 on the world interest rate, the current account in country 1 and country 2, and the equilibrium price of non-traded goods in each period in each country, and (ii) a rise in the output of non-traded goods in period 1 in country 1 on the same variables as part (i)