This problem aims at rationalising these cross-country differences through the lens of the RBC model studied in class. 1. (8 marks)For now on, countries will be indexed by i. Suppose that the economy in each country i is populated by a representative household. The household lives for two periods. She chooses consumption in the first and second period Ci and C i , respectively, and leisure li in the first period to maximise her utility U(Ci ,li ,C i ) = log(Ci) log(li) log(C i ) subject to her lifetime budget constraint Ci C i 1 ri = wi(h li)(1i) i i T i 1 ri , where h is the total number of hours available for productive work, wi is the hourly wage, ri is the real interest rate, i and i are dividends in the first and second period, i is a proportional tax levied in the first period, and T i is a lump-sum tax levied in the second period. Show that, at the optimum, the following condition holds for each country i: Ci li = wi(1i)