can you please show me the math to these answers please

Consider a two-period model of a small open economy with a single good each period and no investment. Let preferences of the representative household be described by the utility function U(C, C2) = VC+ BVC2The parameter S is known as the subjective discount factor. It measures the consumer's degree of impatience in the sense that the smaller is A , the higher is the weight the consumer assigns to present consumption relative to future consumption. Assume that = 1/1.1. The representative household has initial net foreign wealth of (1 + To) By = 1, with To = 0.1, and is endowed with 21 = 5 units of goods in period I and Q2 = 10 units in period 2. The world interest rate paid on assets held from period I to period 2, rs, equals 10% (i.e., "* = 0.1) and there is free international capital mobility. a) Calculate the equilibrium levels of consumption in period 1, Ci,consumption in period 2, C2, the trade balance in period 1, 7'By, and the current account balance in period 1, CA1. (10 marks) Maximizing utility subject to the budget constraint leads to the usual tangency condition: VC2 VCI = B(1 + 7*) = 1 So, we have CI = C2 Plug that in the budget constraint and get: CI = C2 = 7.9 Then, the trade balance is: TB1 = Q1 - C1 = -2.9 And the current account is: CA1 = TB1 + ToBy = -2.9 + .1(.91) = -2.81 b) Suppose now that the government imposes capital controls that require that the country's net foreign asset position at the end of period I be nonnegative (BY > 0). Compute the equilibrium value of the domestic interest rate, 71, consumption in periods 1 and 2, and the trade and current account balances in period 1. (10 marks) From the current account expression: CA1 = BY - By we have BY = 0, since the constraint is binding. Then CA1 = -By = -.91 From CA1 = TB, + To Bu we have TB1 = CA1 - ToBy = -.91 -.1(.91) = -1Then from TB1 = Q1 - CI we have CI = Q1 -TB1 =5+1=6 To find Cause the budget constraint and substitute all knowns into it to get: C2 6+ 7 - =1+5+ 10 1 + 71 or C2 = 10 To find the domestic interest rate, use the tangency condition: C2 = CIA2(1 + m) Plug in the known values and solve for r1: 71 = -1 =1.1V6 10 BV Ci -1 = .42 So, 71 = 42%. c) Evaluate the effect of capital controls on welfare. Specifically, find the level of utility under capital controls and compare it to the level of utility obtained under free capital mobility. (5 marks) To compare utility under both free capital mobility and capital controls, plug the solutions for consumption in the utility function. Under free capital mobility: U = VCi+ BVC2 =V7.9 + .91V7.9 =5.37 Under capital controls: U = VCI+BVC2 =v6+.91v10 =5.33 Then we have U free = 5.37 > Ucc = 5.33 The country is better off under free capital mobility