Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to be called, A, and B). A has the following preferences cit) = In(c) + 0.9 In(c+), while B has the following preferences 4) = In(cf) + 0.81n(cf). Consumer A receives an income YOA = 100 in period O and YIA = 150 in period 1. On the other side, Consumer B receives an income YB = 125 in period O and YIB = 100 in period 1. Assume the interest rate is r. The government wants to spend GO = 50 in period O and GI = 75 in period 1. These spendings are financed through lump-sum taxes. It is assumed that the government collects the necessary tax to finance its spending in each period and the tax burden is equally supported by the consumers in each period. 3 1. Compute the optimal consumption ) for each individual as a function of the interest (12 points] rate r. 2. Find the equilibrium interest rate that clears the credit market. (08 points]