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Question IV [25 points] 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 u"(co, 4 ci) = In(ca) + 0.9 In(ci), while B has the following preferences uB(co,B CP) = In(cB) + 0.8 In(cB). Consumer A receives an income Yo = 100 in period 0 and Y, = 150 in period 1. On the other side, Consumer B receives an income Y. = 125 in period 0 and Y, = 100 in period 1. Assume the interest rate is r. The government wants to spend Go = 50 in period 0 and G1 = 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. 1. Compute the optimal consumption (co, C1) for each individual as a function of the interest rate r. [10 points] 2. Find the equilibrium interest rate that clears the credit market. [10 points] Hint: The credit market is cleared when the sum of the consumers' savings in period 0 is zero. 3. Assume the government decides to increasing its spending in period zero by 10%. How will this policy affect the equilibrium interest rate? Explain.[05 points]