Please answer the question using microeconomic theory

Joe's utility function is given by U = In(c1) + Bin (c2) where c, is Joe's income in this year and c2 is Joe's income next year. He has y, = 10 units of income today and yz = 5 units of income tomorrow. Assume the price of consumption today is 1 (one). If the interest rate is 10%, what is Joe's budget constraint? (5 marks) If the interest rate is r, what's Joe's optimal combination of consumption today and consumption tomorrow? (5 marks) If Joe had nowhere to borrow, what would be his autarky interest rate? What happens to it if B decreases? (5 marks) Let Joe be in an autarky equilibrium. Joe meets Jim, who has preferences identical to Joe's and endowment of 5 units of income today and 10 units of income tomorrow. What would be the equilibrium interest rate on the competitive market of these two consumers? (10 marks)