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Consider a twoperiod eoonomy where consumers have the following lifetime utility: U=lnc1+lnc2 (3) Where (:1 and c2 are consumption in the rst and second period respectively and ,6 is the discount factor. Theyr receive exogenous income Y1, prots 7:1 and pa},r lump sum taxes T1 in the rst period and Y2, 11'2 and T2 respectively in the second period. They buy or sell any amount of bonds at the same interest rate 'r. (i) Derive the expressions for the optimal level of consumption cl and c2, and savings 3. Illustrate the solution with a graph. [10 marks)