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Q6. A consumer lives for two periods. He has incomes Y, and Y2 in the two different periods, and he can borrow or lend at an interest rate r. He maximises the lifetime utility function U = u(C1) +- u(C2) 1 + p Write down the consumer's budget constraint and substitute this into the lifetime utility function in order to find the first-order condition for consumption. The budget constraint is C2 2 = Y1+ Y2 1+r Re-arranging this for C2 yields C2 = (1 +r) Y, + Y2 - (1+r) C, Substituting into the lifetime utility function and maximising with respect to C1 U = u(C1) +- u((1 + r )Y1 + Yz - (1+r) (1) 1 + p du -= u'(c) - (1tru((1+r)Y+Y2 - (1+r)C1) dc -= 0 1 + p u'(C2) - = u'(C1) - (1+r) 1+p - = 0 u' (C2) u'( C 1 ) = (1 + r) 1+p u'(C1) 1+r u' (C2) 1 + p u' ( C ) =1+r u'(C2)/ (1 + p) Either of the last two lines is an acceptable form for the first-order condition (aka the Euler equation)