Consider a representative individual who lives for two periods with preferences (1, 2 ) = 12 over current consumption 1 and future consumption 2. In period 1, they face a budget constraint 1 + 1 and in period 2, 2 2 + (1 + ), where 1 and 2 are their income in periods 1 and 2 respectively. are their savings in period 1, and is the net interest rate.

a) (2 pts.) Derive the two-period budget constraint of the representative individual.