I'm having trouble working out the start of this question:

a) Period t budget constraint: Cyt + at+ 1 = lyt Wt Period t+1 budget constraint: Cotti = (1 + 1t+1)at+1 Lifetime budget constraint: Cyt + Cot+1 at+1 = lyt Wt 1+ rt+1 Utility maximization problem: 1-0 max Cyt - Lyt + 1-a Cyt, Cot+1,lyt 1+n ot + 1) s. t. Cyt + Cot+ 1 - at+1 = lyt Wt 1+rt+1 Form a Langragian: 1+n 1-0 L (Cyt, Cot+1, 1 ) = a yt Cyt 1 + n Cotti ) - A ( Cyt + 1 + It+ 1 Cot+1 at+1 - lytWt ) F.O.C: ac - = a (n + 1) (Cyt (n+ 1) -lye"+1)- - 1=0 acyt ac - = Cot+1-(-a + 1) - = 0 acot+1 1+ rt+1 alt =-alve"+ + awt = 0a 11:" H 1 a U(Cytacot+17lyt):1i J Cyt 1:7? + (17 (7)03325101 where cm is consumption when young in period t, cat\" is consumption when old in period t | 1, lm is the labour supplied when young in period t and we assume that 0' > 0, 77 2 l and 0