Answer the following question.

1. Consider the life-cycle model discussed in Lecture 3-5. Now suppose that each member of each generation chooses how much labour to supply when working while young, and that there is a disutility associated with supplying labour. I Specifically, a member of generation t now has the followmg preferences U (cut, cot+l, lyt) c;tc10t+01 exp 2 yt 2 and recieves a wage of wt per unit of labour supply (lyt) worked while young. Note 4) that exp(.) is the exponential function (i.e. exp (a) (10 marks) Write down the period t and period t + 1 budget constraints and use them to derive the lifetime budget constraint. Formulate the individuals' utility maximisation problem and solve it to find the optimal values for: consumption when young, consumption when old, labour supply and saving of a generation t individual.