please help with answering part a, and b

To keep things relatively simple, let's assume that lifetime utility is given by a (c1) + 11(11) + t: ((32) . Here, ll is the HH's leisure in the rst period, with Nf = 1 11 as in LNl. The function a obeys the usual assumptions. The function 1: now captures the utility of leisure, and we assume it has the same general properties as u (i.e., strictly increasing and concave). To make things even simpler, let's do away with labour in the second period, and make the production functions linear in both periods. That is, we assume output in the rst period is given by m = 21(n1 + In] and output in the second period by yg = 22kg- Note that, as rms don't hire any labour in the second period, household labour income will be zero in that period. All other elements of the model are the same as in LNT. (NOTE: You may assume throughout that none of the HH's non-negativity constraints ever bind.) (a) (4 marks] Write down the household's budget constraints for each period. (b) (6 marks] Set up the household problem, being sure to state the objective function, the choice variables, and the constraints (you can ignore any NNCS). Solve this problem, being sure to combine equations to eliminate any Lagrange multipliers- You should be