Consider the two-period consumption-labor model. Suppose that lifetime utility of the representative household is given by: V(C,41, 02, l2)= u(c,41) + Bu(c, 12) where > 0 is the discount factor and %> 0 determines the relative preference for leisure. For both t= 1, 2, the period utility function given by: u(a, 4) Inc + In and the household faces the following real lifetime budget constraint: C + w(1-1) 1+r w (1-)+ 1+r (a) Using the lifetime Lagrangian, compute all relevant first-order conditions. (b) Derive the consumption-labor optimality conditions for periods 1 and 2, and the consumption-savings optimality condition across periods 1 and 2. (c) Solve for the optimal values (c*, 1, c2*, 12*) in terms of exogenous variables only. (d) Perform comparative static analysis to mathematically show an increase patience by the household will affect how each optimal choice variable. (HINT: An increase in patience is given by an increase in the discount factor, 3).