4. Consider the two-period consumption-labor model. Suppose that lifetime utility of the representative household is giv

[answerhappygod]

4 Consider The Two Period Consumption Labor Model Suppose That Lifetime Utility Of The Representative Household Is Giv 1 (38.92 KiB) Viewed 37 times

4. Consider the two-period consumption-labor model. Suppose that lifetime utility of the representative household is given by: V(C1, 11, c2, l2)= u(c₁,41) + Bu(c2, 12) where ß> 0 is the discount factor and t> 0 determines the relative preference for leisure. For both t= 1, 2, the period utility function given by: u(c. 4) Inc+ In l = and the household faces the following real lifetime budget constraint: €₂ +r C₁ + w₂(1-12) 1+r w₁(1-₁) + (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 (c₁*, l1*, 02*, 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).