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

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Consider The Two Period Consumption Labor Model Suppose That Lifetime Utility Of The Representative Household Is Given 1 (83.32 KiB) Viewed 10 times

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, l₂) where 3 > 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: C₁ + w₂(1-12) 1+r w₁ (1-₁)+ 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 (c₁*, 41, 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).