c1-o -0 - - = = 1-0 (Consumption-Labor Choice) Consider a Crusoe choosing the optimal consumption (C) and labor supply (L). The utility function is given by u(C,L) = - L. The production function is Y = F(L) = AL1/2. (a) (4 points) While the problem may be setup or solved without using the Lagrangian method write down Crusoes Lagrangian function. Then, solve for the first-order conditions. (b) (8 points) Suppose A increases, what would happen to the shadow-price for Crusoe? How would this affect Crusoe's valuation of labor and its labor supply decisions? Explain in the context of substitution and income effects. c1-o -0 - - = = 1-0 (Consumption-Labor Choice) Consider a Crusoe choosing the optimal consumption (C) and labor supply (L). The utility function is given by u(C,L) = - L. The production function is Y = F(L) = AL1/2. (a) (4 points) While the problem may be setup or solved without using the Lagrangian method write down Crusoes Lagrangian function. Then, solve for the first-order conditions. (b) (8 points) Suppose A increases, what would happen to the shadow-price for Crusoe? How would this affect Crusoe's valuation of labor and its labor supply decisions? Explain in the context of substitution and income effects