Question:

Constrained maximization - the mechanics.For the objective function and constraint shown below,

set up the solution

(a) using the MRS = slope of budget line condition (you will have 2 equations and 2 unknowns; put the equations in the boxes)

(b) using the Lagrange multiplier approach (3 equations).

(c) Then solve for C , S, and the multiplier however you like.Be sure to include a value for in your answers.

(d)Explain in one or two sentences what represents, economically.

maximize U(C,S) = 4 C ^0.7 S ^0.5, subject top_cC + p_sS = I,where p_c = 8, p_s = 7, I (budget) = 50