CS 373 Quiz: CS 373 Binghamton Quiz6f03 sol post
15 Feb 2019
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Mathematical economics final, december 4, 2018: on r2, maximize 3x + y under the constraint x2 + y 9. Answer: the derivative of the constraint is (2x, 1), which has rank one, satisfying constraint quali cation. The lagrangian is l = 3x + y (x2 + y 9). This implies = 1 and x = 3/2. Using the constraint, we nd the solution is (x, y) = (3/2, 27/4). Lagrangian and evaluating at (3/2, 27/4) to obtain. Since there are two variables, this must have the same sign as ( 1)2 = +1, which it does. The second order conditions are satis ed: on r2. +, nd demand by maximizing the utility function u(x, y) = 3x e y subject to the constraints pxx + pyy m, x 0, y 0 where px, py, m > 0. Don"t forget to check constraint quali cation and the second order conditions. Answer: the derivative of the constraint equations is py px.
