A firm wants to maximize output subject to a budget constraint. The Lagrangian for this problem is given by:

Arm wants to maximize output subject to a budget constraint. The Lagrangian for this problem is given by: G=q(K,L)+/i(BrKwL) In this setup, q is the rm's production function, B is the xed budget the rm can spend on capital (K) and labor (L), and r, w are the prices of capital and labor respectively. a. Write out the rst order conditions for this optimization problem. b. Take the total derivatives of your three rst order conditions with respect to the rm's budget B. 53 . . . . . . 5L Express these total derivatives In matrix form such that your variable vector IS 5 E 53 c. Use Cramer's rule to derive an expression for %. d. Assuming that the second-order condition for output maximization is met, under what condition will % > 0