1. (25 points) Suppose that a perfectly competitive firm uses three inputs-l, k, and s with prices w, r, and v, respectively-sells its output at price p, and operates with a production function given by q (1, k, s) = 3(lk) 1/3 + In (s). a) (5 points) Write the expression for the firm's profits. What are the first-order conditions? Given an economic interpretation of the first-order conditions. b) (5 points) Check the second-order conditions. c) (10 points) Using implicit differentiation: i. Find the effect of a change in r on the optimal value of I. ii. Find the effect of a change in v on the optimal value of l. d) (5 points) Solve for the optimal value of I and explicitly differentiate it to confirm your results in part c)