2. A Comparative Statics Exercise. A firm produces output q using two inputs, labor, and raw materials. The labor cost of producing q units of output is c(q), where c(q) is a thrice differentiable, non- negative, strictly increasing, and strictly convex function with c(0) = 0. Each unit of output requires m units of material. The price of output is p. , and the cost of each unit of material is p.. Both prices are strictly positive. 28. Write down an expression for the firm's profit. What are the exogenous and endogenous variables in this problem? 20. Assuming the firm maximizes its profit, derive the first-order condition describing the firm's optimal choice of q. Let q" denote the solution to this first-order condition. You may assume that q* exists and is strictly positive. 2c. Are the second-order conditions for a maximum satisfied at q"? Explain why or why not? 2d. Noting the dependence of q' on the exogenous variables, rewrite the first-order condition in part bas an identity