(30 points) Suppose that a perfectly competitive firm uses three inputs 1, k, and m with input prices w,r, and v, respectively, to produce output q, which it sells at price p. Its production function is given by: q = 12.5(lk) + In10m. 2 a) (10 points) Derive the first-order condition with respect to input m using the limit definition of the derivative. Hint: lim (1 + )" = lim(1 + nze + b) (10 points) Given that the optimal amount of all inputs is positive, check whether the second-order conditions hold. c) (10 points) Calculate the total differential of the first-order conditions to sign the effect of: 2 i) v on m*; ii v on k*; 111 r on m*; iv) r on k*