Give me the answer for 36, 37, and 38

Manuel's bike company has the following production function, q = f (k, l) : Isl/4E1\". 33. Manuel rst solves his cost minimization problem. What is the Lagrangian for his costminimization problem? (a) : wl + vk + A(k1/4il'4 + q) (b) = wi + We + Mg Isl/411M) ANSWER (c) f. = Isl/45134 + /\\(wl + 'Uk C) (d) = k1/4l1/4 + MC wl wk) 34. What are his contingent demands for l and k? 35. What is his cost function? (a) C = 2q2vl/2w1/2 ANSWER (b) C = q + we (c) C : 2gw'1/2'v1/2 (d) C : 29-1/2 + um 36. What explains the shape of the cost function in quantity? (a) The cost function is convex in quantity because capital becomes fixed for high levels of output. (b) The cost function is convex in quantity because production is decreasing returns to scale. ANSWER (c) The cost function is concave in quantity because production is increasing returns to scale. (d) The cost function is concave in quantity because both inputs are required for any production. 37. Suppose that in the short-run Manuel's bike company has capital fixed to K = 16. What is his short-run contingent demand for labor? (a) L = q*/4w (b) L = q4/16 ANSWER (c) L = q2/4 -16/v (d) L = q2/2 -8 38. What is his short-run cost function? (a) C = 16v + wq4/16 ANSWER (b) C = q(w + 16v) (c) C = q(w4/4 + 16v) (d) C = 16(v + w)