3. For each of the following production functions, graph the total (TPL), average ( APL), and marginal (MPL) products of labor. Your 'PL curve should be on a separate graph than your APL and MPI curves. Also say whether each function is Cobb-Douglas, Perfect Complements, Perfect Substitutes, Quasi-Linear, or other. (a) f(L, K) = ming L, 2K), with K fixed at 2. (b) f ( L, K ) = 24+ K2, with K fixed at 9. (c) f(L, K) = L2 + 4KL, with K fixed at 2. (d) f (L, K) = LIK?, with K fixed at 9. (e) f(L, K) = K + 2L, with K fixed at 2. 4. Consider the production of widgets, which are produced using labor (L) and captial (K). The production function for widgets is given by: q = f(L, K) = 3LIK3 The wage rate is $10 and the rental rate is $40. (a) What are the cost-minimizing values of * and A * consistent with an output level of 300? (b) What are the short-run values of L and A consistent with a temporary increase in output to 600? (c) Show your solutions to (a) and (b) graphically. Include the relevant isoquants, isocosts, and input bundles. Include the production expansion path. (d) Derive a short-run cost function (C as a function of q). 5. Consider the production of gadgets, which are produced using labor (L) and captial (K). The production function for gadgets is given by: q = f ( L, K ) = 7- I + 6K The wage rate is $8 and the rental rate is $2. (a) What is the lowest possible cost associated with producing 60 units of output