I only need help on D, E,F and the next question A,B,C

You work for the manager of a small single-product rm. Assume that you have data for your rm on costs, capital rental rate, wages and output. You realize through regression analysis that the data ts very well the following equation: ln(C) : 1.18 + 0.33 1110) + 0.671n(w) + 0.811n(q) a. Determine the production function from which costs were derived. Explain whether it exhibits constant, increasing or decreasing returns to scale. b. From your answer in (a), determine whether your rm should explore the possi bility of expanding, knowing that the market is perfectly competitive. The market consists of a couple of large rms producing around 1,000,000 units each, multiple mediumsized rms producing 100,000 units each and a huge amount of small rms (yours included) producing around 10,000 units each. After running the same regression for both big and mediumsized rms you obtain the following: Mediumsized: ln(C') : 3.68 + 0.34 ln(r) + 0.66 ln(w) 1.051n(q) Large rms: ln(C) : 5.05 + 0.33 ln(r) + 0.67ln(w) 1.151n(q) c. Determine the production functions associated with Medium and Large rms respectively and comment on the returns to scale. (1. Explain why its very likely that you misspecied the production technology. To account for the possibility of having misspecied the production function, you run a more general regression using the data for all rms. The data ts the following equation: ln(C) : 1 + 0.33ln(r) + 0.67ln(w) + 0.3 ln(q) + 0.03[1n(q)]2 e. Assuming that 'w = 25 and r = 500, complete the following table (in excel): q ln(q) ln(C) C AC MC 1,000 2,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000 f. The cost of expanding is very low. Knowing that this market will very soon stabilize at the long-run equilibrium levels of perfectly competitive prices and out put. Decide on whether you would recommend your manager to go ahead with the expansion or not, and if so, by how much (in terms of output produced). NOTE: In order to answer these questions and give a recommendation you should understand the relation between the above regressions and the solution to the cost minimization problem when technoloy can be summarized by the following pro duction function: g = Azi'xg, where 9:1 and z; are the inputs used to produce output q. For more information about this you can refer to the following three videos: 'T'mm Production Technology to Total Cast\