You work for the manager of a small single-product firm. Assume that you have data for your firm on costs, capital rental rate, wages and output. You realize through regression analysis that the data fits very well the following equation: ln(C) = -1.18 + 0.33 ln(r) + 0.67 ln(w) + 0.81 ln(q) D. Explain why its very likely that you misspecified the production technology. To account for the possibility of having misspecified the production function, you run a more general regression using the data for all firms. The data fits the following equation: ln(C) = 1 + 0.33 ln(r) + 0.67 ln(w) + 0.3 ln(q) + 0.03[ln(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 output. 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).
Economics: Industrial Economics
Since only 3 questions allowed = Please Answer Parts D. - F. (and include answers to the NOTE PART: sub-questions a.; b.; c. In order to solve the Parts D. - F. questions). Thanks
QUESTION:
You work for the manager of a small single-product firm. Assume that you have data for your firm on costs, capital rental rate, wages and output. You realize through regression analysis that the data fits very well the following equation:
ln(C) = -1.18 + 0.33 ln(r) + 0.67 ln(w) + 0.81 ln(q)
D. Explain why its very likely that you misspecified the production technology.
To account for the possibility of having misspecified the production function, you run a more general regression using the data for all firms. The data fits the following equation:
ln(C) = 1 + 0.33 ln(r) + 0.67 ln(w) + 0.3 ln(q) + 0.03[ln(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
NOTE PART: 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 technology can be summarized by the following pro- duction function:
q = Axα1 xβ2 , where x1 and x2 are the inputs used to produce output q.
For more information about this you can refer to the following three videos: “From Production Technology to Total Cost”, “Cost Function Estimation” and “Scale Economies and Cost
a. Using the above production function, solve the cost minimization problem and obtain the cost function C(q). The cost function will also depend on technology parameters A, α, β and input prices w1, w2.
b. Graph AC(q), MC(q) and S ≡ AC(q)/MC(q) for the following cases:
- α + β > 1.
- 2. α + β = 1.
- 3. α + β < 1.
c. Plot the following relationships: ln(C) vs. ln(w1), ln(C) vs. ln(w2), ln(C) vs. ln(q). In each case determine how the slope of your plots depends on the values of α and β.
Thank you for your help and support Academic Agent!
PARTS A. - C. If needed for clarification
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 firm should explore the possibility of expanding, knowing that the market is perfectly competitive.
The market consists of a couple of large firms producing around 1,000,000 units each, multiple medium-sized firms producing 100,000 units each and a huge amount of small firms (yours included) producing around 10,000 units each.
After running the same regression for both big and medium-sized firms you obtain the following:
Medium-sized: ln(C) = -3.68 + 0.34 ln(r) + 0.66 ln(w) 1.05 ln(q)
Large firms: ln(C) = -5.05 + 0.33 ln(r) + 0.67 ln(w) 1.15 ln(q)
C. Determine the production functions associated with Medium and Large firms respectively and comment on the returns to scale.
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