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BSNS 6130 Regression Project

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Question:

Suppose that you are the manager of Rockford Enterprises in a competitive market. You are asked to estimate the average variable cost (AVC) function for the firm. Based upon the estimated AVC, you can obtain the predicted values of AVC and SMC. You should decide i) whether to produce output or go out of business; and, ii) if you decided to produce output, how many units of output you would produce. Currently, the market price is given at $50.
You have already paid the total fixed cost (TFC) of $2,000.
1. The following table shows the output-cost data of Rockford Enterprises (see p. 377 in the textbook).Table 1: Output and Deflated Average Variable Cost ($)
Quarter Output Deflated AVC ($)
2012-II 300 36.26
2012-III 100 37.33
2012-IV 150 27.10
2013-I 250 26.89
2013-II 400 45.10
2013-III 200 31.34
2013-IV 350 42.24
2014-I 450 55.13
2014-II 500 61.73
You are asked to estimate the following AVC function:AV C = a + bQ + cQ2

(a) Using the data above, estimate the coefficients of AVC, a, b, and c, in MS Excel,and check if you obtain the same regression result as that on the p. 377 of the textbook. Submit the printout of your own regression table.
(b) Check if the estimated coefficients of AVC, ˆa,ˆb and ˆc, are statistically significant at the 5% level, using the p-values shown in your regression tables. Explain why or why not.

2. Using the estimated coefficients of AVC above, implement the profit-maximizing output decision for the firm. Refer to Chapter 11.6 of the textbook. When you know the estimated coefficients of AVC, you can obtain the predicted values of AVC and SMC as:
AV Cˆ = ˆa + ˆbQ + ˆcQ2 .
SMCˆ = ˆa + 2ˆbQ + 3ˆcQ2

(a) Determine whether the rm should shut down or not, and explain why or why not.
(b) Suppose that you decided to produce output in the short run. Find the firms profit-maximizing output level. (Note: You can use the online quadratic equation calculator to solve a quadratic equation for Q. Refer to the following website.)
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