ZANCATEX produces clothing, specifically men\'s shirts. This is one of many firm
ID: 3327147 • Letter: Z
Question
ZANCATEX produces clothing, specifically men's shirts. This is one of many firms that produce a homogeneous product, and none of them uses advertising to make their product known. By early December 2016, the manager of this firm must prepare the production plan for the first quarter of the following year. For this, it was necessary to first estimate the possible market prices of the shirts for that time. Accordingly, to these estimates, the firm could establish its production volume.
The marketing direction estimated three possible scenarios for the next quarter. These prices (per shirt) were: Scenario 1: $ 28; Scenario 2: $ 36; And, Scenario 3: $ 48. Using production information and costs, the company wants to estimate its average variable cost using the following quadratic specification
AVCt = a + bQt + cQ2t + errort
Trimester
AVC
Q
2014-3
$36.26
300
2014-4
37.33
100
2015-1
27.11
150
2015-2
26.89
250
2015-3
45.10
400
2015-4
31.34
200
2016-1
42.24
350
2016-2
55.13
450
2016-3
61.73
500
It is also known that the monthly total fixed cost (TFC) of ZANCATEX, Inc. amounts to $ 2,000 per month. It is also known that the market wage is $ 10 an hour.
A) Run a regression to estimate the average variable cost (CVA) function. Evaluate the statistical significance (p-values) of the three estimated parameters using a significance level of 5% [Present your results using the summary format used in the module 3 quiz]. Be sure to comment on the algebraic signs of the three parameter estimates [Hint: see help for this module].
B) Using the (estimated) AVC found in the first question1, calculate the total cost (TC), total variable cost (CVT), average total cost (ATC) and Zancatex short-term marginal cost (SMC). In the same table should compute the number of workers, the marginal product of labor (MP), and the average product of labor (AP). [Hint: Before doing these calculations order Q from least to greatest, and AVC (estimated) has to be aligned with your production level]
C) Present in a graph ATC (estimated), AVC (estimated) and SMC (estimated) [ATC (estimated) and SMC (estimated) are found in 2)]. Do they resemble the ATC, AVC, and SMC functions that the theory presents? [Remember that the production level (Q) is on the abscissa (X) axis and the other variables on the ordinate (Y) axis]
D) If Scenario 3 is met, should the firm produce or not? And if it produces, what level of production will it be? Also if the company produces, find its economic benefit. Use for your answer the production rule [And the table I use to make the graph in c)]
E) Assuming that we are in Scenario 2, present in a graph, the value of the marginal product (MRP) and the average value of the average (ARP). To find these variables, you must multiply the price of Scenario 2 by MP and AP, respectively. [Remember that the number of workers (L) goes on the abscissa axis (X) and the other variables on the ordinate (Y) axis].
F) If Scenario 2 is fulfilled, should the firm operate or not? And if it operates, how many workers should it hire? Use the recruitment rule for your answer. [And the table I use to make the graph in the]]
Trimester
AVC
Q
2014-3
$36.26
300
2014-4
37.33
100
2015-1
27.11
150
2015-2
26.89
250
2015-3
45.10
400
2015-4
31.34
200
2016-1
42.24
350
2016-2
55.13
450
2016-3
61.73
500
Explanation / Answer
If the production information increases by 1, we predict the average variable cost will decrease by approximately -0.14267.
B)
SUMMARY OUTPUT Regression Statistics Multiple R 0.968626 R Square 0.938236 Adjusted R Square 0.917648 Standard Error 3.463289 Observations 9 ANOVA df SS MS F Significance F Regression 2 1093.219 546.6095 45.57218 0.000236 Residual 6 71.96621 11.99437 Total 8 1165.185 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% a 44.47986 6.483626 6.860337 0.000472 28.615 60.34472 b -0.14267 0.048198 -2.96009 0.02528 -0.26061 -0.02473 c 0.000363 7.89E-05 4.592648 0.003721 0.000169 0.000556Related Questions
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