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Make sure you show ALL your work and explain where asked. Groups who do not provide explanations or simply provide final answers will not receive credit for that question. See the assignment handout...

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Make sure you show ALL your work and explain where asked. Groups who do not provide explanations or simply provide final answers will not receive credit for that question. See the assignment handout for more information.
Groups should answer the following questions:
  1. (13 points) The following table shows the number of calculators that can be assembled per week by various numbers of workers.
Quantity of Number of Calculators Average Marginal
Labor Per Week Product Product
0 0 -- --
1 60
2 160 100
3 80
4 280
5 60

a. (5) Fill in the missing numbers in the table. Show all your calculations.
b. (8) Identify the level of output above where the firm is in Stage II of production. Why will the rational producer never operate in Stages I or III? Explain your answers well.
2. (39 points) Using linear regression and 24 months of data, a firm estimated its demand function for its Good A and achieved the following results:
QA = 445 – 6.5PA + 0.75PB + 1.85Y
(1.4) (0.35) (0.95) (standard errors)
_
R2 = 0.81 R2 = 0.782 F = 28.42 SEE = 5.25
where QA = quantity sold per month of good A, in units
PA = price of good A, in US$
PB = price of good B, in US$

Y = average income, in thousands US$


a. (5) Interpret the estimated coefficients of PA, Y and PB. In other words, how much a one unit change in each variable influence sales of Good A? Be specific (use numbers).
b. (5) Evaluate the overall explanatory power of the regression model. Use a 0.05 level of significance. State all your hypotheses and explain your results. Do not use rules of thumb.
c. (10) Which of the independent variables, if any, appear to be statistically significant at the 0.05 level in explaining sales? State all your hypotheses and explain your results. Do not use rules of thumb.
d. (8) At present, the price of Good A is $40, the price of Good B is $65, and average income is $40,000 (be careful of units used in the equation for this variable!). Calculate the price, cross-price, and income elasticities of demand at present. Interpret each elasticity and say what each tells you about how much a 1% change in each impacts the quantity demanded in percent.
e. (3) What proportion of the total variation in sales is explained by the independent variables in this regression equation? Is the answer influenced significantly by the size of n relative to k? Explain.
f. (8) Derive a 95% confidence interval for current sales at the present values of each variable given in part D. Do not use rules of thumb.
Answered Same Day Dec 22, 2021

Solution

David answered on Dec 22 2021
131 Votes
Make sure you show ALL your work and explain where asked
ECO-6655: Application Problem Set #2, T4-13
Dr. Dominic F. Minadeo
Make sure you show ALL your work and explain where asked. Groups who do not provide explanations or simply provide final answers will not receive credit for that question. See the assignment handout for more information.
Groups should answer the following questions:
1. (13 points) The following table shows the number of calculators that can be assembled per week by various numbers of workers.
    Quantity of
    Number of Calculators
    Average
    Marginal
    Labo
    Per Week
    Product
    Product
    0
    0
    --
    --
    1
    
    60
    
    2
    160
    
    100
    3
    
    
    80
    4
    280
    
    
    5
    
    60
    
a. (5) Fill in the missing numbers in the table. Show all your calculations.
Answer:
    Quantity of Labo
    Number of Calculations per week
    Average product
    Marginal product
    0
    0
    Â 
    Â 
    1
    =Average product*Quantity of labor = 60*1 = 60 
    60
    =Calculators when there is only one labor unit – calculators when there zero labor unit = 60-0 = 60 
    2
    160
    =total calculators/quantity of labor = 160/2 = 80 
    100
    3
    Â =160+80 = 240
    Â =total calculators/Quantity of labor = 240/3 = 80
    80
    4
    280
    =total calculators/quantity of labor = 280/4 =70
    =Calculators when there are four labor units – calculators when there are three labor units = 280-240 = 40
    5
    =Average product*Quantity of labor = 60*5 = 300
    60
    =Calculators when there are five labor units – calculators when there are four labor units = 300-280 = 20
. (8) Identify the level of output above where the firm is in Stage II of production. Why will the rational producer never operate in Stages I or III? Explain your answers well.
Answer:
From the table above, we note that marginal product of labor is falling between output level 160 and 300. So firm is in Stage II of production in this output range.
In the Stage I of production, total output increases at increasing rate while in the Stage II of production, total output increases at decreasing rate. A firm which is in the first stage knows that it can increase its production by moving to stage two. Therefore a rational firm will not operate in first stage and move to second stage of production.
In the Stage III of production, total output starts falling. So a firm will not operate in this stage as well.
Thus we conclude that a firm will never operate in Stage I and Stage III.
2.
(39 points) Using linear regression and 24 months...
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