Explore BrainMass
Share

Explore BrainMass

    Managerial Economics: Appalachian Coal Mining, Vanguard Corp

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Can you help me get started with this assignment?

    Managerial Economics

    (1) Appalachian coal mining believes that it can increase labor productivity and, therefore, net revenues by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
    MC= 40P

    Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution the marginal increase in revenue ( MR) is

    MR= 1,000- 10p

    How much pollution reduction should Appalachian Coal Mining undertake?

    (2) Twenty first century electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week.

    Number of security guards-------------- Number of radios stolen per week

    0--------------------------------------50
    1---------------------------------------30
    2----------------------------------------20
    3----------------------------------------14
    4-----------------------------------------8
    5-----------------------------------------6

    (a) If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

    (b) If the cost of a stolen radio is $25, what is the most firm would be willing to pay to hire the first security guard?

    (c) If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?

    (3) The director of Marketing at Vanguard Corporation believes that sales of the company's bright side laundry detergent(s) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents ®. The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation:
    S= a + bA + cR

    Where S, A and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better.

    (a) What sign does the marketing director expect a, b, and c to have?
    (b) Interpret the coefficients a, b, and c.

    The regression output from the computer is as follows:

    Dependent Variable: S-------- R- Square F- Ratio p-Value on F
    OBSERVATIONS: 36 0.2247 4.781 0.0150

    PARAMETER STANDARD
    VARIABLE ESTIMATE ERROR T-RATIO P-VALUE
    INTERCEPT 175086.0 63821.0 2.74 0.0098
    A 0.8550 0.3250 2.63 0.0128
    R - 0.284 0.164 -1.73 0.0927

    (c) Does Vanguard's advertising expenditure have a statistically significant effect on the sales of bright side detergent? Explain, using the appropriate p-value.
    (d) Does advertising by its three largest rivals affect sales of bright side detergent in a statistically significant way? Explain, using the appropriate p-value
    (e) What fraction of the total variation in sale of bright side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?
    (f) What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditure for the three rivals are $100,000 per week?

    © BrainMass Inc. brainmass.com October 10, 2019, 12:29 am ad1c9bdddf
    https://brainmass.com/business/management-accounting/managerial-economics-appalachian-coal-mining-vanguard-corp-293958

    Solution Preview

    Please open attachment for solution.

    Thanks for using BrainMass. Have a good day.

    -------------
    Managerial Economics

    (1) Appalachian coal mining believes that it can increase labor productivity and, therefore, net revenues by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
    MC= 40P

    Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution the marginal increase in revenue ( MR) is

    MR= 1,000- 10p

    How much pollution reduction should Appalachian Coal Mining undertake?

    The installation of additional capital equipment will reduce the pollution and thereby increases the labor productivity. But we should take into account the additional cost of such activity. We should see to that the cost is not offsetting the benefit.
    Thus we should fix the level of pollution reduction in an optimal manner. This optimal value of P (Pollution reduction) is given by the following condition.
    Marginal Cost = Marginal Revenue
    In the given problem we have Marginal cost = MC = 40P
    and Marginal Revenue = MR = 1,000 - 10P
    Thus to get the optimal value we should have: MC = MR
    40P = 1,000 - 10P
    40P + 10P = 1,000
    50P = 1,000
    P = 1,000 / 50
    P = 20
    Thus the required unit of reduction in the pollution is 20 units.

    (2) Twenty first century ...

    Solution Summary

    This solution is comprised of detailed explanation for these managerial economics questions:

    (1) Appalachian coal mining believes that it can increase labor productivity and, therefore, net revenues by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
    MC= 40P

    Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution the marginal increase in revenue ( MR) is

    MR= 1,000- 10p

    How much pollution reduction should Appalachian Coal Mining undertake?

    (2) Twenty first century electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week.

    Number of security guards-------------- Number of radios stolen per week

    0--------------------------------------50
    1---------------------------------------30
    2----------------------------------------20
    3----------------------------------------14
    4-----------------------------------------8
    5-----------------------------------------6

    (a) If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

    (b) If the cost of a stolen radio is $25, what is the most firm would be willing to pay to hire the first security guard?

    (c) If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?

    (3) The director of Marketing at Vanguard Corporation believes that sales of the company's bright side laundry detergent(s) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents ®. The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation:
    S= a + bA + cR

    Where S, A and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better.

    (a) What sign does the marketing director expect a, b, and c to have?
    (b) Interpret the coefficients a, b, and c.

    The regression output from the computer is as follows:

    Dependent Variable: S-------- R- Square F- Ratio p-Value on F
    OBSERVATIONS: 36 0.2247 4.781 0.0150

    PARAMETER STANDARD
    VARIABLE ESTIMATE ERROR T-RATIO P-VALUE
    INTERCEPT 175086.0 63821.0 2.74 0.0098
    A 0.8550 0.3250 2.63 0.0128
    R - 0.284 0.164 -1.73 0.0927

    (c) Does Vanguard's advertising expenditure have a statistically significant effect on the sales of bright side detergent? Explain, using the appropriate p-value.
    (d) Does advertising by its three largest rivals affect sales of bright side detergent in a statistically significant way? Explain, using the appropriate p-value
    (e) What fraction of the total variation in sale of bright side remains unexplained? What can the marketing director do to increase the explanatory power of the sales equation? What other explanatory variables might be added to this equation?
    (f) What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditure for the three rivals are $100,000 per week?

    $2.19