Reference no: EM132576882
MFE 6050 Managerial Economics - Ohio University
Question 1:
Fill in the blanks in the following table to answer the question below.
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A
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TB
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TC
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NB
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MB
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MC
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0
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$0
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$
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$0
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|
|
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1
|
|
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27
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$35
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$
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2
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65
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|
|
|
|
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3
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85
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30
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|
|
|
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4
|
|
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51
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14
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5
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60
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8
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|
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6
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|
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5
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20
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a. What is the optimal level o activity in the table above?
b. What is the value of net benefit at the optimal level of activity? Can net benefit be increased by moving to any other level of A? Explain.
c. Using the numerical values in the table comment on the statement, "The optimal level of activity occurs where marginal benefit is closest to marginal cost."
Question 2:
Now suppose the decision maker in Technical Problem 6 faces a fixed cost of $24. Fill in the blanks in the following table to answer the questions below. AC is the average cost per unit of activity.
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A
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TB
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TC
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NB
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MB
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MC
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AC
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0
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$0
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$24
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1
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3
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$35
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$
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$32
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2
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65
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54
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10
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3
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85
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4
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27
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14
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5
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8
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16.80
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6
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5
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20
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a. How does adding $24 of fixed costs affect total cost? Net benefit?
b. How does adding $24 of fixed cost affect marginal cost?
c. Compared to A* in Technical Problem 6, does adding $24 of fixed cost change the optimal level of activity? Why or why not?
d. What advice can you give decision makers about the role of fixed costs in finding A*?
e. What level of activity minimizes average cost per unit of activity? Is this level also the optimal level of activity? Should it be? Explain.
f. Suppose a government agency requires payment of a one-time, nonrefundable license fee of $100 to engage in activity A, and this license fee was paid last month. What kind of cost is this? How does this cost affect the decision maker's choice of activity level now? Explain.
Question 3:
A decision maker is choosing the levels of two activities, A and B, so as to maximize total benefits under a given budget. The prices and marginal benefits of the last units of A and B are denoted PA, PB, MBA, and MBB.
a. If PA = $20, PB = $15, MBA = 400, and MBB = 600, what should the decision maker do?
b. If PA = $20, PB = $30 MBA = 200, and MBB = 300, what should the decision maker do?
c. If PA = $20, PB= $40 MBA= 300, and MBB= 400, how many units of A can be obtained if B is reduced by one unit? How much will benefits increase if this exchange is made?
d. If the substitution in part c continues to equilibrium and MBA falls to 250, what will MBB be?
Question 4:
Suppose a firm is considering two different activities, X and Y, which yield the total benefits presented in the schedule below. The price of X is $2 per unit, and the price of Y is $10 per unit.
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Level of activity
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Total benefit of activity X (TBX)
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Total benefit of activity Y(TBY)
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0
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$0
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$0
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1
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30
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100
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2
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54
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190
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3
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72
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270
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4
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84
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340
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5
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92
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400
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6
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98
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450
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a. The firm places a budget constraint of $26 on expenditures on activities Z and Y. What are the levels of X and Y that maximize total benefit subject to the budget constraint?
b. What is the total benefit associated with the optimal levels of X and Y in part a?
c. Now let the budget constraint increase to $58. What are the optimal levels of X and Y now? What is the total benefit when the budget constraint is $58?
Question 5:
A multiple regression model, R = a + bW + cX + dZ, is estimated by a computer package, which produces the following output:
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DEPENDENT VARIABLE: R
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R-Square
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F-Ratio
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P-Value on F
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Observation: 34
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0.3179
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4.660
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0.00865
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Variable
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Parameter Estimate
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Standard Error
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T-Ratio
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P-Value
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Intercept
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12.6
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8.34
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1.51
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0.1413
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W
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22.0
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3.61
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6.09
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0.0001
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X
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-4.1
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1.65
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-2.48
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0.0188
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Y
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16.3
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4.45
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3.66
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0.0010
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a. How many degrees of freedom does this regression analysis have?
b. What is the critical value of t at the 2 percent level of significance?
c. Test to see if the estimates of a, b, c, and d are statistically significant at the 2 percent significance level. What are the exact levels of significance for each of the parameter estimates?
d. How much of the total variation in R is explained by this regression equation? How much of the total variation in R s unexplained by this regression equation?
e. What is the critical value of the F-statistic at the 1 percent level of significance? Is the overall regression equation statistically significant at the 1 percent level of significance? What is the exact level of significance for the F-statistic?
f. If W equals 10, X equals 5, and Z equals 30, what value do you predict R will take? If W, X, and Z are all equal to 0?
Question 10.
Eighteen data points on M and X are used to estimate the quadratic regression model M = a + bX + cX2. A new variable, Z is created to transform the regression into a linear form. The computer output from this regression is
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DEPENDENT VARIABLE: M
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R-Square
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F-Ratio
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P-Value on F
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Observation: 18
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0.6713
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15.32
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0.0002
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Variable
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Parameter Estimate
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Standard Error
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T-Ratio
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P-Value
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Intercept
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290.0630
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53.991
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5.37
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0.0001
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X
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-5.8401
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2.1973
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-2.66
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0.0179
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Z
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0.07126
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0.01967
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3.62
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0.0025
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a. What is the variable Z equal to?
b. Write the estimated quadratic relation between M and X.
c. Test each of the three estimated parameters for statistical significance at the 2 percent level of significance. Show how you performed these tests and present the results.
d. Interpret the p-value for c.
e. What is the predicted value of M when X is 300?
Question 11.
Suppose Y is related to R and S in the following nonlinear way:
Y = aRbSc
a. How can this nonlinear equation be transformed into a linear form that can be analyzed by using multiple regression analysis?
Sixty-three observations are used to obtain the following regression results:
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DEPENDENT VARIABLE: LNY
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R-Square
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F-Ratio
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P-Value on F
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Observation: 63
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0.8151
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132.22
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0.0001
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Variable
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Parameter Estimate
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Standard Error
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T-Ratio
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P-Value
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Intercept
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-1.386
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0.83
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-1.67
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0.1002
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LNR
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0.452
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0.175
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2.58
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0.0123
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LNS
|
0.30
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0.098
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3.06
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0.0033
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b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?
c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value on the F-statistic.
d. How well does this nonlinear model fit the data?
e. Using the estimated value of the intercept, compute an estimate of a.
f. If R = 200 and S = 1,500, compute the expected value of Y.
g. What is the estimated elasticity of R? OF S?
Attachment:- Managerial Economics.rar