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# The following table presents data on three leading indicators for a three-month period. Construct the composite index (with each indicator assigned...

7. The following table presents data on three leading indicators for a three-month period. Construct the composite index (with each indicator assigned equal weight) and the diffusion index.

Indicator A Indicator B Indicator C

1 100 200 30
2 110 230 27
3 120 240 33
Note:
1. Revised P7: Just construct the diffusion index. In this problem, we have 3 leading indicators. The diffusion index from month 1 to 2 is 66.7 (=2/3) because 2 indicators move up and 1 moves down.

1. The following table reports the Consumer Price Index for the Los Angeles area on a monthly basis from January 1998 to December 2000 (base year = 1982–1984). Eliminating the data for 2000, use Excel to forecast the index for all of 2000 using a three- and six-month average. Which provides a better forecast for 2000 using the data provided?

3. Forecast the data for 2000 again in Problem 1 with exponential smoothing with w = 0.3 and w = 0.7. Is this a better forecast than the moving average? Note: For appendix problem 3, please compare RMSEs for moving average and exponential smoothing forecasts to answer “Is this a better forecast than the moving average?”

4. Ms. Smith, the owner and manager of the Clear Duplicating Service located near a major university, is contemplating keeping her shop open after 4 p.m. and until midnight. In order to do so, she would have to hire additional workers. She estimates that the additional workers would generate the following total output (where each unit of output refers to 100 pages duplicated). If the price of each unit of output is \$10 and each worker hired must be paid \$40 per day, how many workers should Ms. Smith hire?
Workers hired 0 1 2 3 4 5 6
Total product 0 12 22 30 36 40 42

Note:
1. P4: Ms. Smith should hire workers as long as their Marginal Revenue Product (MRP) exceeds their Marginal Resource Cost (MRC), and until MRP=MRC.
MRP=MR x MP = P x MP = \$10 x MP (Use information in the problem to calculate MP)
MRC=wages=\$40.

12. Suppose that the production function for a commodity is given by
Q = 10√LK
where Q is the quantity of output, L is the quantity of labor, and K is the quantity of capital. (a) Indicate whether this production function exhibits constant, increasing, or decreasing returns to scale. (b) Does the production function exhibit diminishing returns? If so, when does the law of diminishing returns begin to operate? Could we ever get negative returns?
Notes:
2. P12(a): Calculate Q when L=1and K=1, and L=2 and K=2, then compare and answer the question about the returns to scale.
3. P12(b), Given K=1, show the change in Q if L changes from 1 to 2, and 2 to 3, and answer the question about diminishing returns.

3. Airway Express has an evening flight from Los Angeles to New York with an average of 80 passengers and a return flight the next afternoon with an average of 50 passengers. The plane makes no other trip. The charge for the plane remaining in New York overnight is \$1,200 and would be zero in Los Angeles. The airline is contemplating eliminating the night flight out of Los Angeles and replacing it with a morning flight. The estimated number of passengers is 70 in the morning flight and 50 in the return afternoon flight. The one-way ticket for any flight is \$200. The operating cost of the plane for each flight is \$11,000. The fixed costs for the plane are \$3,000 per day whether it flies or not. (a) Should the airline replace its night flight from Los Angeles with a morning flight? (b) Should the airline remain in business?
Note:
1. P3(a): Please calculate and compare the profit under each flight.
2. P3(b) is asking should Airway Express continue providing the flight between Los Angeles and New York? Even Airway Express decides not to fly, it still has to pay the fixed costs of \$3,000 per day. The evening flight with the return flight the next afternoon is counted as one day, not two days.

11. The Goldberg-Scheinman Publishing Company is publishing a new managerial economics text for which it has estimated the following total fixed and average variable costs:

Total fixed costs:
Copy editing \$ 10,000
Typesetting 70,000
Selling and promotion 20,000
Total fixed costs \$100,000

Average variable costs:
Printing and binding \$ 6
Sales commissions 1
Bookstore discounts 7
Author’s royalties 4
Average variable costs \$20
Project selling price \$30

(a) Determine the breakeven output and total sales revenues and draw the cost–volume–profit chart, and (b) determine the output that would generate a total profit of \$60,000 and the total sales revenues at that output level; draw the cost–volume–profit chart.

7. From Figure 9-4, determine the effect of a 33 percent import tariff on commodity X.
Note:
P7: The tariff-inclusive price will be \$3(1+.33) = \$4. What are the impacts of tariff on domestic consumption, domestic production, imports, and government’s tariff revenue? Please show the numbers, for example, the domestic consumption will decrease from 600X to 500X.
7. The following table presents data on three leading indicators for a three-month period. Construct the composite index (with each indicator assigned equal weight) and the diffusion index. Month Leading Leading Leading Indicator A Indicator B Indicator C 1 100 200 30 2 110 230 27 3 120 240 33 Note: 1. Revised P7: Just construct the diffusion index. In this problem, we have 3 leading indicators. The diffusion index from month 1 to 2 is 66.7 (=2/3) because 2 indicators move up and 1 moves down. 1. The following table reports the Consumer Price Index for the Los Angeles area on a monthly basis from January 1998 to December 2000 (base year = 1982–1984). Eliminating the data for 2000, use Excel to forecast the index for all of 2000 using a three- and six-month average. Which provides a better forecast for 2000 using the data provided? 3. Forecast the data for 2000 again in Problem 1 with exponential smoothing with w = 0.3 and w = 0.7. Is this a better forecast than the moving average? Note: For appendix problem 3, please compare RMSEs for moving average and exponential smoothing forecasts to answer “Is this a better forecast than the moving average?” 4. Ms. Smith, the owner and manager of the Clear Duplicating Service located near a major university, is contemplating keeping her shop open after 4 p.m. and until midnight. In order to do so, she would have to hire additional workers. She estimates that the additional workers would generate the following total output (where each unit of output refers to 100 pages duplicated). If the price of each unit of output is \$10 and each worker hired must be paid \$40 per day, how many workers should Ms. Smith hire? Workers hired 0 1 2 3 4 5 6 Total product 0 12 22 30 36 40 42
Note: 1. P4: Ms. Smith should hire workers as long as their Marginal Revenue Product (MRP) exceeds their Marginal Resource Cost (MRC), and until MRP=MRC. MRP=MR x MP = P x MP = \$10 x MP (Use information in the problem to calculate MP) MRC=wages=\$40. 12. Suppose that the production function for a commodity is given by Q = 10√LK where Q is the quantity of output, L is the quantity of labor, and K is the quantity of capital. (a) Indicate whether this production function exhibits constant, increasing, or decreasing returns to scale. (b) Does the production function exhibit diminishing returns? If so, when does the law of diminishing returns begin to operate? Could we ever get negative returns? Notes: 2. P12(a): Calculate Q when L=1and K=1, and L=2 and K=2, then compare and answer the question about the returns to scale. 3. P12(b), Given K=1, show the change in Q if L changes from 1 to 2, and 2 to 3, and answer the question about diminishing returns. 3. Airway Express has an evening flight from Los Angeles to New York with an average of 80 passengers and a return flight the next afternoon with an average of 50 passengers. The plane makes no other trip. The charge for the plane remaining in New York overnight is \$1,200 and would be zero in Los Angeles. The airline is contemplating eliminating the night flight out of Los Angeles and replacing it with a morning flight. The estimated number of passengers is 70 in the morning flight and 50 in the return afternoon flight. The one-way ticket for any flight is \$200. The operating cost of the plane for each flight is \$11,000. The fixed costs for the plane are \$3,000 per day whether it flies or not. (a) Should the airline replace its night flight from Los Angeles with a morning flight? (b) Should the airline remain in business? Note: 1. P3(a): Please calculate and compare the profit under each flight. 2. P3(b) is asking should Airway Express continue providing the flight between Los Angeles and New York? Even Airway Express decides not to fly, it still has to pay the fixed costs of \$3,000 per day. The evening flight with the return flight the next afternoon is counted as one day, not two days.
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