Ch6 DQ.2(a). What are qualitative forecasts? What are the most important forms of qualitative forecasts? Qualitative forecasts are used as supplements for quantitative forecasts when the future conditions of consumer tastes or business expectation changes are anticipated and when quantitative forecast data is not available. Qualitative forecasts are invaluable when forecasting demand for a product that the firm intends to introduce in the market. The most important forms of qualitative forecasts are survey techniques and opinions polls. Both these qualitative forecasts techniques helps to plan on the demand of aproducts for consumers and help plan on expenditure for expansion of the firm.
Ch6 DQ.2(b). What is the rationale and usefulness? The survey techniques helps to determine the future of a product or service based on the information provided by the consumers in the survey and the economic activities of the business can be planned based on the results from survey for the companies expenditure on its expansion or other production plans. In case of opinion polling, it helps to determine potential buyers and their requirements and this can help firms to forecast its product demands and improvement of options that will have to be added for customers to buy the goods.
Ch6 DQ.3(a). What are time-series data? What are the possible sources of variation in time-series data? Time-series data is the values of a variable arranged chronologically by days, weeks, months, quarters or years. The time-series analysis attempts to forecast future values of the time series by examining the past observations of the data only. The possible sources of variations are secular trend, cyclical fluctuations, seasonal variations and irregular influences. The trends variation refers to long-run increase or decrease in the data series. Cyclical fluctuations variation are the major expansion and contractions in most economic time series that seems to recur every several years. Seasonal variations refers to the regularly recurring fluctuations in economic activity during each year because of weather or social customs. Irregular or random influences are the variations in the data series resulting from wars, natural disasters, strikes or other unique events.
Ch6 DQ. 3(d). Why does time-series analysis deal primarily with trend and seasonal variations rather than with cyclical and irregular or random variations? In case of irregular or random variations, time-series data various only during unique situations and planning based on unique occurrences will not help for good planning, similarly in case of cyclical variations the changes occur for periods of time, in which case it will not be easy to determine when the expansion or contraction will occur and planning for this kind of fluctuations is difficult. But in case of seasonal variations it is a pattern of occurrence every year or season and in case of trend variations the changes happen with increase in population and increase in per capita spending ability of the population which is predictable. So using seasonal and trend variations of time-series data analysis helps easy planning of the business or production of the firm.
Ch6 DQ.15. Explain why it is still useful to pursue forecasting even though it is often off mark by wide margins. Forecasts helps to estimate approximate needs of the consumers as well as other businesses, so the firms that are using forecasting method can plan accordingly for its development, sales or expansion plans. Experienced manager and stakeholders will be able to analyze the demands using forecasting concurrently with the seasonal and trend variations of time-series analysis to determine the short- and long-term demands of the market and plan to some extent of expansion of the business or production of the firm. Forecasting helps firm to have a plan for future so the business can avoid any sudden surprises or decline in sales of the product and helps to determine if the line of product is still marketable or it has to be changed for the survival of the firm.
Ch6 P.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 Indicator A | Leading Indicator B | Leading Indicator C | 1 | 100 | 200 | 30 | 2 | 110 | 230 | 27 | 3 | 120 | 240 | 33 |
The composite index is obtained by calculating the percentage for each series relative to the base month and averaging these percentages changes. In this case month 1 is considered as base month for calculations.
For indicator A percentage change in month 2 = (110-100) / 100 = 10 %, for month 3 = (120 – 100) / 100 = 20 %.
For indicator B percentage change in month 2 = (230 – 200) / 200 = 15%, for month 3 = (240 – 200) / 200 = 20%.
For indicator C percentage change in month 2 = (27 – 30) / 30 = -10 %, for month 3 = (33-30) / 30 = 10%.
Average for month 2 for all indicators = (10+15-10) / 3 = 5%. The composite index for the base period (1st month) is 100, so adding the 5% average from second month will lead to 105% of composite index.
Average of month 3 for all indicator = (20 + 20 +10) / 3 = 16.67%. So adding 16.67% to 100 gives 116.67% composite index for month 3.
Diffusion index is the percentage of leading indicators that are increasing considering all the leading indicators that are changing in the firm. Diffusion index for month 2 is 2/3 of 100 because in month 2, two of the three indicators have increased and one has decreased, so the diffusion index is 66.67, and in case of month 3 all three indicators have increased so the diffusion index will 100 again.
Ch6 AP. 1. The following table reports the consumer price index for the Los Angles 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 three- and six-month average. Which provides a better forecast for 2000 using the data provided? Time | CPI | 3-month MAF | A-F | (A-F)^2 | 6-month MAF | A-F | (A-F)^2 | Jan-00 | 167.9 | 167.2 | 0.7 | 0.49 | 166.82 | 1.08 | 1.17 | Feb-00 | 169.3 | 167.4 | 1.87 | 3.48 | 167.17 | 2.13 | 4.55 | Mar-00 | 170.7 | 168.2 | 2.53 | 6.42 | 167.67 | 3.03 | 9.2 | Apr-00 | 170.6 | 169.3 | 1.3 | 1.69 | 168.25 | 2.35 | 5.52 | May-00 | 171.1 | 170.2 | 0.9 | 0.81 | 168.82 | 2.28 | 5.21 | Jun-00 | 171 | 170.8 | 0.2 | 0.04 | 169.48 | 1.52 | 2.3 | Jul-00 | 171.7 | 170.9 | 0.8 | 0.64 | 170.1 | 1.6 | 2.56 | Aug-00 | 172.2 | 171.3 | 0.93 | 0.87 | 170.73 | 1.47 | 2.15 | Sep-00 | 173.3 | 171.6 | 1.67 | 2.78 | 171.22 | 2.08 | 4.34 | Oct-00 | 173.8 | 172.4 | 1.4 | 1.96 | 171.65 | 2.15 | 4.62 | Nov-00 | 173.5 | 173.1 | 0.4 | 0.16 | 172.18 | 1.32 | 1.73 | Dec-00 | 173.5 | 173.5 | -0.03 | 0 | 172.58 | 0.92 | 0.84 | | | | MSE | 1.61 | | MSE | 3.68 | | | | RMSE | 1.27 | | RMSE | 1.92 |

Above is the calculated values of 3 month average and 6 month average using consumer price index for Los Angles area on monthly basis from January 1998 to December 2000. Based on the calculated results the RMSE of 3 month average is 1.27 and for 6 month is 1.92 and the 3 month average provides better forecast because the forecasts are better when the RMSE value is closer to 1 and in this case 6 month average is higher than 3 month average. So comparing between the 3 month and 6 month average, 3 month average provides better forecasts.
Ch6 AP.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? Time | CPI | forecast(w=0.3) | (A-F)^2 | forecast(w=0.7) | (A-F)^2 | Jan-00 | 167.9 | 166.85 | 1.1 | 167.24 | 0.44 | Feb-00 | 169.3 | 167.17 | 4.55 | 167.7 | 2.55 | Mar-00 | 170.7 | 167.81 | 8.37 | 168.82 | 3.53 | Apr-00 | 170.6 | 168.67 | 3.71 | 170.14 | 0.22 | May-00 | 171.1 | 169.25 | 3.41 | 170.46 | 0.41 | Jun-00 | 171 | 169.81 | 1.42 | 170.91 | 0.01 | Jul-00 | 171.7 | 170.16 | 2.36 | 170.97 | 0.53 | Aug-00 | 172.2 | 170.63 | 2.48 | 171.48 | 0.52 | Sep-00 | 173.3 | 171.1 | 4.85 | 171.98 | 1.73 | Oct-00 | 173.8 | 171.76 | 4.17 | 172.91 | 0.8 | Nov-00 | 173.5 | 172.37 | 1.28 | 173.53 | 0 | Dec-00 | 173.5 | 172.71 | 0.62 | 173.51 | 0 | | | MSE | 3.19 | MSE | 0.89 | | | RMSE | 1.79 | RMSE | 0.95 |

In this case the RMSE for weight of 0.3 is 1.79 and for a weight of 0.7 is 0.95. So the weight of 0.7 is the best of all four forecasts because its RMSE is close to 1, the next best will be 3 month average with RMSE of 1.27, then the weight smoothing average of 0.7 which has the RMSE of 1.79 and finally the 6 month average which has an RMSE of 1.92.
Ch7 DQ.3(a). How is the law of diminishing returns reflected in the shape of the total product curve? In the total product curve (TP), the increase in productivity is higher until the marginal product labor curve reaches the point where diminishing returns starts where it (MPL) starts to decline. After the MPL starts to decline the TP curve still increases but at a negative rate of increase and at a point where the MPL becomes negative the TP curves starts to decline. The point at which MPL and average product labor (APL) curve meets is where the idle production conditions starts and that is where the TP curve shows the idle products to be produced by the firm. So the total product declines after a point even with increased variable input of the firm after a point of diminishing returns.
Ch7 DQ.3(b). What is the relationship between diminishing returns and the stages of production? The ideal option for an organization to operate would be to be in the stage II of production based on the law of diminishing returns. In stage I the capital cost are much higher and production would be less and in case of stage III as well the labor cost are at higher rate with decreased total product and marginal products because of the less availability of fixed resources and over availability of variable resources. So after a certain point we get diminishing returns in production by using more and more variable input with available fixed inputs. So in stage I the production returns are higher, in stage II the production returns starts to decline and in stage III the production returns turns be negative and it is not worth to produce in stage III. The idle stage of production is stage two where the curves are operating at minimal levels of diminishing returns.
Ch7 DQ.11. Minimum wage legislation requires most firms to pay workers no less than the legislated minimum wage per hour. Using marginal productivity theory, explain how a change in minimum wage affects the employment of unskilled labor. An increase in minimum wage leads to the expectation of increased productivity based on marginal productivity theory. So for increased productivity the firms would need skilled labor to yield more output and products which leads to job lose for unskilled labor because the companies are expecting more productivity due to increase in wages and unskilled labor do not posses the ability to increase the productivity. As long as productivity increases with increase in minimum wage it would be good for labor but if the productivity does not increase it will eventually lead to job loses and hiring of skilled labor.
Ch7 DQ.13. Does the production function of table 7-1 show constant, increasing, or decreasing returns to scale if the firm increases the quantity of labor and capital used from (a) 2L and 2K to 4L and 4K? (b) 2L and 4K to 3L and 6K? In case of increasing from 2L and 2K to 4L and 4K, it is an increase of 100% of input both in labor and capital. The productivity output at 2L and 2K is 18 units and that of 4L and 4K is 40 units. The percentage of increase in units is 122 % because and increase of 22 units from 18 units give a 122 percent increase from 2L and 2K to 4L and 4K level of input. So in this case it is an increase in return of scale because 100% increase in input provides a 122% increase in productivity. In case of increasing from 2L and 4K to 3L and 6K, it is an increase of 50% of input both in labor and capital. The productivity output at 2L and 4K is 28 units and that of 3L and 6K is 31 units. The percentage increase in units is 11% because and increase of 3 units from 28 units provide 11 percent increase from 2L and 3K to 3L and 6K level of input. So in this case it is a decrease in return of scale because 50% increase in input provides only 11% increase in productivity.
Ch7 P.4. Ms. Smith, the owner and manger of the Clear Duplicating Services 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 |

Ms. Smith has to hire 5 workers because at 6 workers the marginal cost is more than the marginal revenue. Until 4 worker the marginal revenue is higher than marginal cost of the payment for the workers based on $10 for each unit of output and at hiring 5 workers the marginal revenue is equal to marginal cost and beyond that point Ms. Smith would incur loses. Below is the table that shows the marginal cost and revenue for addition of each worker. Workers Hired | Total Product | Marginal Product | Marginal Revenue | Marginal Cost | 0 | 0 | - | - | - | 1 | 12 | 12 | 120 | 40 | 2 | 22 | 10 | 100 | 40 | 3 | 30 | 8 | 80 | 40 | 4 | 36 | 6 | 60 | 40 | 5 | 40 | 4 | 40 | 40 | 6 | 42 | 2 | 20 | 40 |

Ch7 P.10. John Wilson, the owner of a fast-food restaurant, estimated that he can sell 1,000 additional hamburgers per day by renting more automated equipment at a cost of $100 per day. Alternatively, he estimated that he could sell and extra 1,200 hamburgers per day by keeping the restaurant open for two more hours per day at a cost of $50 per hour. Which of these two alternative ways of increasing output should Mr. Wilson use? In both the cases the marginal cost for Mr. Wilson is $100 but in case of opening the store for extra two hour, the sales is 200 units more compared to that of renting more automated equipments. So the best way of increasing output for Mr. Wilson will be to open the store for two more hours and pay $100 of marginal cost.
Ch7 P.13. Indicate whether each of the following statements is true or false and give the reason. (a) A firm should stop expanding output after reaching diminishing returns and (b) if large and small firms operate in the same industry, we must have constant return to scale.
(a) False, because after reaching the point of diminishing returns the company still could produce more units but after certain point it starts to decline even with increased variable inputs. So the firm can still continue to expand to some extent even after reaching diminishing return point and operate in stage II of production based on law of diminishing returns.
(b) True, because total products and cost of both large and small firms will be similar so there will be a constant return to scale, so the size of the firms does not matter. Larger firms will have to be more efficient to drive out the smaller firms.