BUSI 620
Answers for QCT 3
Salvatore’s chapter 6:
a. Discussion Questions:
1.
(a) Forecasting refers to the estimation of a variable, such as the sales of the firm, at some
future time. Forecasting is important to business firms, government, and not-for-profit
organizations as a method of reducing the risk and uncertainty inherent in most
managerial decisions.
(b) There are many different types of forecasting. Macro-forecasting estimates the future
level of general economic activity, while micro-forecasting estimates future industry and
firm sales and other economic variables. We have short-term forecasting (i.e., for a
quarter or a year) and long-term forecasting (for periods longer than a year).
Forecasting can be qualitative or quantitative. Forecasting can be based on examining only
past values of the data series to forecast its future values or on the use of complex models.
Some forecasts are performed by the firm itself, while others are purchased from
consulting firms.
(c) In order to determine the most suitable form of forecasting, the firm must consider the
cost of preparing the forecast and the benefit that results from its use, the lead time in
decision making, the time period of the forecast, the level of accuracy required, the
quality and availability of the data, and the level of complexity of the relationships to be
forecasted. In general, the greater the level of accuracy required and the more complex the
relationships to be forecasted, the more sophisticated and expensive will be the forecasting
exercise.
7.
(a) Exponential smoothing is generally better (i.e., gives more accurate forecasts) than
moving averages. The reason is that with exponential smoothing the researcher can
assign a larger weight to more recent values of the time series than to previous ones.
(b) To determine which of two smoothing techniques is better, we measure the root- mean-
square-error (RMSE) of each and choose the technique that minimizes the RMSE. The RMSE
is a weighted average of the forecast errors from the actual time series.
(c) If a time series contains not only a random variation but also a secular trend and a
seasonal variation, we must combine time-series analysis and smoothing techniques. One
way of doing this is to perform the time-series analysis first and then use a smoothing
technique.
A more complicated process that combines time-series analysis and a smoothing technique
in a single operation is the double exponential technique. This, however, is beyond the
scope of the text. The interested reader can be directed to the two books on this topic
indicated in the supplementary readings at the end of Chapter 5.
15. There are two reasons for it still being useful to pursue forecasting even though it is
often off the mark by wide margins. The first is that even if off the mark (often by wide
margins), it is still better to forecast than not to forecast. Firms need to have a forecast of
future sales to be able to forecast the need for all types of inputs. Without forecasts they
would simply have to guess. The second reason for forecasting is that by examining and
trying to improve on the forecasts, firms learn more about their operation and the market.
b. Problems:
7. Since two indicators rise and one falls from the first to the second period, the diffusion
index for the second period is 66.7 percent. On the other hand, since all three indicators
rise from the second to the third month, the diffusion index for the third month is 100
percent.
MonthComposite IndexDiffusion Index
1 100.00 --
2 105.00 66.70
3 113.33 100.00
Appendix problems
1. Since the three-month moving average RMSE = 1.27 and the six-month moving
average RMSE = 1.92 in forecasting year 2000, the three-month moving average is a
better forecaster.
3. Since the RMSE for the forecast with w = 0.7 is 0.95 which is less than that of 1.79 for
the forecast with w = 0.3, the w = 0.7 forecast is better. The forecast with w=0.7 is also
better than the three-month and six-month moving averages.
Salvatore’s chapter 7:
a.Discussion Questions:
3.
(a) The law of diminishing returns refers to the range over which the marginal product of
the variable input declines. This corresponds to the portion of the total product curve
from the point of inflection onward (i.e., from the point where the total product curve
begins to increase at a decreasing rate).
Diminishing returns continues to operate as the total product curve reaches its maximum
point (so that the marginal product of the variable input is zero) and when the total
product curve declines (so that the marginal product curve of the variable input is
negative).
(b) Diminishing returns operates over part of stage I for the variable input and in all of
stage II (where the marginal product of the variable input is declining but positive) and
stage III (where the marginal product of the variable input is declining but negative).
While not shown in Figure 7-3 in the text, stage I of the variable input corresponds to
stage III of the fixed input (where the marginal product resulting from using fractional
units of the variable input together with the constant quantity of the fixed input leads to
declining and negative marginal product for the fixed input).
Since in stage III for the variable input the MP of the variable input is negative and in stage
I of the variable input (which corresponds to stage III of the fixed input) the MP of the fixed
input is negative, the rational producer would only produce in stage II, where
the marginal products of both inputs are positive but declining.
11. Most workers in the United States earn more than the legislated minimum wage. Only
some unskilled low-wage labor is affected by a change in the minimum wage. An
increase in the minimum wage will lead firms to substitute capital (machines) for those
unskilled workers whose marginal revenue product falls below the new higher minimum
wage.
Thus, the benefit resulting from an increase in the minimum wage to those unskilled
workers who remain employed must be balanced against the loss of jobs of other
unskilled workers. The workers who lose their jobs need to be trained so that their marginal
revenue product increases sufficiently to make it profitable for firms to hire them.
12. The statement is false. To maximize profits a firm should hire any input as long as its
marginal revenue product exceeds the marginal cost of hiring the input, and until they are
equal. Assuming that the input price is constant, the condition for profit maximization
requires that the firm hire any input until its marginal revenue product equals its price.
According to marginal productivity theory, in order to hire the most qualified and productive
worker the firm must also pay a wage higher than for a less qualified and productive
worker. The firm will hire the most productive and qualified worker only if the ratio of the
marginal revenue product to the wage of the most qualified and
productive worker exceeds the ratio of the marginal revenue product to the wage of the
less qualified and productive worker.
b.Problems:
4. Ms. Smith should hire workers as long as their marginal revenue product (MRP) exceeds
their marginal resource cost (MRC), and until MRP = MRC. We can find the
MRP and MRC of labor by constructing a table analogous to Table 6-3 in the text. Since Ms.
Smith can hire additional workers at the given daily wage (w) of $40, RC = w = $40, the
firm's total profits will be maximum when it hires five workers at which MRP = MRC = $40.
Number of TPMPLMR=PMRPLMRCL=w
workers (L)
0 0 $10
1 12 12 10 $120 $40
2 22 10 10 100 40
3308108040
4366106040
5404104040
6422102040
12.
(a) The production function exhibits constant returns to scale because
when L = 1 and K = 1, Q = 10 1 =10; when L = 2 and K = 2, Q = 10 4 = 20; and when L =
3 and K = 3, Q = 30.
(b) The production function exhibits diminishing returns to capital and labor throughout.
For example, holding capital constant at K = 1 and increasing labor from L = 1 to L = 2
increases Q from 10 to 10 2 = 14.14. Therefore, MPL = 4.14. Increasing labor to L = 3
results in Q = 10 3 = 17.32, and MPL = 3.18 (i.e., the MPL declines).
13.
(a) False. A firm always produces in the area of diminishing returns in the short run (see
Figure 7-4 in the text).
(b) True. If economies of scale were present, larger and more efficient firms would drive
smaller firms out of business in the long run.
