Problem 1:
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
|
1. Note: P7: The composite index is obtained by calculating the percentage change for each series relative to the base month and then averaging these percentage changes. The percentage change from the first to the second month is 10 for indicator A, 15 for indicator B, and -10 for indicator C. Their simple average (since each indicator is given equal weight) is 5 percent. Taking the first month as the base period with a composite index of 100, we obtain the composite index of 105 for the second month.The diffusion index from month 1 to 2 is 66.7 (=2/3) because two indicators move up and move down.
1. The following table reports the consumer price index for the LA area on monthly basis from Jan. 1998 to Dec. 2000 (base year= 1982-1984). Eliminating the data for 2000, use Excel to forecast the index.
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: Appendix problem 1:Delete "Eliminating the data for 2000." You need to calculate the moving average forecasts and RMSEs for year 2000, not the whole data period.
2. Campare RMSEs for moving average and exponential forecasts to answer "Is this a better forecast than the moving average?" Use 166.63, the mean of all 36 months, as the initial forecastfor Jan. 1998 for both exponential smoothing forecasts.
3. How is the law of diminishing returns reflected in the shape of the total product curve? What is the relationship between diminishing returns and the stages of production?
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 the minimum wage affects the employment of unskilled labor.
Problem 2:
Ms. Smith, the owner and manager of the clear duplicating service located near a major university, is contemplating keeping her shop open after 4pm and until midnight. In order to do, 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
|