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? (Ms. Smith should hire workers as long as their marginal revenue product (MRP) exceeds their marginal resource cost (MRC), and until MRP=MRC. MRP=MRxMP=PxMP=$10xMP use the information in the problem to calculate MP) MRC=wages=$40.
12. Suppose that the production function for a commodity is given by Q = 10vLK
Where Q is the quantity of output, L is the quantity of labor, and K is the quantity of capital. (a) Calculate Q when L=1 and K=1, and L=2 and K=2, then indicate whether this production function exhibits constant, increasing, or decreasing returns to scale. (b) Given K=1, show the change in Q if L changes from 1 to 2, and 2 to 3, and 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?
7. The following table presents data on three leading indicators for a three-month period. Construct the diffusion index from month 2 to 3. This problem, we have three leading indicators. The diffusion index from month 1 to 2 is 66.7 (=2/3) because two indicators move up and one moves down (p.236).
| Month | Leading Indicator A | Leading Indicator B | Leading Indicator C |
| 1 | 100 | 200 | 30 |
| 2 | 110 | 230 | 27 |
| 3 | 120 | 240 | 33 |
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 = XXXXXXXXXXEliminating the data for 2000, use Excel to forecast the index for all of 2000 using a three month average 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. Compare RMSEs for moving average and exponential smoothing forecasts to answer if this is a better forecast than the moving average?