■ Definition: The engineering technique consists of developing the physical production function that exists between the inputs and the output and of attaching cost values to the inputs in order to obtain a total variable cost figure for each output level. For each output level we must therefore calculate, or test for, the amountqfeachofThe variable factors necessary to produce that output level. Attaching costs to these^ari- able inputs we can subsequently calculate the total variable cost for each output level and hence the average variable costs and marginal costs at each output level. Let us demonstrate this in the context of a hypothetical example.
Example: Suppose a metal-stamping plant has one large machine that can be operated at five different speeds up to a maximum speed of 100 revolutions per minute (rpm). On each revolution it stamps out one unit of the product, and hence output is proportional to the operating speed of the machine. However, the requirements of materials, labor, electric power, and repairs and maintenance need not be proportional to the operating speed of the machine. In Table 8-3 we show the relationships that have been found between the output and the inputs of the v ariable factors, using this machine at each of its five speeds. 5
By observing the various input components, you will notice that the ratio of materials used to output per hour increases as the operating speed of the machine is
Table captionTABLE 8-3. Physical Requirements of a Metal-Stamping Machine at Various Operating Speeds _ y __
|
Operating Speed (rpm>b |
Output per Hour^ (units) |
Materials Used (lb) |
Labor (hours) |
Power Requirements (kWh) |
R&M Requirements (units) |
|
20 , |
1,200 |
1,320 |
20 |
2,585 |
10 |
|
40 * L |
2,400 |
2,880 |
25 ; |
4,523 |
20 |
|
60 |
3,600 |
4,680 |
27, |
5,262 |
30 |
|
80 |
4,800 |
6,720 |
28 z. |
6,708 |
35 |
|
100 |
6,000 |
9,000 |
30 ^ |
10,954 |
60 |
|
8. o ° |
<°32-4" |
) ° |
Table caption“Throughout the regression analysis we required ceteris paribus to hold. Specifically, the prices of the input factors and the productivities of the factors must reasonably be expected to have remained constant over the period of data collection. The same costs and productivities must be expected to prevail over the prediction period as well.
Table captionThe figures at any output level should be regarded as the central tendency of the actually observed levels, since we should expect small day-to-day variations in material wastage, labor efficiency, and actual repairs and maintenance requirements.
increased, indicating increased wastage or spoilage as the machine is operated at faster speeds. Labor input, however, increases by different amounts as the operating speed is increased. It apparently requires twenty workers to operate the machine at its minimum speed, and the labor requirement increases at an irregular rate as the operating speed is increased, until at maximum speed thirty workers are required per hour of operation. Electric power requirements, measured in kilowatt-hours, increase rapidly at first, then more slowly, and then more rapidly again as maximum operating speed is attained. Repairs and maintenance requirements are indicated by an index of labor and materials necessary to maintain the machine in operating condition, and they evidently increase quite dramatically as the machine attains its maximum operating speed.
Suppose the variable inputs have the following costs per unit: Materials cost is $0.15 per pound; labor cost is $8.00 per hour; power cost is $0.0325 per kilowatt-hour; and repairs and maintenance cost is $10.00 per unit. With this information we can calculate the total variable cost of the output at various levels, as shown in Table 8-4. Dividing tot al va riable cost at each output level by that output level, we derive the average vari able c ost for e ach output level, and the marginal cost figures are derived by the gradient method and are in effect the average marginal costs over each 1,200- unit interval. Note that both average and marginal costs decline at first and later rise.
In Figure 8-7 we plot these average variable and marginal cost figures against the output level. Interpolating between these observations we are able to sketch in the average variable and marginal cost curves as indicated by the engineering technique. The production process appears to be most efficient in terms of the variable factors at about 4,600 units, where average variable cost appears to reach a minimum at something like $0.37 per unit. If the speed of the machine were infinitely variable, the firm might wish to operate at this output level by running the machine at approximately 77 rpm. If the firm wishes to maximize profits rather than simply minimize costs, it will seek the output level at which marginal revenues from the sale of these output units equal the marginal cost of producing the last unit of output. Note that by multiplying the scale on the horizontal axis in Figure 8-7 by the appropriate factor, the same cost curves will be applicable for output per day, per week, or for a longer period.
Incremental costs associated with any decision to increase or decrease output
Table captionTABLE 8-4. Costs Associated with Operating the Metal-Stamping Machine at Various
Table captionOutput Levels
|
Output |
Materials |
Labor |
Power |
R&M |
TVo V |
||
|
Levels |
Cost |
Cost |
Cost |
Cost |
TVC |
AVC |
MC |
|
(units) |
($) |
($) |
($) |
($) |
($) |
($) |
($) |
|
1,200 |
198 f |
160 |
84 t |
100 |
542 |
0.452 |
0 364 |
|
2,400 |
432 |
200 |
147 |
200 |
979 |
0.408 |
0 342 |
|
3,600 |
702 |
216 |
171 |
300 |
1,389 |
0.386 |
0 343 |
|
4,800 |
1,008 |
224 |
218 |
350 |
1,800 |
0.375 |
0 622 |
|
6,000 |
1,350 |
240 |
356 |
600 |
2,546 |
0.424 |
Table caption, /■»
330 Production and Cost Analysis
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