Suppose that your work force is becoming so specialized that you decide to apply some concepts you learned in college. The data in columns 1 and 2 of Table 1 relate production and various levels of labor inputs, holding other resources constant. This data represents the total product curve. Note that total product curves and production functions are not the same things. A production function allows all inputs to vary, while the total product curve assumes that only one input changes. We are using labor as the variable input, but had we held labor constant and varied capital (or land), the analysis would be quite similar, although the specific curves would differ.

 

Table 1 Total Output and the Average and Marginal Physical Products of Labor (Sand and Gravel Operation)

(1) LABOR Workers per 8-hr. Shift      (L)	(2) OUTPUT Tons of Sand and Gravel Removed Daily           (q)	(3) APPL Average Physical Product of Labor            (q/L)	(4) MPPL Marginal Physical Product of Labor (Dq/DL)
0	0	0	0
1	10	10.00	10
2	22	11.00	12
3	36	12.00	14
4	52	13.00	16
5	70	14.00	18
6	86	14.33	16
7	100	14.28	14
8	112	14.00	12
9	122	13.55	10
10	130	13.00	8
11	137	12.45	7
12	143	11.92	6
13	148	11.38	5
14	152	10.85	4
15	155	10.33	3
16	157	9.81	2
17	158	9.29	1
18	158	8.78	0
19	157	8.26	-1

Table 2           Total Output, Total Costs, and Fixed and Variable Costs (Sand and Gravel Example)

 

(1)     Workers per 8-hr Shift (L)	(2)   Tons of Sand & Gravel Removed Daily (q)	(3)   Wages per worker ($) (8 hrs. Daily) (w)	(4) Total Variable Cost ($) (w x L) (TVC)	(5)     Total Fixed Cost ($) (TFC)	(6)       Total Costs ($) (TVC+TFC=TC)
0	0	50	0	100	100
1	10	50	50	100	150
2	22	50	100	100	200
3	36	50	150	100	250
4	52	50	200	100	300
5	70	50	250	100	350
6	86	50	300	100	400
7	100	50	350	100	450
8	112	50	400	100	500
9	122	50	450	100	550
10	130	50	500	100	600
11	137	50	550	100	650
12	143	50	600	100	700
13	148	50	650	100	750
14	152	50	700	100	800
15	155	50	750	100	850
16	157	50	800	100	900
17	158	50	850	100	950
18	158	50	900	100	1000
19	157	50	950	100	1050

 

            If you know total output for each level of labor hired (columns 1 and 2), output per worker is calculated by dividing total output (q) by labor (L).

The average physical product of labor (APPL) equals total output divided by labor (q/L).

These figures are entered in column 3 of the table. You will also want to know how much each extra worker adds to total output.

 

The marginal physical product of labor (MPPL) is the additional output produced by an additional unit of labor   -   computed by dividing the change in total output (Dq) by the change in labor (DL): Dq/DL.

 

            Hiring decisions intended to maximize profit hinge on labor's marginal physical product. Extra workers will not be hired unless the extra revenue from their marginal physical products would exceed the extra costs of hiring them. Only workers generating at least as much revenue as it costs to hire them will be employed. In most cases, each worker's productivity (the MPPL) will be higher as the amounts of other resources used rise---a worker operating a bulldozer on a dry riverbed will produce more sand and gravel than a shovel wielder digging on a city lot.

 

            The MPPL is calculated by looking at small changes in labor hired and the resulting changes in output. With large numbers of workers (as at a steel mill), a given change in the amount of labor (DL) is divided into the resulting change in output (Dq) to approximate the MPPL. One worker = DL for a small firm like your operation.  Labor's marginal physical products (Dq/DL) for your firm are listed in column 4 of Table 1.

 

            The total product curve graphed in Panel A of Figure 1 (from columns 1 and 2 of Table 1) for your sand-and-gravel operation relates production and various levels of labor inputs, holding other resources constant. Panel B shows the corresponding marginal and average physical products of labor.

As more and more labor is employed, total output (Panel A) initially rises at an increasing rate because of gains from specialization. In this range, the marginal and average physical products of labor both grow (Panel B). As congestion begins to emerge, total output continues to grow, but at a falling rate. In this range, average physical product continues to climb, but marginal productivity diminishes. Once marginal physical product falls below average physical product, average physical product begins to fall. However, total output continues to rise until the marginal physical product is zero. This occurs when congestion or other problems are so severe that further labor inputs cause output to fall.