## Monday, February 05, 2007

### Example With Heterogeneous Labor (Part 2 of 3)

3.0 Quantity Flows
The example is constructed by comparing constant prices associated with stationary states for producing the net output of a bushel corn. Four stationary states are possible, or linear combinations of them. Each of the four pure stationary states corresponds to a choice of one of the techniques. Table 4 shows the quantity flows for a stationary state in which the alpha technique is used. The quantity flows for the stationary states in which the other techniques are used are shown in Appendix B.
 Inputs Steel Industry Corn Industry Category 1 Labor (1/379) Person-Year (350/379) Person-Year Category 2 Labor (100/379) Person-Years (400/379) Person-Years Steel 0 Ton (100/379) Ton Corn (71/379) Bushel (50/379) Bushel Outputs (100/379) Tons Steel (500/379) Bushels Corn
Notice that the steel used up as an input in the stationary state shown in Table 4 is exactly replaced by the output of the steel industry. After replacing the corn used up as inputs in the two industries, the net output of this stationary state is one bushel corn. And (500/379) person-years of category 2 labor are used to produce this net output. Thus, for the alpha technique, the category 2 labor intensity of corn output is (500/379) person-years per bushel, as shown in Figure 1. The category 2 labor intensities for the other techniques can easily be calculated from the Tables in the appendix.
 Figure 1: Technique By Category 2 Labor Intensity
Appendix B
 Inputs Steel Industry Corn Industry Category 1 Labor (1/929) Person-Year (1,000/929) Person-Years Category 2 Labor (100/929) Person-Year (1,000/929) Person-Years Steel 0 Ton (100/929) Ton Corn (71/929) Bushel 0 Bushel Outputs (100/929) Tons Steel (1,000/929) Bushels Corn

 Inputs Steel Industry Corn Industry Category 1 Labor (33/349) Person-Year (350/349) Person-Years Category 2 Labor (60/349) Person-Year (350/349) Person-Years Steel (15/349) Ton (35/349) Ton Corn (1/349) Bushel 0 Bushel Outputs (50/349) Tons Steel (350/349) Bushels Corn

 Inputs Steel Industry Corn Industry Category 1 Labor (66/313) Person-Years (245/313) Person-Years Category 2 Labor (120/313) Person-Years (280/313) Person-Years Steel (30/313) Ton (70/313) Tons Corn (2/313) Bushel (35/313) Bushel Outputs (100/313) Tons Steel (350/313) Bushels Corn