Tuesday , June 18 2024
Home / Post-Keynesian / Wages, Employment Not Determined By Supply And Demand

Wages, Employment Not Determined By Supply And Demand

Summary:
1.0 Introduction I do not think I have presented an introductory example in a while in which an increased wage is associated with firms wanting to employ more labor, given the level of net output. This example is presented as a matter of accounting for a vertically integrated firm. Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this, they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats. 2.0 Technology The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1. Corn is a consumption good and also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron,

Topics:
Robert Vienneau considers the following as important: , ,

This could be interesting, too:

Robert Vienneau writes A Perverse Switch Point For Neoclassical Economics, Non-Perverse For Austrians

Robert Vienneau writes The Fundamental Sraffian Theorem

Robert Vienneau writes Perverse Switch Point For Austrian Economics

Robert Vienneau writes Traditional And ‘Perverse’ Switch Points For Austrian And Neoclassical Economics

1.0 Introduction

I do not think I have presented an introductory example in a while in which an increased wage is associated with firms wanting to employ more labor, given the level of net output. This example is presented as a matter of accounting for a vertically integrated firm.

Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this, they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats.

2.0 Technology

The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1. Corn is a consumption good and also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. The first process produces iron, the second process produces steel, and the last two processes produce corn. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce the specified unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The data on technology are taken from a larger example.

Table 1: Technology
InputProcess
adef
Labor1/3 person-year7/20 person-year1 person-year3/2 person-year
Iron1/6 ton1/100 ton1 ton0 tons
Steel1/200 ton3/10 ton0 tons1/4 ton
Corn1/300 bushel0 bushel0 bushels0 bushels
Output1 ton iron1 ton steel1 bushel corn1 bushel corn

The managers of the firm have available two techniques for producing corn from inputs of labor, with intermediate inputs being constantly replaced. The iron-producing, steel-producing, and first corn-producing processes are operated in the Gamma technique. The second corn-producing process, as well as the iron and steel-producing processes, are operated in the Delta technique. Iron, steel, and corn all enter, either directly or indirectly, into the production of corn in both techniques. Vertically-integrated firms can also operate a linear combination of the Gamma and Delta technique.

3.0 Quantity Flows

One can consider various levels of operations in each of the processes for each of the technique. I consider two examples of snychronized production, in which inputs of labor simultaneously produce a net output of corn for consumption. A structure of production, consisting of specific capital goods, intervenes between the inputs and output. The labor input reproduces that structure, as well as producing the output.

3.1 Gamma Quantity Flows

Suppose 14,000/11,619 ≈ 1.205 tons iron are produced with the first process, 100/11,619 ≈ 0.0086 tons steel are produced with the second process, and 34,997/34,857 ≈ 1.004 bushels corn are produced with the third process. Then the quantity flows illustrated in Table 2 result. 14,000/11,619 tons iron are used as inputs among the three industries. These inputs are replaced by the output of the iron-producing process. 100/11,619 tons of steel are used as inputs among the three industries, and these inputs are replaced by the output of the steel-producing process. 140/34,857 bushels of corn are used as inputs among the three industries, leaving a net output of one bushel corn. In short, these quantity flows are such that 49,102/34,857 ≈ 1.409 person-years produce one bushel corn net. Obviously, I did not pick a very good set of coefficients for this example to support exact calculations in rational numbers.

Table 2: Vertically-Integrated Production with the Gamma Technique
InputProcess
ade
Labor14,000/34,857 person-year35/11,619 person-year34,997/34,857 person-year
Iron7000/34,857 ton1/11,619 ton34,997/34,857 ton
Steel70/11,619 ton30/11,619 ton0 tons
Corn140/34,857 bushel0 bushel0 bushels
Output14,000/11,619 ton iron100/11,619 ton steel34,997/34,857 bushel corn
3.2 Delta Quantity Flows

Suppose 100/23,331 ≈ 0.00429 tons iron are produced with the first process, 25,000/69,993 ≈ 0.3572 tons steel are produced with the second process, and 69,994/69,993 ≈ 1.00001 bushels corn are produced with the fourth process. By the same logic as above, these quantity flows are such that 1807/1111 ≈ 1.626 person-years produce one bushel corn net.

Table 3: Vertically-Integrated Production with the Delta Technique
InputProcess
adf
Labor100/69,993 person-year1,250/9,999 person-year34,997/23,331 person-year
Iron50/69,993 ton250/69,993 ton0 ton
Steel1/46,662 ton7,500/69,993 ton34,997/139,986 tons
Corn1/69,993 bushel0 bushel0 bushels
Output100/23,331 ton iron25,000/69,993 ton steel69,994/69,993 bushel corn
4.0 Prices

Which technique will the managers of the firm choose to adopt? By assumption, they take the price of corn and the wage as given on the consumer and labor markets. For simplicity, assume that price of a bushel corn is unity. That is firms treat the price of the consumer good as numeraire. At the end of the year, firms own a stock of iron, steel, and corn. They sell some of the corn to consumers. They retain the iron, steel, and enough corn to continue production the next year.

In a consistent accounting scheme, the price of iron and steel are such that:

  • The same (accounting) rate of profits is obtained in all operated processes.
  • The cost of the inputs, per bushel corn produced gross, for the corn-producing process not operated for a technique does not fall below that for the operated process.

The first condition specifies prices of intermediate goods and the rate of profits the accountants register. The second condition states that no pure economic profits can be obtained. Under these conditions, the managers of the firm can price their capital stock at the end of any year.

4.1 Prices at a Low Wage

Suppose the wage is w = 19,296/352,547 ≈ 0.05473 bushels per person-year. The accountants set the price of iron at p1 = 6,860/27,119 ≈ 0.2530 bushels per ton iron and the price of steel at p2 = 76,454 ≈ 2.819 bushels per ton steel. Table 4 shows the cost per unit output for each process and the resulting rate of profits obtained by operating each process. In constructing the tables for price systems, wages are assumed to be advanced. Under these assumptions, the rate of profits is 9/4, that is 225 percent, in each process comprising the Gamma technique. A lower rate of profits is obtained in the remaining corn-producing process, and it will not be operated. This is a consistent accounting system for the vertically-integrated firm, given the wage.

Table 4: Costs and the Rate of Profits at a Low Wage
ProcessCostRate of Profits
a(1/6)p1 + (1/200)p2 + (1/300) + (1/3)w = 27,440/352,547225 percent
d(1/100)p1 + (3/10)p2 + (7/20)w = 305,816/352,547225 percent
ep1 + w = 2,308/7,501225 percent
f(1/4)p2 + (3/2)w = 554,839/705,094≈ 27.1 percent
4.2 Prices at a Higher Wage with the Original Technique

Now suppose the wage is higher, namely w = 1,332/5,197 ≈ 0.2563 bushels per person-year. Consider prices of p1 ≈ 0.2622 bushels per ton iron and p2 ≈ 0.4167 bushels per ton steel. Table 5 shows cost accounting for these prices.

Table 5: Costs and the Rate of Profits at a High Wage (Incomplete)
ProcessCostRate of Profits
a0.141 Bushels per ton iron85.9 percent
d0.2241 Bushels per ton steel85.9 percent
e0.5379 Bushels per bushel85.9 percent
f0.5178 Bushels per bushel93.1 percent

Notice the same rate of profits is obtained in operating the first three processes. But the cost of producing a bushel corn with the last process is lower than in producing corn with process e. A larger rate of profits is obtained in operating that process. The managers of the firm will realize that their accounting implies that the Delta technique should be operated. If this firm were not vertically integrated and iron and steel were purchased on the market, a market algorithm would also lead to the Delta technique being adopted at this wage.

4.3 Prices at the Higher Wage with the Cost-Minimizing Technique

Continue to consider a wage of w = 1,332/5,197 ≈ 0.2563 bushels per person-year. The accountants report prices of p1 = 1,420/5,197 ≈ 0.2732 bushels per ton iron and p2 = 2,402/5,197 ≈ 0.4622 bushels per ton steel. Table 6 shows costs per unit output for the five processes under these prices.

Table 6: Costs and the Rate of Profits at a High Wage
ProcessCostRate of Profits
a710/5,197100 percent
d1,201/5,197100 percent
e2,752/5,197≈ 88.8 percent
f1/2100 percent

With this set of prices, the Delta technique is operated, and a rate of profits of 100 percent is obtained. The cost of operating the first corn-producing process exceeds the cost of operating the corn-producing process in the Delta technique. With a higher wage, the managers of a cost-minimizing firm will choose to operate a corn-producing process that requires more labor per bushel corn produced gross. (3/2 person-years is greater than 1 person-year.) More labor will also be hired per bushel corn produced net.

5.0 Conclusion

Table 7 summarizes these calculations. The ultimate result of a higher wage in the range considered is the adoption of a more labor-intensive technique. If this firm continues to produce the same level of net output and maximizes profits, its managers will want to employ more workers at the higher of the two wages considered. So much for the theory that, given competitive markets, wages and employment are determined by the interaction of well-behaved supply and demand curves on the labor market.

Table 7: A More Labor-Intensive Technique at a Higher Wage
WageTechniqueLabor Intensity
0.05473 bushels per person-yearGamma1.409 person-years per bushel
0.2563 bushels per person-yearDelta1.626 person-years per bushel

This example can be generalized in many ways. Different types of labor can be introduced. More intermediate produced capital goods can be included. Any number of processes can be available for producing each good, including an uncountable infinity. The use of fixed capital introduces more complications. The introductory marginalist textbook story about wages and employment in competitive markets is without foundation.

Why do so many economists teach nonsense?

Leave a Reply

Your email address will not be published. Required fields are marked *