Heterodox
Figure 1: Hayekian Triangles for The Two Techniques1.0 Introduction This post is a variation on this one. 2.0 Technology and Net Output Suppose technology is as characterized by the coefficients of production in Table 1. All techniques are characterized by single production, no fixed capital, and no joint production. In the Alpha technique, the first corn-producing process is operated. The second corn-producing process is operated in the Beta technique. The ale-producing process is operated in both techniques. Table 1: Regions InputCorn IndustryAle IndustryProcess IProcess IIProcess IIILabor1 person-yr.275/464 person-yrs.1 person-yr.Corn1/10 kilo-bushels113/232 kilo-bushels2 kilo-bushelsAle1/40 kilo-liters1/200 kilo-liters2/5 kilo-litersOUTPUTS1 kilo-bushel1 kilo-bushel1 kilo-liter
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| Figure 1: Hayekian Triangles for The Two Techniques |
This post is a variation on this one.
2.0 Technology and Net OutputSuppose technology is as characterized by the coefficients of production in Table 1. All techniques are characterized by single production, no fixed capital, and no joint production. In the Alpha technique, the first corn-producing process is operated. The second corn-producing process is operated in the Beta technique. The ale-producing process is operated in both techniques.
| Input | Corn Industry | Ale Industry | |
| Process I | Process II | Process III | |
| Labor | 1 person-yr. | 275/464 person-yrs. | 1 person-yr. |
| Corn | 1/10 kilo-bushels | 113/232 kilo-bushels | 2 kilo-bushels |
| Ale | 1/40 kilo-liters | 1/200 kilo-liters | 2/5 kilo-liters |
| OUTPUTS | 1 kilo-bushel | 1 kilo-bushel | 1 kilo-liter |
Each column in the Leontief matrix and corresponding direct labor coefficient defines a production process. Each process exhibits constant returns to scale and requires a year to complete. Each of the produced commodities are available at the end of the year. All commodities enter, either directly or indirectly, into the production of all commodities and the economy is productive. Labor is directly required to operate each process.
This analysis takes the proportions in the net product as given. These proportions are specified by a column vector, as in Table 2. This numeraire is the net product or net output of Sraffa's standard system for the Alpha technique. This special case has implications for the shape of Hayekian triangles, as seen below.
| Commodity | Amount |
| Corn | d1 = (337 - 29 (29)1/2)/455 kilo-bushels |
| Ale | d2 = (17 + 25 (29)1/2)/1,820 kilo-kiters |
The usual analysis of prices and production and the choice of technique yields the wage curves in Figure 2 below. The Beta technique is cost-minimizing for a low interest rate. The Alpha technique is cost-minimizing for a higher interest rate.
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| Figure 2: Wage Curves for the Two Techniques |
Figure 1, at the top of this post, shows the Hayekian triangles at the single switch point. Around this switch point, a lower interest rate does extend the structure of production. But it does not require more savings to achieve that extension.
4.0 ConclusionThe above has constructed Hayekian triangles not consistent with Austrian business cycle theory. A coordinated state does not necessarily rotate the Hayekian triangle to have a longer structure of production with less consumption (more savings).