Monday, November 20, 2006

No Influence Of Tastes On Prices (Part 1 of 2)

1.0 Introduction
This short sequence of posts illustrates the so-called non-substitution theorem. (Luigi Pasinetti argues this theorem is misleadingly named.)

Consider three islands, Alpha, Beta, and Gamma, where a competitive capitalist economy exists on each island. These islands are identical in some respects and differ in others. The point is to understand that differences in tastes need have no influence on prices.

All three islands have the same Constant-Returns-to-Scale technology available. They also face the same wage, and have fully adapted production to requirements for use. Thus, they will choose to adopt the same technique. This technique consists of a process to produce rye and another one to produce wheat. Each process requires a year to complete. Each process requires inputs of labor, rye, and wheat. These processes fully use up their inputs in producing their output. Table 1 specifies the coefficients of production for the selected technique.
Table 1: The Technique of Production
Inputs Hired
At Start
Of Year
Labor1 Person-Year1 Person-Year
Rye1/8 Bushel3/8 Bushel
Wheat1/16 Bushel1/16 Bushel
Outputs1 Bushel Rye1 Bushel Wheat
2.0 Quantity Flows
The employed labor force grows at a rate of 100% per year on each island. Each island differs, however, in the mix of outputs that they produce. Table 2 shows the quantity flows per employed laborer on Alpha. Notice that the commodity inputs purchased at the start of the year total 5/32 bushesl rye and 1/16 bushels wheat. Since the rate of growth is 100%, 5/16 bushels rye and 1/8 bushels wheat will be needed for inputs into production in the following year. This leaves 9/16 bushels rye available for consumption at the end of the year per employed worker.
Table 2: Quantity Flows On The Alpha Island Per Worker
InputsRye IndustryWheat Industry
Labor7/8 Person-Year1/8 Person-Year
Rye7/64 Bushel Rye3/64 Bushel Rye
Wheat7/128 Bushel Wheat1/128 Bushel Wheat
Outputs7/8 Bushel Rye1/8 Bushel Wheat
Table 3 shows the quantity flows on Beta. Here the same sort of calculations reveal that Beta has 3/8 bushels wheat available for consumption at the end of the year per employed worker.
Table 3: Quantity Flows On The Beta Island Per Worker
InputsRye IndustryWheat Industry
Labor1/2 Person-Year1/2 Person-Year
Rye1/16 Bushel Rye3/16 Bushel Rye
Wheat1/32 Bushel Wheat1/32 Bushel Wheat
Outputs1/2 Bushel Rye1/2 Bushel Wheat
Gamma's quantity flows, shown in Table 4, are an intermediate case. Gamma has 3/8 bushel rye and 1/8 bushel wheat available for consumption at the end of the year per employed worker.
Table 4: Quantity Flows On The Gamma Island Per Worker
InputsRye IndustryWheat Industry
Labor3/4 Person-Year1/4 Person-Year
Rye3/32 Bushel Rye3/32 Bushel Rye
Wheat3/64 Bushel Wheat1/64 Bushel Wheat
Outputs3/4 Bushel Rye1/4 Bushel Wheat
In the next part, I will describe a system of prices consistent with each and every one of the three islands.

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