[Terrapreta] 200 tons per day Dynamotive plant in Missouri

[MMBTUPR at aol.com]

           from      Lewis L Smith

In conventional economics, the profit function [ in simplified form ] may 
written as follows, where R is revenue, x is the volume of product and C is cost 
of product.   >

π (x) =   R (x) — C (x)

Taking the first derivative of π with respect to x, we have >

dπ/dx = dR/dx — dC/dx

Now at the optimal point in a competitive market, that of maximum profit or 
minimum loss, we have   >

0 = dR/dx — dC/dx

Rearranging >

dR/dx = dC/dx

In plain English, incremental revenue equals incremental cost. The optimal 
volume of output is the point at which the above is true.

Sean's point about distinguishing   between outputs of a joint-products 
process and the "slate" of products for sale is a good one. With many bio and/or 
chemical processes, the last stage in the manufacturing process which produces a 
variety of intermediate products jointly is not necessarily the final stage 
of processing. Additional processing stages applicable to individual products 
may occur. Needless to say, these latter process are the principle source of 
the product-specific costs which I mentioned in my post.

Examples are sugar, ethanol and/or molasses from the crystals which the 
centrifuge separates out of the cane juice. And the subsequent products which may 
be made from each of them. Also the various products which may be obtained from 
glycerol produced as a byproduct of making biodiesel. 

[ Incidentally disposing of glycerol at acceptable prices is a big problem 
for some biodiesel producers in the States. ]

A copy of 'Output pricing for biomass energy projects" will go out Monday to 
Sean.

Cordially. #


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