obtain the per capita value. If we then apply the integrals above limits as described, we can determine, for example how much per capita product exceeds a unit value of $100/kg. These techniques were used to establish plausible values for the constants. Fig. 5 illustrates results for a US gross national goods product (services excluded) of 2 trillion dollars, and a population of 250 million. The per capita product is $8000/year. The constant K is where a = 2.5, and C=$0.1/kg. similarly, K can be calculated for a = 2.2 and 2.8. The integral values for mass and value above a range of lower limits were then calculated. For a = 2.5, this projection states that there will be about 5 kg of product per capita produced that exceeds a value of $100/kg. An example product is commercial jet aircraft. US annual production is roughly 400 aircraft at roughly 100000 kg each, for a total of 40 million kg, or about 0.16 kg per person per year. The associated value is about $1000 per year. Most US products exceeding $100/kg are in the aerospace sector; there are very few consumer products so expensive (my lap portable computer exceeds $100/kg but I know of nothing else in our household that does except jewelry). From inspection of Fig. 5, I concluded that the exponent a probably falls within the range of about 2.3 to 2.7. One can convert the constant K to man-hours instead of dollars. The lower limit of the integral must be similarly converted. The number of working hours in a year (40 hours per week, less vacations, holidays and leaves) is about 1800. The lower limit is 0.0045 man-hours/kg instead of $0.1 /kg; the gross national product per worker in the product (as opposed to services) sector is about $40000, yielding a value per hour of
RkJQdWJsaXNoZXIy MTU5NjU0Mg==