Tariff to promote productivity-per-hour equation version 2

In the previous blog-post ( http://davidvirgil.blogspot.com/2009/04/tariff-equation-productivity-per-hour.html ) I described the advantages of a world focused on maximizing productivity per hour instead of maximizing productivity per dollar. I wrote, regarding a formula for a productivity per hour promoting tariff:

"A first estimate for an equation representing what this tariff should be:

Xaph = productivity per hour producing product Theta in location Xa.

Aph = productivity per hour producing product Theta in location A.

XAprice = price of product Theta when imported into location A from location Xa for sale in location A

Aprice = price of product Theta when product Theta produced in location A

Pdiff = Aprice - Xaprice

The productivity per man-hour tariff applied to all imports in the new world emphasizing productivity per hour would be (javascript style):

if (Aph > Xaph & Aprice > Xaprice)
{productivity_per_hour_tariff = mult * Aph/Xaph * Pdiff}
//mult represents number between 0 and 1 "

I have continued with efforts to improve on this first attempt. I call the effort I describe here in this blog-post, productivity-per-hour-promoting tariff Version 2.0 (PPHPT v 2.0); henceforth I will refer to the formula set forth in the first attempt as version 1.0 (PPHPT v 1.0).

Version 2.0 (javascript style):

// what the variables represent is described above

if (Aph > Xaph)
{productivity_per_hour_tariff = (Aph/Xph * Xaprice) - Xaprice};

if (Aph == Xaph)
{productivity_per_hour_tariff = (Aph/Xph * Xaprice) - Xaprice};

if (Aph < Xaph)
{productivity_per_hour_tariff = ( (Aph/Xph * Xaprice) - Xaprice)};

The above in common english means:

if Aph is greater than Xaph, the productivity per hour tariff is: what Aph divided by Xph times Xaprice is equal to, minus xaprice;

if Aph is equal to Xaph, the productivity per hour tariff is: zero.

if Aph is less than Xaph, the productivity per hour tariff is: what Aph divided by Xph times Xaprice is equal to, minus xaprice

Thus productivity-per-hour-promoting tariff version 2.0 (PPHPT v 2.0) can produce a negative number when Xaph is greater than Aph. That is because ultimately the productivity-per-hour-promoting tariff is combined with the transportation-inefficiency-inhibiting tariff (described at http://davidvirgil.blogspot.com/2009/04/tariff-for-world-trade-could-properly.html ), which I now christen as transportation-inefficiency-inhibiting tariff version 1.0 (TIIT v 1.0).

Both the transportation tariff and the productivity tariff could be negative or positive numbers. When they are added together, the result could be negative, zero or positive. When they are added together if the result is greater than zero, a tariff I call the Productivity and transportation tariff (PATT) is applied.

Comparison of productivity-per-hour-promoting tariff Version 2.0 (PPHPT v 2.0) to productivity-per-hour-promoting tariff Version 1.0 (PPHPT v 1.0):

PPHPT v 1.0, produces a tariff of zero when Xaprice and Aprice are the same, even if Aph is much greater than Xaph. In a tariff designed to promote high productivity per hour, one would logically expect some level of tariff to kick in when Xaprice equals Aprice and Aph is much higher than Xaph. The logical inconsistency in this case indicates imperfection in other cases involving different Xaprice, Aprice, Xaph, and Aph values.

PPHPT v 2.0 by way of contrast, produces a tariff of higher than zero when Xaprice equals Aprice and Aph is greater than Xaph.

PPHPT v 1.0's effect, is to cause, after the tariff is applied, all imports that involve lower productivity per hour, to cost more than the domestically produced alternative when the domestic alternative is produced using higher productivity per hour; the only variation being that the lower Xaph is compared to Aph, the higher the tariff. PPHPT v 2.0 by way of contrast, allows situations wherein the Xaph is lower than the Aph but still the tariff plus Xaprice, is lower than Aprice.

PPHPT v 2.0 does not punish the producers of the world for taking advantage of local natural resources that are relatively inexpensive and or of relatively high quality. The sale price of an exported product in the presence of such advantages combined with a productivity per hour rate of X amongst the employees, could be lower than the sale price of the product in the absence of such advantages with productivity per hour still the same unchanged at X.

The Xat - Pdiff transportation-inefficiency-inhibiting tariff version 1.0 (TIIT v 1.0), seemed reasonable, without logical fault; it allowed for an imported good's price taking into account the tariff, to be cheaper than the domestically produced alternative, despite the existence of transportation costs that would not be incurred if the product were to be domestically produced. Thus the TIIT v 1.0 that worked well resembles PPHPT v 2.0.

PPHPT v 2.0 being more similar to TIIT v 1.0 than PPHPT v 1.0, is advantageous because the TIIT is combined with the PPHPT to produce the final tariff, and dissimilarity could result in one or the other of the two, exerting disproportionate effect on the total.

Rewarding those whose productivity per hour though lower than competing productivity per hour rates, is high relative to their pay in terms of money per hour, accords with a grudging respect society has traditionally shown for such persons. PPHPT v 2.0 allows for the total of the tariff plus Xaprice to be less than Aprice in certain cases when Xaph is lower than Aph, but v 1.0 does not.

The promotion of a high level of productivity per hour relative to pay per hour, as opposed to productivity per hour in and of itself, is a promotion worth considering, that could exert positive impact on global wealth and income.

PPHPT v 2.0 is more compatible with free trade purism and the theory that the world economy is harmed by excess regulation, compared to PPHPT v 1.0.

A new idea such as emphasis on productivity per hour should, especially at first, respect and accomodate older traditional economic ideas. PPHPT v 2.0 in this respect excels v 1.0, because it can allow imports produced at a lower level in terms of productivity per hour to be have a price including tariff cost, that is lower than the domestic production alternative price.

Elaborations that might produce improvements in the PPHPT in the future:

Differences between locations Xa and location A in terms of price of raw materials could be worked into the equation.

Tests could be carried out to find the 'mult' multiplier value in the PPHPT equation that produces optimal results and assures that advantage derived from the promotion of productivity per hour outweighs disadvantage incurred through suppression of the utilization of local raw-material advantages by exporters.

These tests could involve plugging real-life values into the PPHPT equation and looking at the tariff level outcomes. The multiplier could be constant or it could change being effected by other variables according to some formula.

Nevertheless, I now estimate that PPHPT v 2.0 would improve the total wealth and income of the global economy, especially if the value of leisure time is competently accounted for, without producing tariffs that are high enough to damage the total global economy.

@2009 David Virgil Hobbs