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

Tariff equation: productivity-per-hour promotion formula for a productivity per hour focused Utopia

The previous blog-post ( http://davidvirgil.blogspot.com/2009/04/tariff-for-world-trade-could-properly.html ), I suggested a formula for a basic tariff on imports focused on globally discouraging transportation inefficiency, isolating the situation to foreign labor cost (Xaw) in location Xa, domestic labor cost (Aw) in location A, and cost of transporting product Theta from Xa to A for sale in location A (Xat).

The formula can be expanded to include non-wage production costs.

Let Xap represent the non-wage production cost at location Xa, and Ap the non-wage production cost at location A.

One obtains a situation wherein: Xap + Xaw + Xat = Ap + Aw in equilibrium, when the price of a given product, product Theta, using the alternative of importing to location A from location Xa, is equal to the price of product Theta if the alternative of location A producing product Theta in location A is used.

Non wage production costs reflect productivity per hour.

Productivity per hour is affected by: natural resources, environment, human talent, human skill, humans paid at levels that maximize productivity per hour, managers organizing humans to work together in efficient ways, geographic location advantages, etc.

Productivity per hour is not the same thing as productivity per dollar paid. Ed could be more productive per hour than Joe, at the same time Joe could be more productive per dollar paid than Ed.

A world dedicated to productivity per hour would tend to pay workers more because in the current world that emphasizes productivity per dollar paid, workers are paid less than the level at which their productivity per hour is maximum.

Productivity per hour changes depending upon the amount paid per hour, and is effected by the amount paid per hour.

It is possible to determine the wage level at which a worker's productivity per hour is maximized. If there is more than one such wage level, the lower of these wage levels is what I call the minimum productivity maximizing wage level, or MPMWL.

A world that emphasizes productivity per hour, would be a world where the workforce producing a given product, product Theta, would be composed of the persons whose productivity per hour is superior with regards to production of product Theta. This would improve the world's economy in terms of the amount of hours the world put into producing the things that it consumed.

Thus the world's wealth would increase in terms of leisure time, which reasonably must be considered a significant type of wealth.

At university I learned one way to measure such leisure time is based on the concept of opportunity cost; if a person can get paid $10/hour working, his time is said to be worth $10 per hour.

Fact is, a sports team does not perform as well, when you have the goalie play center -forward, and transfer the center forward to play goalie.

When you have people who excel in terms of productivity-per-hour when it comes to the building automobiles engaged in agriculture instead, and those who excel in productivity-per-hour in agriculture engaged in building automobiles, you have a non-optimal situation similar to the goalie being switched with the center-forward.

A world focused on productivity per dollar paid, to a significant extent fails to respect and reward those who excel in terms of productivity per hour; this inhibits human reproduction amongst those who excel in terms of productivity per hour; this in turn results in long term economic damage to such a world.

World X could be superior in wealth and income, compared to a world Y which is a much better place to live in compared to world X, even though world Y is inferior in total wealth and income--because world Y is superior in terms of wealth and income per hour worked.

Generally I would expect that a world which competently emphasized productivity per hour (without losing sight of the lessons that have been produced by an economic history derived from a world focused on productivity per dollar paid), to be superior in terms of wealth and income to a world focused on productivity per dollar paid.

A world focused on productivity per hour, would be a world in which employees were paid enough to be able to buy goods and services that increase their productivity. Such a world, would feature employees with money, time, and energy available to invest in improving their own productivity.

A mature economics is able to place quantitative values on leisure time and on the advantages of high pay per hour worked, able to discern and appreciate a world that excels in terms of productivity per hour.

If I gave you the choice between having to work 70 hours per week to make $700 a week, and working 20 hours per week to make $600 per week, which would you prefer? You'd prefer $600 per 20 hours work. Likewise, a world focused on productivity per hour could excel a world focused on productivity per dollar paid.

A world focused on productivity per hour would utilize tariffs to help insure that the employees whose productivity per hour is the greatest got the work that is to be done, as opposed to employees excelling in terms of productivity per dollar paid. This would rectify situations involving products being produced in locations featuring low productivity per hour and exported for sale to locations featuring high productivity per hour for the product in question.

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 = Aph/Xaph * Pdiff}

Cognizant of: the need to be cautious with a new method; the fact the productivity-per-hour promoting tariff could be combined with other tariffs; the possibility that a nation may need to be given a chance to improve its productivity per hour; and, inaccuracy re productivity per hour measurements, this could be adjusted as follows:

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

Note: the asterisk of course represents the multiplier sign.


@2009 David Virgil Hobbs

Tariff for world trade could properly be import transportation cost minus difference between import price and domestic production price

Note: to understand this post, it may be necessary to read yesterday's post, 'Transportation costs of imported products can result in cheap imports damaging the overall world economy' ( http://davidvirgil.blogspot.com/2009/04/transportation-costs-of-imported.html ).

Let: Xaw = wage cost in foreign low-wage land for production of product Theta; Xat = transportation cost to move product from location Xa to location A; Xa = wage cost in location A, the high-wage homeland; wdiff= Aw - Xaw.

when the alternative of production in location A the high-wage homeland is used, the money spent producing product Theta, is an amount equal to Xaw, what would be paid if product Theta were to be produced in location Xa, plus wdiff, which is the difference in wage cost between high wage location A and low wage location Xa.

When the alternative of production in location Xa the foreign low-wage area is used, the money spent on product Theta, is Xaw the wages paid to the workers at location Xa, plus Xat, the money paid to transport the product Theta from location Xa where it is built to location A where it is sold.

Thus in the equlibrium condition when Xaw + Xat = Xa, an important comparison becomes wdiff compared to Xat.

Xat money is spent on employing persons to engage in unnecessary busy-work type activity that does not contribute anything to the quality or quantity of product Theta.

Wdiff represents money spent donated or invested by workers in high wage location A, using the money as they see fit; this is money spent on necessities, pleasures, errands of conscience.

Looking at the world as one being, conceivably in one case Mr. World is engaged in moving things from one place to another for no good reason, using time and energy he does not need to expend on moving things from one place to another; and Mr. World is not doing this not because he enjoys moving things from one place to another or because moving things from one place to another accomplishes anything.

In the other case, Mr. World is enjoying purchasing goods and services he wants to purchase or needs to purchase.

It can be a shocking surprising thing, the realization that in the state of equilibrium, in equation terms Xaw + Xat = Aw, the alternative involving production of product Theta at location A the high wage location is superior to production at location Xa the low wage location, from the total world economy perspective.

What one naturally expects, is that in the state of equilibrium, Xaw = Xat = Aw, the production in location Xa and production in location A alternatives, would have equal impacts on the world economy as a whole.

The concept that in the state of equilibrium the produce-in- location-A the high wage location alternative is superior in terms of impact on the global economy, hits the mind and the world like a bolt of lightning; similarly Einstein and others were and still are shocked and surprised by the concepts Einstein's equations pointed to.

The importance of, equationally speaking, location A being superior from the global perspective should not be underestimated, because it leads in the direction of the world becoming competent in the art of applying the proper level and type of transportation-inhibiting tariff; this compared to the world being relatively speaking much poorer, as it is in its present beknighted condition, due to its belief that in ( Xaw + Xat = Aw ) equilibrium type conditions no tariff should be applied.

Tariffs applied to equilibrium ( Xaw + Xat = Xa ) or near-equilibrium conditions would have the maximum beneficial effect on the world's economy, if tariff were to be applied in the right amount.

Looking at and using as a basis the equilibrium equation, Xaw + Xat = Aw, I produced a first estimate regarding what the tariff applied to conditions of near-equilibrium or equilibrium ( Xaw + Xat = Aw) should be.

The first estimate, is that a tariff placed on generally speaking all imports in the world should be:

Xat which is the cost transporting product from Xa to A, MINUS Pdiff which is the difference in price when produced at location A compared to location Xa; Pdiff = Aw - (Xaw + Xat).

This tariff may not be perfect from the impact-on-world-economy or fairness perspectives. However extremely complicated, verbose, unpredictable tariff laws that are constantly tinkered with, and that vary enormously from location to location and product to product, have their own disadvantages which could easily outweigh the disadvantage of a very simple, consistent, comprehensible, easy to work with tariff.

Plug in various possible numerical values for Xaw, Xat, Aw, and you get impressive results. Try 6 to 9 for Xaw, 1 to 3 for Xat, Xa held steady at 10.

As the Xaw + Xat falls below Aw, the tariff declines to zero.

As the cost gap between the cheaper Xaw + Xat and the more expensive Aw increases, the tariff declines to zero, in honor of price of the import being respectably low compared to the price of domestic production (this could satisfy the free-market purists & unleash positive free-market forces). This allows for a certain level of downwards pressure on the home nation's wages, symbolized as Aw.

With the Xat MINUS Wdiff tariff, as Xat declines, the tariff declines to zero; this promotes trade with importers whose transportation of product costs are low.

The greater Xat - Pdiff is, the higher the tariff is; and as Xat - pdiff declines to zero or a negative number, the tariff declines to zero.

Thus the Xat - Pdiff tariff is directly proportionate to the Xat - Pdiff result, which is the equation I established, which measures the extent to which using imports instead of home production has damaged the global economy, by balancing transportation cost of a imported product against the extent to which the product is cheaper when imported, compared to when domestically produced.

The Xat - Pdiff tariff, would, I now estimate, dramatically and quickly boost the world economy; at the same time, its structure is such that it bends to the winds of free market doctrine, and is unlikely to economically damage the world through excess of tariff. Thus I now see the Xat = Pdiff tariff as an ideal solution for the global economy; it is a tariff that can with ease and simplicity be applied to all imports everywhere.

Note: by transportation costs, Xat, I mean those incurred due to production in location Xa, that would not be incurred if production was at A; factors omitted from the equation are assumed to be the same in both locations Xa and A; the concept can be further developed through inclusion of omitted factors; the equation can be considered with costs defined on the basis of man-hours put into production or transportation, as opposed to money wage costs.

@2009 David Virgil Hobbs

Transportation costs of imported products can result in cheap imports damaging the overall world economy

A typical situation involving transportation of products long distances from point of production to point of sale, follows the Xaw + Xat < Aw equation, where Xaw is the wage cost for producing product Theta in location Xa which exports product Theta, Xat is the transportation cost for moving product Theta from location Xa to location A for sale in location A, and Aw is the wage cost in order to produce product Theta in location A the location importing product Theta.

There exists, a hyper-enthusiasm for utilizing low-cost labor to build things and then ship these things long distances to the point of sale, in situations of the type described in the equation. This hyper-enthusiasm damages the overall world economy.

Building on the equation, the wage costs that would occur if product Theta were to be produced in nation A the importing nation, exceed the wages paid at location Xa by wdiff, the wage differential.

Wdiff is not lost to the world economy if the alternative of using the higher wage labor in location A is employed, because wdiff is spent and invested by the workers in location A.

At the same time the world economy incurs (the inefficiency of?) the loss of expending time, energy, money, and natural resources, on the unnecessary (busy-work of?) transporting product Theta thousands of miles from production point Xa to sale point A, if the alternative of producing product Theta in location Xa, where wage costs are lower, and then transporting the productto point of sale at location A is followed. I call this effect the Tloss effect.

(Transportation of a product is not a necessary aspect of the production of the product.The world underestimates the extent to which unnecessarily transporting products long distances is inefficient busy-work).

At the same time, there is a negative impact on the world income/prices ratio equation, which acts to reduce the real world GDP as measured taking into account prices, when consumers in location A consume higher-priced product Theta made in location A, instead of lower-priced product Theta made in location Xa. I call this the price-index effect.

Thus the judgement regarding comparing the expensive domestic labor approach vs the cheap foreign labor approach, with regards to the effect on the world economy, comes down to the Tloss (unnecessary transportation of product Theta), weighed against the price-index effect (world prices pushed upwards through higher prices for product Theta when product Theta is produced in location A where wages are higher).

If the Tloss negative impact on the world economy outweighs the price-index effect, the alternative involving the goods produced where wages are cheaper and then unnecessarily transported thousands of miles to point of sale, is inferior from the total world economy perspective compared to the alternative involving domestic production.

Forces of supply and demand tend to establish an equilibrium wherein approximately speaking, Xaw (wage cost in location Xa) + Xat (cost of transporting product from Xa to location A) = Aw (wage cost for producing product in location A). Changes to this equilibrium tend to be balanced by other changes that restore the equilibrium.

The equilibrium illustrated through the Xaw + Xat = Aw equation, is an equilibrium that persons religiously devoted to persecuting what they call "protectionism", seek to disrupt in favor of the alternative involving using the cheaper labor located in location Xa:

"SENATOR BLATHER: Internashunal trade is th' engine of wo'ld economic growth. Internashunal trade is superio' t'domestic trade in terms of effeck on wo'ld economic growth. Domestic trade is shamefully proteckshunist an' interferes wif th' superio' internashunal trade. Ev'ry time a produck crosses internashunal bo'ders, waves of psychic wo'ld unity spread throughout th' wo'ld, promotin' wo'ld economic prosperity.

Docko' Easterneuropinsky has invented a brilliant noo fo'mula thet explains th' situashun. When th' low foreign labor costs Docko' Easterneuropinsky calls Xaw, plus th' transpo'tashun costs he calls Xat, is equal t'th' domestic labor cost he calls Aw, we sh'd step in t'make sho'nuff thet th' low foreign labor combined wif th' transpo'tashun shippin' costs alternative is used. We sh'd tax th' expensive domestic labor alternative an' use th' money t'subsidize th' cheap fo'eign labor combined wif shippin' th' produck t'th' point of sale even eff'n its a million miles away fum th' produckshun locashun."

A simple analysis of the equation shows that such interpretation of the Xaw + Xat = Aw equation is irrational.

The price-index effect, which is the effect on world prices when the alternative of more expensive domestic labor is used, is Aw - (Xaw + Xat), that is, the expensive domestic labor cost minus the combination of the cheap foreign labor cost and the transportation cost. This is always zero, when the equilibrium condition (Xaw + Xat = Aw) exists.

However the unnecessary transportation cost, is always greater than zero when the Xaw + Xat = Aw condition exists.

Since that which is greater than zero is always greater than zero, when the Xaw + Xat = Aw condition exists, the (unnecessary) transportation cost outweighs the non-existent advantage derived through lower prices, indicating that when such conditions hold, the domestic production alternative is superior for the world economy as a whole. This correct interpretation directly contradicts Senator Blather quoted above.

Even when Xaw (foreign labor cost) + Xat (cost of transportation of product from production point to sale point) < (is less than) Aw (domestic labor cost), the equation incisively illustrates how using the less espensive foreign labor, Xaw, could be worse for the overall world economy compared to use of the more expensive domestic labor, Aw.

If Xaw is 7, and Xat is 2, and Aw is 10, then: the price of the product using the produce-in-the-foreign-location and import to home alternative is 7+2=9; the price of the product using the produce-at-home alternative is 10; the effect on the world price index if the produce at home alternative is used is 1; the shipping cost effect is 2 if the produce-foreign-and -import alternative is used.

Since 2 is greater than 1, the equation shows that the world economy in this case featuring the situation illustrated by the Xaw 7 + Xat 2 < Aw 10 equation, would be better off if the domestic production alternative were to be employed, despite the fact that the cost of the product is less using the produce-using-cheap-foreign -labor and import-via-shipping-to-point-of -sale approach.

An economy featuring an emphasis on doing lots of unnecessary things, begins to become an absurd economy. What is unnecessary becomes a source of inefficiency and busy work. The lower cost of a transported product, is balanced by the cost of the unnecessary transportation of the product; the higher wages paid when the product is not transported, are used not for madcap unnecessary busy-work purposes, but rather to satisfy the normal rational desires of persons.
@2009 David Virgil Hobbs