Counter Example

The claim of the ideal state of affairs can only come about, if it includes this criteria is false:

The claim:

The marginal rate of transformation in production is identical for all products. This occurs when it is impossible to increase the production of any good without reducing the production of other goods.

This is a false claim with the following counter-example:

The United States no longer sees horse-carriages that have been replaced by the automobile.  The increased production of the automobile reduced the production of the horse-carriage implying that Pareto efficiency never existed or could never exist, because it cannot account for all things including future technology that greatly improved the efficiency of all things by the automobile (the United State production capability after adjusting for inflation and other economic factors from 1950 to 1990 and the automobile and resulting highways was just one technology influence of this).  The automobile technology is about 120 years old, and the horse-carriage has been around since time immemorial, but the horse-carriage is now is very uncommon and replaced by the automobile.  This is a counter-example, therefore the description of ideal state of affairs is inadequate, and you know in mathematics and philosophy that means it is worthless.