- I92 / PARADOXES OF, FORCED LABOR the relative efliciency of the agriculture in the North and youth is called the “geometric index of total factor produc- tivity.” With this index, efficiency is measured by the ratio of output to the average amount of the inputs. The higher the output per average unit of input, the greater the efficiency. The geometric index of total factor productivity was originally devised in the early 1940s. It was used, in a celebrated paper published in 1957, to measure the growth in the efficiency of the American economy between 1903 and 1949. It has been widely used since that time to evaluate and compare the economic performances of various sectors of the economy within the US. during many different time periods, as well as to compare the economic performance of various nations. The equation for the index is presented in appendix B, along with a discussion of the characteristics of this measure and the way in which it has been applied to determine the relative efficiency of slave agriculture. The following are the main interim findings: 1. Southern agriculture as a whole was about 35 percent more efficient than northern agriculture in 1860; that is, on average, a southern farm using a given amount of labor, land, and capital could produce about 35 percent more output than a northern farm, or group of farms, using I: the same quantities of these inputs. 2. Both southern farms using free labor and southern farms using slave labor were more efl'-icient than north- ern farms. Compared with each other, however, southern slave farms were 28 percent more efficient than southern free farms. Compared with northern farms, southern free farms were 9 percent more efficient, while slave farms were 40 bercent more efficient. 3. There were eco le in southernagriculture. This means that a single large farm using given quantities of inputs could produce, more output than a group of small farms which together used the same quantities of ipputsv. 1 L‘ Not all of the superior efficiency of slave farms was due Flgun 42 A comparlson of the Efllelency of Southern Farms wllh Norlham Farms In 1860 Ffyuro 43 A comparlson ol the Efllclency of Large and Small Souiherllfarms In 1860 Mumwot sum pa rum