Can you please indicate all steps required to solve this? Thank you!! This is not a graded assignment

Number of slaves/farm Total factor productivity index (All southern states) 100.0 1-15 107.7 16-50 144.7 51+ 133.5 Source: Fogel, Without Consent or Contract, 1989. The above table presents information on the total factor productivity of free farms relative to slave farms of different sizes in the southern economy in 1860. Recall that total factor productivity is derived from an agricultural production function: Y = AL"KBAccording to Robert Fogel, "nearly one-third of slave laborers were untrained children". In contrast, on free farms, young children did not work. Would adjusting for this difference in labor quality widen or narrow the productivity gap between free and slave farms? Explain your reasoning. (hint: you may assume that children have no productive capacity so that 100 slave workers is equivalent to 66.6 free workers in terms of output produced. You also might want to think about how we calculate A from data)