Problema Solution
Last year producing one unit (then worth $390) required 4 hours of labor ($24 per hour) and $60 worth of overhead. This year, producing one unit requires only 3.5 hours of labor, but the cost of an hour of labor has increased by 20%. Further, while overhead cost has remained constant, the value of a unit of output has fallen by 10%. By how much (% basis), has multifactor productivity decreased?
Answer provided by our tutors
Very ambiguous wording, but we assume that 'multifactor productivity' is represented by 'x'
producing one unit (then worth $390) required 4 hours of labor ($24 per hour) and $60 worth of overhead ...so some multifactor variable would be expressed by this equation:
(4*24+60)x=390
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x=2.5
The either scenario described as "producing one unit requires only 3.5 hours of labor, but the cost of an hour of labor has increased by 20%. Further, while overhead cost has remained constant, the value of a unit of output has fallen by 10%" and would be expressed by this equation:
(3.5(24+0.2*24)+60)x=390-0.1*390
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x=2.1828
multifactor productivity decrease:
2.5-2.1328=0.36719
(% basis) is an unclear term:
(2.5-2.1328)/2.5 = 0.1468
So multifactor productivity has decreased by approximately 0.37. The description is unclear but "% basis" perhaps refers to approximately 15%.