The manager of a crew that installs wood floors has tracked the crew's output over the past several weeks. Each worker works 40 hours per week and earns $17 per hour. The wholesale cost of lumber to the company is $5 per square foot and the company charges its customers $15 per square foot of flooring installed. Week Crew Size Lumber Used (sq. ft.) Flooring Installed (sq. ft.)
1 4 480 420
2 3 351 325
3 2 250 238

a. Calculate labor productivity for each of the weeks.
b. Suppose that in addition to labor cost and wholesale lumber cost, the firm's overhead is 120% of its labor cost. Calculate multifactor productivity for each of the weeks shown.

Week      Crew Size     Lumber Used     Flooring Installed

                                     (sq. ft.)                 (sq. ft.)

1                    4                 480                   420

2                   3                 351                    325

3                   2                 250                   238

a)

labor productivity = total output / number of employees

week 1 ⇒ 420 / 4 = 105 sq. ft. of floors installed per worker

week 2 ⇒ 325 / 3 = 108.33 sq. ft. of floors installed per worker

week 3 ⇒ 238 / 2 = 119 sq. ft. of floors installed per worker

b)

multi-factor productivity = total output in $ / (labor + materials + overhead)

week 1 ⇒ (420 x $15) / [(4 x 40 x $17) + (480 x $5) + (4 x 40 x $17 x 1.2) = $6,300 / ($2,720 + $2,400 + $3,264) = 0.75

week 2 ⇒ (325 x $15) / [(3 x 40 x $17) + (351 x $5) + (3 x 40 x $17 x 1.2) = $4,875 / ($2,040 + $1,755 + $2,448) = 0.78

week 3 ⇒ (238 x $15) / [(2 x 40 x $17) + (250 x $5) + (2 x 40 x $17 x 1.2) = $3,570 / ($1,360 + $1,250 + $1,632) = 0.84

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