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A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 6 workers, who together produced an average of 80 carts per hour. Workers receive \[tex]$16 per hour, and machine cost was \$[/tex]30 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by \$11 per hour, while output increased by 4 carts per hour.

a. Compute labor productivity under each system. Use carts per worker per hour as the measure of labor productivity. Note: Round your answers to 3 decimal places.

\begin{tabular}{|c|c|}
\hline
& carts per worker per hour \\
\hline
Before & \\
\hline
After & \\
\hline
\end{tabular}

b. Compute the multifactor productivity under each system. Use carts per dollar cost (labor plus equipment) as the measure. Note: Round your answers to 3 decimal places.

\begin{tabular}{|l|l|l|}
\hline
& & carts per dollar cost \\
\hline
Before & & \\
\hline
After & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's solve the problem in a detailed, step-by-step manner.

### Part (a) Compute Labor Productivity

Labor productivity is defined as the average number of carts produced per worker per hour.

#### Before the new equipment:
- Number of workers: 6
- Total carts produced per hour: 80

Labor productivity before = Total carts produced / Number of workers
[tex]\[ \text{Labor productivity before} = \frac{80\ \text{carts}}{6\ \text{workers}} = 13.333\ \text{carts per worker per hour} \][/tex]

#### After the new equipment:
- Number of workers: 5 (One worker was transferred to another department)
- Total carts produced per hour: 84

Labor productivity after = Total carts produced / Number of workers
[tex]\[ \text{Labor productivity after} = \frac{84\ \text{carts}}{5\ \text{workers}} = 16.800\ \text{carts per worker per hour} \][/tex]

So, the answers for part (a) are:
[tex]\[ \begin{tabular}{|c|c|} \hline Before & 13.333 \\ \hline After & 16.800 \\ \hline \end{tabular} \][/tex]

### Part (b) Compute Multifactor Productivity

Multifactor productivity is defined as the number of carts produced per dollar cost, where the cost includes both labor and equipment.

#### Before the new equipment:
- Number of workers: 6
- Worker wage per hour: [tex]$\$[/tex]16[tex]$ - Equipment cost per hour: $[/tex]\[tex]$30$[/tex]
- Total carts produced per hour: 80

Total labor cost per hour (before) = Number of workers * Worker wage per hour
[tex]\[ \text{Total labor cost (before)} = 6\ \text{workers} \times \$16\ \text{per hour} = \$96\ \text{per hour} \][/tex]

Total cost per hour (before) = Total labor cost per hour + Equipment cost per hour
[tex]\[ \text{Total cost (before)} = \$96\ \text{(labor cost)} + \$30\ \text{(equipment cost)} = \$126\ \text{per hour} \][/tex]

Multifactor productivity before = Total carts produced / Total cost
[tex]\[ \text{Multifactor productivity before} = \frac{80\ \text{carts}}{\$126} = 0.635\ \text{carts per dollar cost} \][/tex]

#### After the new equipment:
- Number of workers: 5
- Worker wage per hour: [tex]$\$[/tex]16[tex]$ - Equipment cost per hour: $[/tex]\[tex]$30 + \$[/tex]11 = \[tex]$41$[/tex]
- Total carts produced per hour: 84

Total labor cost per hour (after) = Number of workers * Worker wage per hour
[tex]\[ \text{Total labor cost (after)} = 5\ \text{workers} \times \$16\ \text{per hour} = \$80\ \text{per hour} \][/tex]

Total cost per hour (after) = Total labor cost per hour + Equipment cost per hour
[tex]\[ \text{Total cost (after)} = \$80\ \text{(labor cost)} + \$41\ \text{(equipment cost)} = \$121\ \text{per hour} \][/tex]

Multifactor productivity after = Total carts produced / Total cost
[tex]\[ \text{Multifactor productivity after} = \frac{84\ \text{carts}}{\$121} = 0.694\ \text{carts per dollar cost} \][/tex]

So, the answers for part (b) are:
[tex]\[ \begin{tabular}{|l|l|l|} \hline Before & & 0.635 \\ \hline After & & 0.694 \\ \hline \end{tabular} \][/tex]

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