Questions: QUESTION 8 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 five workers, who produced an average of 80 carts per hour. Workers receive 10 per hour, and machine cost was 40 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by 10 per hour while output increased by four carts per hour. What is the multifactor productivity before buying new equipment (consider labor and equipment as inputs)? (Please keep two digits after the decimal point.)

QUESTION 8

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 five workers, who produced an average of 80 carts per hour. Workers receive 10 per hour, and machine cost was 40 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by 10 per hour while output increased by four carts per hour.
What is the multifactor productivity before buying new equipment (consider labor and equipment as inputs)? (Please keep two digits after the decimal point.)

Transcript text: QUESTION 8 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 five workers, who produced an average of 80 carts per hour. Workers receive $\$ 10$ per hour, and machine cost was $\$ 40$ per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $\$ 10$ per hour while output increased by four carts per hour. What is the multifactor productivity before buying new equipment (consider labor and equipment as inputs)? (Please keep two digits after the decimal point.)

Solution

Solution Steps

To find the multifactor productivity (MFP) before buying the new equipment, we need to calculate the ratio of output to the sum of the inputs (labor and equipment costs). The formula for MFP is:

\[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Costs}} \]

Where:

Output is the number of carts produced per hour.
Total Input Costs is the sum of labor costs and equipment costs per hour.

Given:

Number of workers = 5
Output (carts per hour) = 80
Labor cost per worker per hour = \$10
Equipment cost per hour = \$40

We can now calculate the MFP.

Step 1: Calculate Total Labor Cost per Hour

Given:

Number of workers: $5$
Labor cost per worker per hour: $\$10$

The total labor cost per hour is calculated as: \[ \text{Total Labor Cost per Hour} = \text{Number of Workers} \times \text{Labor Cost per Worker per Hour} = 5 \times 10 = \$50 \]

Step 2: Calculate Total Input Costs per Hour

Given:

Equipment cost per hour: $\$40$

The total input costs per hour is the sum of the total labor cost per hour and the equipment cost per hour: \[ \text{Total Input Costs per Hour} = \text{Total Labor Cost per Hour} + \text{Equipment Cost per Hour} = 50 + 40 = \$90 \]

Step 3: Calculate Multifactor Productivity (MFP) Before Buying New Equipment

Given:

Output (carts per hour): $80$

The multifactor productivity (MFP) is calculated as: \[ \text{MFP} = \frac{\text{Output}}{\text{Total Input Costs per Hour}} = \frac{80}{90} \approx 0.8889 \]

Final Answer

$\boxed{\frac{8}{9}}$

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