Economics Tasks on the Topics: Calculating Labor Productivity and Labor Intensity

Note: The problems is taken from the forum without changes.

In this lesson:

1. Increase in labor productivity based on percentage indicators
2. Change in percentage labor productivity
3. Increase in labor productivity based on change in labor intensity
4. Change in productivity with change in production volume
5. Change in productivity with decrease in labor intensity and number of personnel
6. Change in the number and volume of production
7. Determine labor productivity for commercial products
8. Change in labor productivity as a result of change in the number and output
9. Change in labor productivity as a result of change in fulfillment of production standards
10. Change in labor productivity with decrease in labor intensity of the product
11. Change in labor intensity with change in labor productivity
12. Calculations with change in productivity growth and labor intensity simultaneously
13. Determine the decrease in labor intensity due to increase in labor productivity
14. Increase in labor productivity due to several measures

Problem 1. Increase in Labor Productivity Based on Percentage Indicators

Given:

• Total number of workers at the enterprise: 3650
• Number of workers whose productivity increased: 100
• Increase in productivity for these 100 workers: 2.5%

Solution:

1. Calculate the number of workers whose productivity did not change: [ 3650 - 100 = 3550 ]

2. Determine the new productivity level for the entire workforce: 
   ( 3550 * 100% + 100 *102,5% ) / 3650 = 100,07% (More precisely, 100.0684932%)

3. Calculate the increase in labor productivity: 100,07% - 100% = 0,07%

Answer: The increase in labor productivity was 0.07%.

Problem 2. Change in Percentage Labor Productivity

Given:

• Group 1 of activities: +2%
• Group 2 of activities: -4%
• Group 3 of activities: -12.5%

Solution:

1. Calculate the indices of labor productivity for each group of activities: 
   I_{Group 1} = (100 + 2) / 100 = 1.02 ;  
   I_{Group 2} = ( 100 - 4 ) / 100 = 0.96 ; 
   I_{Group 3} = ( 100 - 12.5 ) / 100 = 0.875 ;

2. Determine the overall change in labor productivity: To find the overall change, multiply the indices:
   I_total = 1.02 x 0.96 x 0.875 ≈ 0.8574

3. Convert the index back to a percentage change: ( I_total  - 1) x 100% = (0.8574 - 1) x 100% ≈ -14.26% 

Answer: The overall change in labor productivity is approximately -14.26%.

Problem 3. Increase in labor productivity based on changes in labor intensity

Problem 4: Change in Productivity with Change in Production Volume

Determine how labor productivity will change if the change in production volume is +11%
and the change in the number of employees is +5.

Solution:

To find the change in labor productivity, calculate the indices of production volume and number of employees
and substitute the obtained values into the formula:

I_pt = I_v / I_h

Where:

• I_pt is the labor productivity index.
• I_v is the production volume index.
• I_h is the employee number index.

Let’s solve the problem:

I_v = (100 + 11 ) / 100 = 1.11

I_h =  ( 100 + 5 ) / 100 = 1.05

I_pt = 1.11 / 1.05  = 1.057

Answer: Labor productivity increased by 5.7%.

Problem 5: Change in Productivity with a Decrease in Labor Intensity and Number of Personnel

Determine how labor productivity will change in the planning year if it is assumed that the number of main workers will decrease
from 450 to 430 people. At the same time, a number of measures are planned that will reduce labor intensity by 9%,
and it is also possible to increase productivity due to organizational measures by 7%.

Solution:

1. Find the index of the number of workers:

I_h =  430 / 450 = 0.955

The number of personnel decreased by 4.5%.

• Find the change in labor productivity due to a decrease in labor intensity:

Labor productivity - the reciprocal of labor intensity

Δpt = 100% - 100% / (100% - 9% )  ≈ 9.89%

Labor productivity increased by 9.89% due to a decrease in labor intensity.

• Find the production volume index:

I_v = ( 100% + 7% ) / 100% = 1.07

• Find the labor productivity index due to a decrease in labor intensity:

I_pti = ( 100% + 9.89% ) / 100% = 1.0989

• Find the final productivity index using the formula:

I_pt = 1.07 / 0.955 * 1.0989 ≈ 1.22976

Answer: Labor productivity increased by 22.976%.

Problem 6: Change in the Number and Volume of Production

In the base year, the number of workers was 330. In the planning year, it is planned to increase the number of workers by 10%.
The volume of manufactured commercial products is 4 550 000 USD, and in the planned year, the increase in production volume
is expected to be 6%. Determine labor productivity in the base and planned years, and determine the change in labor productivity
in absolute and relative terms.

Solution:

• Find labor productivity in the base year using the formula:

P_t = V / C_h

Where:

• (V) is the volume of production.
• (C_h) is the number of workers.
• (P_t) is labor productivity.

Pt = 4 550 000 / 330 ≈ 13 788 USD/person

• Find the change in the number of workers and the volume of production in the planned year:

C_hpl = 330 * 1.1 = 363  workers

V_pl = 4 550 000 * 1.06 = 4 823 000 USD

• Find labor productivity in the planned year:

Pt_pl = 4 823 000 / 363 ≈ 13 286 USD/person

• Find the change in labor productivity in relative terms:

I_Pt = 13 286 / 13 788 ≈ 0.964

Labor productivity decreased by 3.6%.

• Find the decrease in labor productivity in absolute terms:

Δ_Pt = 13 788 - 13 286 = 502 USD

Answer:

• Pt_b  = 13 788 USD / person
• Pt_pl  = 13 286 USD / person
• I_Pt= 0.964
• Δ_Pt = - 502 USD

Problem 7: Determine Labor Productivity for Commercial Output

Determine the labor productivity of workers employed at the enterprise if it is known that the volume
of commercial output is 2 950 thousand USD, and the number of workers is 58 people.

Solution:

Labor productivity is an indicator of the efficiency of personnel. It is the amount of products produced by a worker per unit of time.

P_t = V / C_h

Where:

• (V) is the volume of marketable products.
• (C_h) is the number of employees.

Let’s find labor productivity:

P_t = 2,950,000 / 58 ≈ 50 862 USD / person

Answer: Labor productivity was 50 862 USD of marketable products per person.

Problem 8: Change in Labor Productivity as a Result of Changes in the Number and Output

In the planning year, the output of product B increased by 30%. The number of workers increased by 2 people.
In the base year, the number of workers was 274 people. The number of other categories of workers does not change.
Determine how the labor productivity of the main workers engaged in the production of product B will change.

Solution:

The change in labor productivity of workers is calculated using the formula:

ΔPT = I_v / I_h

Where:

• I_v is the index of commercial output.
• I_h is the index of workers.

The numerator takes into account the change in the volume of production, and the denominator takes into account
the change in the number of workers. These values are used as indices.

• Find the change in the number of employees at the enterprise:

I_h = ( 274 + 2 ) / 274 = 1.0073

• Find the index of commercial output:

I_v = 1.30

• Find the change in labor productivity:

ΔPT = 1.30 / 1.0073 ≈ 1.291

Labor productivity increased by 29.1%.

Answer: Labor productivity increased by 29.1%.

Problem 9: Change in Labor Productivity as a Result of Change in Fulfillment of Production Standards

In the base period, workers on average fulfilled time standards by 115%. After the introduction of organizational and technical measures,
time standards began to be fulfilled by 125%. How did labor productivity change as a result?

Solution:

Along with the labor productivity indicator, there are indicators of fulfillment of time standards and fulfillment of production standards.

• Fulfillment of time standards is the time required to produce one product.
• Production standard is the amount of product that must be produced per unit of time.

The percentage of fulfillment of standards is determined as the ratio of actual indicators to planned indicators.

• Calculate the change in labor productivity:

ΔPT = ( 125 / 115 ) * 100% - 100% ≈ 8.7\%

Answer: Labor productivity increased by 8.7%.

Problem 10: Change in Labor Productivity with a Decrease in the Labor Intensity of the Product

The labor intensity of the product decreased by 15%. Determine how labor productivity will change.

Solution:

The labor intensity indicator is the inverse of the labor productivity indicator. There are inversely proportional relationships between labor productivity and the labor intensity of a product.

• ΔI is the percentage decrease in labor intensity of a product.
• ΔPt is the percentage increase in labor productivity of a product.

1. Find the change in labor productivity:

ΔPT = 15% / ( 100% - 15% ) * 100 ≈ 17.65%

Answer: Due to a 15% decrease in labor intensity, labor productivity increased by 17.65%.

Problem 11: Change in Labor Intensity When Labor Productivity Changes

Determine how the labor intensity of a manufactured product will change if it is known that the change in labor productivity is 20%.

Solution:

Let’s calculate the change in labor intensity using the formula:

• ΔI  is the percentage change in labor intensity.
• ΔPt is the percentage change in labor productivity.

ΔI = 20% / (100% - 20%) * 100% = 25%

Answer: Labor intensity decreased by 25% due to an increase in labor productivity by 20%.

Problem 12: Calculations for Changing Productivity Growth and Labor Intensity Simultaneously

As a result of organizational measures, labor productivity in the team increased by 14.5%.
Partial modernization of equipment allowed reducing labor intensity by 7%.
Determine the growth for each measure separately.

Solution:

1. Change in labor intensity due to the increase in labor productivity:

The change in labor intensity ΔI can be calculated using the formula:

ΔI= ΔPt / (100% - ΔPt ) * 100%

Where:

• ΔPt is the percentage increase in labor productivity.

ΔI = 14.5% / ( 100% - 14.5% ) * 100% ≈ 16.96%

The labor intensity of the product decreased by 16.96% due to an increase in labor productivity by 14.5%.

The increase in labor productivity ΔPt can be calculated using the formula:

ΔPt   = ΔI  / ( 100% - ΔI  ) * 100%

Where:

• ΔI  is the percentage decrease in labor intensity.

ΔPt = ( 7% / ( 100% - 7%)  * 100% ≈ 7.53%

Labor productivity increased by 7.53% due to a decrease in labor intensity by 7%.

Answer: The first event led to a decrease in the labor intensity of the product by 16.96%,
and the second event led to an increase in labor productivity by 7.53%.

Problem 13: Determine the Decrease in Labor Intensity Due to an Increase in Labor Productivity

Labor productivity in the section increased by 16%, and the number of personnel remained unchanged.
Determine the decrease in labor intensity of products in the section and the change in production volume.

Solution:

Since the number of workers remained unchanged, the production volume increased by 16%.

The reduction in labor intensity ΔI can be calculated using the formula:

ΔI = ΔPt  / ( 100% - ΔPt ) * 100%

Where:

• ΔPt  is the percentage increase in labor productivity.

ΔI = 16% / ( 100% - 16% ) * 100% ≈ 19.05%

Labor intensity decreased by 19.05%.

Answer: The reduction in labor intensity was 19.05%, and the production volume increased by 16%.

Problem 14: Increase in Labor Productivity Due to Several Measures

The increase in labor productivity with the help of the first group of measures was 17%,
and with the help of the second by 7%. Determine the total change in labor productivity.

Solution:

Labor productivity changes due to the implementation of various measures at the enterprise. To find the total increase
in labor productivity due to several measures, you need to multiply the indices of growth (or decrease) in labor productivity.

1. Find the total change in labor productivity:

ΔPt  = 1.17 * 1.07 ≈ 1.2519

Labor productivity increased by 25.19% overall with the help of all the measures.

Answer: Labor productivity increased by 25.19% overall with the help of all the measures.