Suppose that 20 workers were required in 2010 to produce 120,000 bushels of wheat on a 1,000-acre farm.
a. What is the average output per acre? (?) bushels per acre
What is the average output per worker? (?) bushels per worker
b. If in 2020 only 16 workers produce 132,000 bushels of wheat on that same 1,000-acre farm, what will be the average output per acre? What will be the average output per worker?
(?)bushels per acre
(?)bushels per worker
c. By what percentage does productivity (output per worker) increase over those 10 years?
Instructions: Round your answer to one decimal place.
(?)%
Over those 10 years, what is the average annual percentage increase in productivity?
Instructions: Round your answer to two decimal places.
(?)% per year
To find the answers to these questions, you need to calculate the average output per acre and the average output per worker for both the years 2010 and 2020. Then, you can use these values to determine the percentage increase in productivity and the average annual percentage increase in productivity.
a. To calculate the average output per acre in 2010, divide the total output (120,000 bushels) by the number of acres (1,000):
Average Output per Acre = Total Output / Number of Acres
Average Output per Acre in 2010 = 120,000 bushels / 1,000 acres = 120 bushels per acre
To calculate the average output per worker in 2010, divide the total output (120,000 bushels) by the number of workers (20):
Average Output per Worker = Total Output / Number of Workers
Average Output per Worker in 2010 = 120,000 bushels / 20 workers = 6,000 bushels per worker
b. To calculate the average output per acre in 2020, divide the total output (132,000 bushels) by the number of acres (1,000):
Average Output per Acre in 2020 = 132,000 bushels / 1,000 acres = 132 bushels per acre
To calculate the average output per worker in 2020, divide the total output (132,000 bushels) by the number of workers (16):
Average Output per Worker in 2020 = 132,000 bushels / 16 workers = 8,250 bushels per worker
c. To find the percentage increase in productivity, compare the average output per worker in 2020 to that in 2010 and calculate the percentage increase:
Percentage Increase in Productivity = (New Value - Old Value) / Old Value * 100
Percentage Increase in Productivity = (8,250 - 6,000) / 6,000 * 100 = 37.5%
To find the average annual percentage increase in productivity, divide the total percentage increase over 10 years by the number of years (10):
Average Annual Percentage Increase in Productivity = Percentage Increase in Productivity / Number of Years
Average Annual Percentage Increase in Productivity = 37.5% / 10 years = 3.75% per year
Therefore, the answers to the questions are:
a. Average output per acre in 2010: 120 bushels per acre.
Average output per worker in 2010: 6,000 bushels per worker.
b. Average output per acre in 2020: 132 bushels per acre.
Average output per worker in 2020: 8,250 bushels per worker.
c. Percentage increase in productivity over 10 years: 37.5%.
Average annual percentage increase in productivity: 3.75% per year.