Question

As part of a study for the Department of Labor Statistics, you are assigned the task of evaluating the improvement in productivity of small businesses. Data for one of the small businesses you are to evaluate is shown below. The data are the monthly average of last year and the monthly average this year. Labor $6 per hour; Capital 0.79% per month of investment; Energy $0.85 per BTU. Click the icon to view the data for one of the small businesses you are to evaluate. a) Determine the multifactor productivity with dollars as the common denominator for last year. The multifactor productivity with dollars as the common denominator for last year is dozen/\$. (Round your response to three decimal places.)

Answer 1

U.S. productivity per worker is measured by the dollar value per hour contributed to the employer's output, excluding government workers and farming. To forecast future productivity levels, use the formula for compound growth with the provided annual growth rates. Upon calculation, compare the productivity levels to determine which country will have a higher level of productivity after the specified time.

Step-by-step explanation:

The scenario presented involves calculating multifactor productivity for a small business, comparing the monthly averages of last year with this year. Based on the information provided about U.S. productivity per worker, for which the common measure is the dollar value per hour contributed by the worker to the employer's output, we can understand historical trends in the productivity of U.S. workers. These trends show that productivity has more than doubled since the 1970s and experienced fluctuations with periods of increase and decrease over the decades. When considering the scenarios of worker productivity growth between Canada and the UK, or between the U.S. and Mexico, it's important to apply the given growth rates to forecast future productivity levels.

To determine who will have the higher productivity level after five years between Canada and the UK, we can use the formula for compound growth:

1. Canada's productivity after five years = $30 * (1 + 0.01)^5
2. UK's productivity after five years = $25 * (1 + 0.03)^5

After calculating, we compare the results to see which country has the higher productivity level. Similarly, to find out which country will have higher worker productivity between the U.S. and Mexico after 25 years, we use the compound growth rates provided:

1. U.S. productivity after 25 years = Initial U.S. productivity * (1 + 0.02)^25
2. Mexico's productivity after 25 years = Initial Mexico's productivity * (1 + 0.06)^25

By solving these, we'd get the answer to which country will be more productive after 25 years.

Answer 2

After five years, Canada's productivity will be approximately $31.53 per hour while the UK's will be about $29.04 per hour, making Canada still more productive by about $2.49 per hour. The U.S. is projected to maintain a higher productivity level than Mexico after 25 years despite Mexico's higher growth rate due to the large initial productivity ratio.

Step-by-step explanation:

To evaluate which country will have higher worker productivity after five years, we begin by calculating the projected productivity for Canada and the United Kingdom (UK). Canada starts at $30 per hour, growing at 1% per year. Using compound growth, the formula to calculate the final productivity after 5 years is $30 × (1 + 0.01)^5. For the UK, starting at $25 per hour and growing at 3% per year, the formula is $25 × (1 + 0.03)^5.

Calculating these, Canada's productivity after 5 years would be approximately $31.53 per hour and the UK's productivity would be about $29.04 per hour. Therefore, Canada will still have the higher productivity level by approximately $2.49 per hour.

For the case involving the U.S. and Mexico, we apply a similar approach. The current productivity ratio is 8:1 in favor of the U.S. After 25 years, with the U.S. growing at 2% per year and Mexico at 6% per year, we use the formula for compound growth again to determine the projected productivity. Even with faster growth, Mexico's productivity won't surpass that of the U.S. within this time frame.