Worked Problems (2024)

Chapter25:Economic Growth

Worked Problems

Problem 25.1 - GDP growth

Problem:

Consider the following data for a hypothetical economy:

Year

Real GDP

Population

1

$50,000

200

2

$51,400

202

  1. Calculate the growth rate of real GDP over the year.
  2. At this rate of growth, approximately how many years will pass before real GDP doubles?
  3. Find real GDP per capita in each of the two years. Using these two values, calculate the growth rate of real GDP per capita over the year.
  4. At this rate of growth, approximately how many years will pass before real GDP per capita doubles?

Answer:

  1. The rate of growth is [($51,400 - $50,000)/$50,000] x 100 = 2.8%.
  2. The rule of 70 tells us that real GDP will double in approximately 70/2.8 = 25 years.
  3. Real GDP per capita in year 1 is $50,000/200 = $250, while in year 2 it is $51,400/202 = $254.46. The growth rate of real GDP per capita is then found as [($254.46 - 250)/250] x 100 = 1.78%.
  4. The rule of 70 suggests that real GDP per capita will double in approximately 70/1.78 = 39.3 years.

Problem 25.2 - Productivity and economic growth

Problem:

Suppose an economy's real GDP is $5,000 billion. There are 125 million workers, each working an average of 2,000 hours per year.

  1. What is labor productivity per hour in this economy?
  2. Suppose worker productivity rises by 5% over the following year and the labor force grows by 1%. What is the projected value of real GDP?
  3. Based on your previous answer, what is this economy's rate of growth?

Answer:

  1. Labor productivity can be found as real GDP divided by hours of work. There are 2,000 x 125 million = 250 billion worker hours available in the economy, producing a real GDP of $5,000 billion. Labor productivity is then $5,000/250 = $20 per worker-hour.
  2. Productivity will rise by 5% to $21 (20 + .05 x 20 = 21) and work hours will rise by 1% to 252.5 billion (250 + .01 x 250 = 252.5). Since real GDP equals work hours times productivity, real GDP will rise to 252.5 billion x $21 = $5302.5 billion.
  3. The rate of growth is just over 6% [100 x (5,302.5 – 5,000) / 5,000 = 6.05].
Worked Problems (1)
Worked Problems (2024)

FAQs

What are examples of work problems? ›

Ernie can plow a field alone in four hours. It takes Sid five hours to plow the same field alone. If they work together (and each has a plow), how long will it take to plow the field?

What is a working problem? ›

Work problems are those that involve the speeds of people and/or machines. We will teach you how to calculate how long it will take for multiple workers to perform a job. This lesson is broken down into three sections: Rationale for Learning Work Problems.

What is the formula for the work problem? ›

Given below are a few such important time and work formulas for your reference: Work Done = Time Taken × Rate of Work. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work.

What is the work problem word problem? ›

What is a 'Work' Word Problem? It involves a number of people or machines working together to complete a task. We are usually given individual rates of completion. We are asked to find out how long it would take if they work together.

What is a common work problem? ›

Employees of every position face challenges at work such as communication, lack of motivation, workload, technology issues, and more. Hence, workplace challenges make it difficult for everyone to perform their tasks smoothly.

What is an example of a problem at work? ›

Bullying or harassment. Performance issues. Bad job fit or lack of training. No job satisfaction.

What is job related problems? ›

Work-related problems can affect our physical, emotional and mental health. Common issues include job dissatisfaction, workplace injury, stress, discrimination and bullying, violence, accidental death and retirement. Job loss, retrenchment or unexpected loss of income can also cause distress and hardship.

What are complex problems at work? ›

Complex problems are those problems that do not have a simple answer. Instead, there are lots of potential answers, and there are links or interdependencies between different things that mean that solving part of a problem might create new ones.

What is a workplace issue? ›

Workplace issues are incidents that are seen as inappropriate by the person experiencing or. observing the issue; they can arise every day and in many different situations. Workplace issues can. vary in terms of seriousness; they may be low level or a one off incident that is inappropriate in.

What is an example of a real life word problem? ›

A simple example of a math word problem is, "If Becky has 7 apples and gives 2 away, how many apples does she have left?" An example of a more complex word problem featuring algebra is, "Ben is three times as old as John. The sum of their ages is 40 years. How old is each of them?"

How to solve a work problem? ›

Here are seven-steps for an effective problem-solving process.
  1. Identify the issues.
  2. Understand everyone's interests.
  3. List the possible solutions (options)
  4. Evaluate the options.
  5. Select an option or options.
  6. Document the agreement(s).
  7. Agree on contingencies, monitoring, and evaluation.
Jul 11, 2023

What is an example of work done? ›

There are many examples of work done in our everyday life. For example, a horse pulling a plow through the field, a father pushing a grocery cart in a shopping mall, or a student lifting a bag on his back or his shoulder full of books and many more.

What are the 3 types of word problems? ›

Combine problems are problems that put together two or more separate parts to make a total. Compare problems are when two sets are compared to find the difference. Change problems are when an amount increases (goes up) or decreases (goes down) because something changes or happens to the starting number.

How to solve time work problems? ›

Time and Work Formula for Competitive Exams
  1. Work = time taken × Rate of work.
  2. Rate of work = 1/time taken.
  3. Time taken to finish a task = 1/rate of work.
  4. work done in 1 day = 1/n, where n = total number of days required to do the work.
  5. Efficiency = work/time.
  6. work = efficiency x number of days.
Oct 28, 2023

How to solve work together problems? ›

How do you solve a problem where 2 people work together, but one person leaves after some days? 1) Add their hourly rates to determine how much they complete in 1 day. 2) Multiply that figure by how many days they work together. 3) Subtract that rate from the whole, to determine how much work still needs to be done.

What is an example of a concern at work? ›

Common workplace concerns include respect and civility, work style differences, excessive stress, job/role clarity, general climate, management skills, and performance issues. For example, an employee may bring issues to the Staff Ombuds Office when the employee: Feels they have been treated rudely or excluded.

What are examples of causes of the problem in a workplace? ›

What causes workplace conflict?
  • poor management.
  • unfair treatment.
  • unclear job roles.
  • inadequate training.
  • poor communication.
  • poor work environment.
  • lack of equal opportunities.
  • bullying and harassment.

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