Practice Problems (Module 1)

Question #1: Crammerville has a population of 100 people, where 50% of the population is working. Each worker produces $5,000 worth of output per year. What is the value of the average Standard of Living?

To find the value of the average standard of living, we first need to decide (1) how much was produced and (2) by how many people. 

We can do this with the following equation:

Total # of Workers * Output per Worker = Total Output

Based on the problem, we know that 50% of the population of 100 people are working...

Question #1: Crammerville has a population of 100 people, where 50% of the population is working. Each worker produces $5,000 worth of output per year. What is the value of the average Standard of Living?

...which equates to 50 total workers.

50 * Output per Worker = Total Output

The problem also states that each worker producers $5,000 in output per year.

Question #1: Crammerville has a population of 100 people, where 50% of the population is working. Each worker produces $5,000 worth of output per year. What is the value of the average Standard of Living?

50 * $5,000 = Total Output

Therefore, the total output is $250,000!

50 * $5,000 = $250,000

Now that we know the total output, we need to distribute it among the entire population. To do so, we'll utilize the following equation:

Total Output / Total Population = Average Standard of Living

Out total output is $250,000...

$250,000 / Total Population = Average Standard of Living

...and based on the problem, the total population of Crammerville is 100...

Question #1: Crammerville has a population of 100 people, where 50% of the population is working. Each worker produces $5000 worth of output per year. What is the value of the average Standard of Living?

$250,000 / 100 = Average Standard of Living

...therefore, the average standard of living for residents of Crammerville is $2,500!

$250,000 / Total Population = $2,500

Question #2: What is the value of labor productivity in Question #1?

Answer: $5,000

Because each worker produces $5,000 worth of goods...

Question #1: Crammerville has a population of 100 people, where 50% of the population is working. Each worker produces $5,000 worth of output per year. What is the value of the average Standard of Living?

...therefore, labor productivity is $5,000.

Question #3: What is the value for Okun’s Gap in % terms if a country has an actual unemployment rate of 5% and a natural unemployment rate of 8%?

Answer: -6%.

Remember, Okun's Gap % is represented by the following formula:

(Yp - Y) / Yp

In addition, Okun's Law is represented by the following equation:

(Yp - Y) / Yp = 2(U - Un)

Notice how Okun's Gap % occurs on the left-side of this equation?

(Yp - Y) / Yp = 2(U - Un)

This means if we solve the right-side, then we'll find Okun's Gap %!

The question states that the unemployment rate is 5%...

Question #3: What is the value for Okun’s Gap in % terms if a country has an actual unemployment rate of 5% and a natural unemployment rate of 8%?

(Yp - Y) / Yp = 2(0.05 - Un)

...and the natural rate of unemployment is 8%...

Question #3: What is the value for Okun’s Gap in % terms if a country has an actual unemployment rate of 5% and a natural unemployment rate of 8%?

(Yp - Y) / Yp = 2(0.05 - 0.08)

...therefore, when we solve the right-side of the equation...

(Yp - Y) / Yp = 2(0.05 - 0.08)
(Yp - Y) / Yp = 2(-0.03)
(Yp - Y) / Yp = -0.06

...we get an Okun's Gap % value of -6%!

Question #4: Labor productivity in a country is decreasing by 2% each year, but the portion of the population who is working is increasing by 5% each year. What is happening to the standard of living each year?

Answer: 3%

To solve this, we can utilize the following equation, with SoL representing "Standard of Living" and %∆ representing "percentage change".

%∆ SoL = %∆ Productivity + %∆ Labor force participation

We know that the % change in productivity is -2%...

Question #4: Labor productivity in a country is decreasing by 2% each year, but the portion of the population who is working is increasing by 5% each year. What is happening to the standard of living each year?

%∆ SoL = -2% + %∆ Labor force participation

...and the % change in labor force participation is +5%...

Question #4: Labor productivity in a country is decreasing by 2% each year, but the portion of the population who is working is increasing by 5% each year. What is happening to the standard of living each year?

%∆ SoL = -2% + 5%

...therefore, the % change in standard of living is 3%!

%∆ SoL = -2% + 5% = 3%

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