Macroeconomics Exam 2 Worksheet Step-by-Step Guidance

Q1a. Calculate nominal GDP for 2015.

Background

Topic: GDP Calculation

This question tests your understanding of how to calculate nominal GDP, which is the total value of goods and services produced in a country in a given year, using current prices.

Key Terms and Formulas

• Nominal GDP: The value of all final goods and services produced within a country in a given year, measured using current prices.

• Formula: $\text{Nominal GDP} = \sum (\text{Price} \times \text{Quantity})$ for each good.

Step-by-Step Guidance

1. Identify the prices and quantities for each good in 2015: Milk ($5$, $250$ quarts), Honey ($5$, $200$ quarts).

2. Multiply the price and quantity for each good to find the total value produced for each.

3. Add the values for milk and honey to get the total nominal GDP for 2015.

Try solving on your own before revealing the answer!

Final Answer: $2250$

$\text{Nominal GDP}_{2015} = (5 \times 250) + (5 \times 200) = 1250 + 1000 = 2250$

The nominal GDP for 2015 is $2250, calculated using current prices and quantities.

Q1b. Calculate real GDP for 2015 using 2013 as the base year.

Background

Topic: Real GDP Calculation

This question tests your ability to calculate real GDP, which measures the value of goods and services produced using constant prices from a base year.

Key Terms and Formulas

• Real GDP: The value of all final goods and services produced within a country in a given year, measured using prices from a base year.

• Formula: $\text{Real GDP}_{2015} = \sum (\text{Price}_{2013} \times \text{Quantity}_{2015})$

Step-by-Step Guidance

1. Identify the base year prices (2013): Milk ($2$), Honey ($2$).

2. Use the 2015 quantities: Milk ($250$), Honey ($200$).

3. Multiply the base year price by the current year quantity for each good.

4. Add the values for milk and honey to get the total real GDP for 2015.

Try solving on your own before revealing the answer!

Final Answer: $900$

$\text{Real GDP}_{2015} = (2 \times 250) + (2 \times 200) = 500 + 400 = 900$

The real GDP for 2015, using 2013 prices, is $900.

Q1c. Calculate the GDP deflator for 2015 using 2013 as the base year.

Background

Topic: GDP Deflator

This question tests your understanding of the GDP deflator, which measures the change in prices of all new, domestically produced, final goods and services in an economy.

Key Terms and Formulas

• GDP Deflator: An index that measures the price level of all domestically produced goods and services.

• Formula: $\text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100$

Step-by-Step Guidance

1. Recall the nominal GDP and real GDP for 2015 from previous parts.

2. Plug these values into the GDP deflator formula.

3. Set up the calculation, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $250$

$\text{GDP Deflator}_{2015} = \frac{2250}{900} \times 100 = 250$

The GDP deflator for 2015, using 2013 as the base year, is 250.

Q1d. What is the inflation rate from 2013 to 2014? From 2014 to 2015?

Background

Topic: Inflation Rate Calculation

This question tests your ability to calculate the inflation rate using the GDP deflator or price indices.

Key Terms and Formulas

• Inflation Rate: The percentage change in the price level from one year to the next.

• Formula: $\text{Inflation Rate} = \frac{\text{Deflator}_{\text{new}} - \text{Deflator}_{\text{old}}}{\text{Deflator}_{\text{old}}} \times 100$

Step-by-Step Guidance

1. Calculate the GDP deflator for each year (2013, 2014, 2015) using the formula from part c.

2. Use the deflator values to set up the inflation rate formula for each period: 2013 to 2014, and 2014 to 2015.

3. Plug in the values, but stop before calculating the final percentage.

Try solving on your own before revealing the answer!

Final Answer: 100% from 2013 to 2014; 25% from 2014 to 2015

From 2013 to 2014: $\frac{200 - 100}{100} \times 100 = 100\%$

From 2014 to 2015: $\frac{250 - 200}{200} \times 100 = 25\%$

The inflation rate was 100% from 2013 to 2014 and 25% from 2014 to 2015.

Q2a. Calculate the unemployment rate.

Background

Topic: Unemployment Rate

This question tests your ability to calculate the unemployment rate, which is the percentage of the labor force that is unemployed.

Key Terms and Formulas

• Unemployment Rate: The percentage of the labor force that is unemployed.

• Formula: $\text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor Force}} \times 100$

• Labor Force: Employed + Unemployed

Step-by-Step Guidance

1. Identify the number of employed (3,500) and unemployed (500).

2. Calculate the labor force: $3,500 + 500$.

3. Plug the values into the unemployment rate formula.

Try solving on your own before revealing the answer!

Final Answer: 12.5%

$\text{Unemployment Rate} = \frac{500}{4,000} \times 100 = 12.5\%$

The unemployment rate is 12.5%.

Q2b. Calculate the labor-force participation rate.

Background

Topic: Labor-Force Participation Rate

This question tests your ability to calculate the labor-force participation rate, which is the percentage of the adult population that is in the labor force.

Key Terms and Formulas

• Labor-Force Participation Rate: The percentage of the adult population that is in the labor force.

• Formula: $\text{Labor-Force Participation Rate} = \frac{\text{Labor Force}}{\text{Adult Population}} \times 100$

• Adult Population: Employed + Unemployed + Not in Labor Force

Step-by-Step Guidance

1. Calculate the adult population: $3,500 + 500 + 1,000$.

2. Calculate the labor force: $3,500 + 500$.

3. Plug the values into the labor-force participation rate formula.

Try solving on your own before revealing the answer!

Final Answer: 80%

$\text{Labor-Force Participation Rate} = \frac{4,000}{5,000} \times 100 = 80\%$

The labor-force participation rate is 80%.

Q3a. Using 2013 as a base year, calculate the CPI in 2014.

Background

Topic: Consumer Price Index (CPI)

This question tests your ability to calculate the CPI, which measures the average change in prices paid by consumers for a fixed basket of goods.

Key Terms and Formulas

• CPI: Consumer Price Index

• Formula: $\text{CPI}_{\text{year}} = \frac{\text{Cost of Basket in Year}}{\text{Cost of Basket in Base Year}} \times 100$

Step-by-Step Guidance

1. Identify the basket: 100 quarts of milk and 50 quarts of honey.

2. Calculate the cost of the basket in 2013: $(100 \times 1) + (50 \times 2)$.

3. Calculate the cost of the basket in 2014: $(100 \times 2) + (50 \times 3)$.

4. Plug these values into the CPI formula for 2014.

Try solving on your own before revealing the answer!

Final Answer: 167

$\text{CPI}_{2014} = \frac{(100 \times 2) + (50 \times 3)}{(100 \times 1) + (50 \times 2)} \times 100 = \frac{200 + 150}{100 + 100} \times 100 = \frac{350}{200} \times 100 = 175$

The CPI in 2014, using 2013 as the base year, is 175.

Q3b. Using 2013 as a base year, calculate the CPI in 2015.

Background

Topic: Consumer Price Index (CPI)

This question tests your ability to calculate the CPI for a later year using the same basket and base year prices.

Key Terms and Formulas

• Formula: $\text{CPI}_{2015} = \frac{\text{Cost of Basket in 2015}}{\text{Cost of Basket in 2013}} \times 100$

Step-by-Step Guidance

1. Calculate the cost of the basket in 2015: $(100 \times 3) + (50 \times 4)$.

2. Recall the cost of the basket in 2013 from previous part.

3. Plug these values into the CPI formula for 2015.

Try solving on your own before revealing the answer!

Final Answer: 250

$\text{CPI}_{2015} = \frac{(100 \times 3) + (50 \times 4)}{(100 \times 1) + (50 \times 2)} \times 100 = \frac{300 + 200}{200} \times 100 = \frac{500}{200} \times 100 = 250$

The CPI in 2015, using 2013 as the base year, is 250.

Q3c. Calculate the inflation rate from 2014 to 2015.

Background

Topic: Inflation Rate Calculation

This question tests your ability to calculate the inflation rate using CPI values.

Key Terms and Formulas

• Formula: $\text{Inflation Rate} = \frac{\text{CPI}_{2015} - \text{CPI}_{2014}}{\text{CPI}_{2014}} \times 100$

Step-by-Step Guidance

1. Recall the CPI values for 2014 and 2015 from previous parts.

2. Plug these values into the inflation rate formula.

3. Set up the calculation, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: 42.86%

$\text{Inflation Rate} = \frac{250 - 175}{175} \times 100 = 42.86\%$

The inflation rate from 2014 to 2015 is approximately 42.86%.

Q4. What is the value of a $45,000 salary in 1991 in 2016 dollars if the CPI in 1991 was 136 and the CPI in 2016 was 240?

Background

Topic: Adjusting for Inflation

This question tests your ability to adjust a past salary to its equivalent value in a later year using CPI values.

Key Terms and Formulas

• Formula: $\text{Value in 2016 dollars} = \text{Value in 1991 dollars} \times \frac{\text{CPI}_{2016}}{\text{CPI}_{1991}}$

Step-by-Step Guidance

1. Identify the original salary ($45,000), CPI in 1991 (136), and CPI in 2016 (240).

2. Plug these values into the formula for adjusting for inflation.

3. Set up the calculation, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $79,411.76

$\text{Value in 2016 dollars} = 45,000 \times \frac{240}{136} \approx 79,411.76$

The equivalent value of a $45,000 salary in 1991 is about $79,411.76 in 2016 dollars.

Q5. If real GDP per capita in the United States grew at a rate of 2.25 percent from 2010 to 2011, how long would it take for the economy to double?

Background

Topic: Rule of 70 (Growth Rates)

This question tests your ability to estimate the time required for a variable to double given a constant growth rate, using the Rule of 70.

Key Terms and Formulas

• Rule of 70: $\text{Years to Double} = \frac{70}{\text{Growth Rate (in percent)}}$

Step-by-Step Guidance

1. Identify the growth rate: 2.25% per year.

2. Plug the growth rate into the Rule of 70 formula.

3. Set up the calculation, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: 31.1 years

$\text{Years to Double} = \frac{70}{2.25} \approx 31.1$

It would take approximately 31.1 years for the economy to double at a 2.25% growth rate.

Q6. If GDP had grown at 2.0%, 3.0%, 3.5%, and 2.5% over the last four years respectively, what would the average growth rate be?

Background

Topic: Average Growth Rate Calculation

This question tests your ability to calculate the average growth rate over multiple periods.

Key Terms and Formulas

• Formula: $\text{Average Growth Rate} = \frac{\text{Sum of Growth Rates}}{\text{Number of Years}}$

Step-by-Step Guidance

1. Add up the growth rates: 2.0%, 3.0%, 3.5%, 2.5%.

2. Divide the sum by the number of years (4).

3. Set up the calculation, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: 2.75%

$\text{Average Growth Rate} = \frac{2.0 + 3.0 + 3.5 + 2.5}{4} = \frac{11.0}{4} = 2.75\%$

The average growth rate over the four years is 2.75%.

Q7. Calculate public and private savings for the Economy of Asgard.

Background

Topic: Savings Calculation

This question tests your ability to calculate public and private savings using national income accounting.

Key Terms and Formulas

• Private Savings: $\text{Private Savings} = \text{GDP} - \text{Taxes} + \text{Transfer Payments} - \text{Consumption}$

• Public Savings: $\text{Public Savings} = \text{Taxes} - \text{Government Purchases} - \text{Transfer Payments}$

Step-by-Step Guidance

1. Identify the relevant values: GDP ($500$million), Consumption ($350$ million), Investment ($100$million), Government Purchases ($50$ million), Taxes ($75$million), Transfer Payments ($40$ million).

2. Plug these values into the formulas for private and public savings.

3. Set up the calculations, but do not compute the final values yet.

Try solving on your own before revealing the answer!

Final Answer: Private Savings = $85 million; Public Savings = -$15 million

$\text{Private Savings} = 500 - 75 + 40 - 350 = 85$ million

$\text{Public Savings} = 75 - 50 - 40 = -15$ million

Private savings is $85 million, and public savings is -$15 million (a deficit).

Q8. Draw the graph of the Market for Loanable Funds that demonstrates the effects of crowding out.

Background

Topic: Loanable Funds Market and Crowding Out

This question tests your understanding of the market for loanable funds and the concept of crowding out, which occurs when increased government borrowing raises interest rates and reduces private investment.

Key Terms and Concepts

• Loanable Funds Market: The market where savers supply funds for borrowers.

• Crowding Out: When government borrowing increases, it shifts the demand for loanable funds, raising interest rates and reducing private investment.

Step-by-Step Guidance

1. Draw axes: vertical axis for real interest rate, horizontal axis for quantity of loanable funds.

2. Draw the supply curve (upward sloping) and the demand curve (downward sloping).

3. Show the initial equilibrium where supply and demand intersect.

4. Demonstrate the effect of increased government borrowing by shifting the demand curve to the right.

5. Indicate the new equilibrium with a higher interest rate and lower private investment.

Try sketching the graph on your own before revealing the answer!

Final Answer: Graph Description

The graph should show the supply and demand curves for loanable funds. When government borrowing increases, the demand curve shifts right, raising the equilibrium interest rate and reducing the quantity of loanable funds available for private investment (crowding out).

Label the axes, curves, and show the shift and new equilibrium clearly.