Step-by-Step Guidance for Problem Set 1

Q1. Calculating Nominal and Real GDP Growth Rates Using Different Base Years

Background

Topic: GDP Measurement and Growth Rates

This question tests your understanding of how to calculate nominal and real GDP, and how the choice of base year affects the measurement of real GDP growth rates.

Key Terms and Formulas:

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

• Real GDP: The value of goods and services produced, measured using prices from a base year.

• Growth Rate Formula: $\frac{GDP_{t+1} - GDP_t}{GDP_t} \times 100\%$

Step-by-Step Guidance

1. Identify the quantities and prices for each good in both years, and calculate nominal GDP for each year by multiplying quantity by price and summing across goods.

2. To calculate real GDP for a given year using a base year, use the quantities from the year in question and the prices from the base year.

3. Compute the real GDP growth rate by applying the growth rate formula to the real GDP values for the two years.

4. Repeat the calculation using a different base year to see how the growth rate changes.

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Q2. Calculating Inflation Rate Using GDP Deflator with Different Base Years

Background

Topic: Inflation Measurement

This question tests your ability to calculate the inflation rate using the GDP deflator, and to understand how the choice of base year affects the inflation rate calculation.

Key Terms and Formulas:

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

• Inflation Rate Formula: $\frac{\text{Deflator}_{t+1} - \text{Deflator}_t}{\text{Deflator}_t} \times 100\%$

Step-by-Step Guidance

1. Calculate the GDP deflator for each year using the formula above.

2. Apply the inflation rate formula to the GDP deflators for the two years.

3. Repeat the calculation using a different base year to see how the inflation rate changes.

4. Compare the results and consider why the inflation rates differ depending on the base year.

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Q3. Income and Output: Equivalent Definitions of GDP

Background

Topic: GDP Measurement Approaches

This question tests your understanding of the three equivalent ways to measure GDP: by final sales, by total income, and by value-added.

Key Terms and Formulas:

• GDP by Final Sales: Sum of sales of final goods and services.

• GDP by Income: Sum of wages, profits, and other income earned in production.

• GDP by Value-Added: Value of output minus value of intermediate goods.

Step-by-Step Guidance

1. Identify which goods are final and which are intermediate in the economy described.

2. Calculate GDP using the value of sales of final goods (applesauce in this case).

3. Sum up wages and profits across all industries to find total income.

4. Calculate value-added for each industry: for the apple industry, value-added equals sales; for the applesauce industry, subtract the cost of apples from sales.

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Q4. Is Positive GDP Growth Sufficient to Reduce Unemployment?

Background

Topic: GDP Growth and Unemployment

This question tests your understanding of the relationship between GDP growth and changes in the unemployment rate, including the role of labor productivity and labor force growth.

Key Terms:

• Labor Productivity Growth: Increase in output per worker.

• Labor Force Growth: Increase in the number of workers.

• Threshold GDP Growth: The minimum GDP growth rate needed to reduce unemployment.

Step-by-Step Guidance

1. Recall that unemployment falls only if GDP growth exceeds the sum of labor productivity growth and labor force growth.

2. Consider how increases in labor productivity and labor force can affect the unemployment rate.

3. Think about why positive GDP growth alone may not be enough to reduce unemployment.

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Q5. Calculating Real Wage and Wage Inflation

Background

Topic: Real vs. Nominal Wages and Inflation

This question tests your ability to calculate real wages, wage inflation, and price inflation, and to understand the relationship between these measures.

Key Terms and Formulas:

• Real Wage: $\text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}}$

• Percentage Change Formula: $\frac{\text{Value}_{t+1} - \text{Value}_t}{\text{Value}_t} \times 100\%$

Step-by-Step Guidance

1. Calculate the real wage for each year using the formula above.

2. Compute the percentage change in real wage between the two years.

3. Calculate the percentage change in nominal wage and CPI separately.

4. Compare the difference between wage inflation and price inflation, and consider why it may not equal the change in real wage.

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Q6. Effects of Asset Transactions and Inventory Changes on GDP

Background

Topic: GDP Components and Measurement

This question tests your understanding of which transactions affect GDP and how inventory changes are treated in GDP accounting.

Key Terms:

• Asset Transactions: Exchanges of existing assets (e.g., stocks) do not affect GDP.

• Inventory Changes: Unsold goods produced in a year are counted as inventory investment and included in GDP.

Step-by-Step Guidance

1. Consider whether the purchase of stock from another resident involves production of goods or services.

2. Analyze how the production and sale of a car in different years affects GDP and its components (consumption, investment).

3. Think about how inventory changes are recorded in GDP accounting.

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Q7. Present Value and Real Interest Rate Calculations

Background

Topic: Present Value and Real Interest Rate

This question tests your ability to calculate the real interest rate using both exact and approximate formulas, and to understand the implications for present value calculations.

Key Formulas:

• Exact Real Interest Rate: $1 + r = \frac{1 + i}{1 + \pi}$

• Approximate Real Interest Rate: $r \approx i - \pi$

Step-by-Step Guidance

1. Identify the nominal interest rate ($i$) and inflation rate ($\pi$) for each scenario.

2. Apply the exact formula to calculate the real interest rate.

3. Use the approximate formula to estimate the real interest rate.

4. Compare the results from the exact and approximate methods.

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Q8. Human Wealth and Professional School Investment

Background

Topic: Human Capital and Present Value

This question tests your ability to calculate human wealth, the present value of lifetime earnings, and the maximum expenditure on professional school based on changes in salary and tax rates.

Key Formulas:

• Human Wealth: $\text{Human Wealth} = N \times (1 - \text{tax rate}) \times \text{annual salary}$

• Maximum Expenditure: Difference in human wealth with and without professional school.

Step-by-Step Guidance

1. Calculate human wealth for both scenarios (with and without professional school) using the formula above.

2. Find the difference between the two to determine the maximum expenditure on professional school.

3. Repeat the calculation with a different tax rate to see how the result changes.

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Q9. Yield Curve Response to Changes in Expected Interest Rates

Background

Topic: Yield Curve and Interest Rate Expectations

This question tests your understanding of how changes in expected future short-term interest rates affect the shape of the yield curve.

Key Terms:

• Yield Curve: Graph showing the relationship between bond yields and maturities.

• Term Premium: Additional yield for holding longer-term bonds.

Step-by-Step Guidance

1. Recall that the yield on a bond is related to the average of expected future short-term interest rates.

2. Consider how a permanent increase in expected short-term rates starting 10 years from now affects yields for bonds with maturities longer than 10 years.

3. Think about how the slope of the yield curve changes as a result.

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Q10. Effects of Real Interest Rate and Equity Premium on Stock Prices

Background

Topic: Stock Valuation and Expected Returns

This question tests your understanding of how changes in the real interest rate and equity premium affect the present value of future dividends and stock prices.

Key Formulas:

• Present Value of Dividends: $\text{PV} = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r + \text{equity premium})^t}$

Step-by-Step Guidance

1. Consider how a decline in the real interest rate affects the discount rate used in present value calculations.

2. Analyze how the present value of future dividends changes as the discount rate decreases.

3. Think about the effect on expected real return on equity investment.

4. Repeat the analysis for a decline in the equity premium.

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Q11. Effects of Changes in Expected Dividends and Earnings on Stock Prices

Background

Topic: Stock Valuation and Information Effects

This question tests your understanding of how changes in expected dividends and historical earnings affect stock prices.

Key Terms:

• Expected Dividends: Forecasted future payments to shareholders.

• Fundamental Value: Present value of expected future dividends.

Step-by-Step Guidance

1. Consider how an increase in expected future dividends affects the present value and stock price.

2. Analyze whether changes in historical earnings (without changes in expected dividends) affect stock price.

3. Think about the role of expectations versus historical information in stock valuation.

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Q12. Present Value of Investment and Labor Income

Background

Topic: Present Value and Saving Decisions

This question tests your ability to calculate the expected present discounted value (EPDV) of investment and labor income, and to analyze saving and wealth accumulation across life stages.

Key Formulas:

• EPDV: $\text{EPDV} = \sum_{t=1}^{N} \frac{\text{Expected Profits}_t}{(1 + r)^t} - \text{Cost}$

• Saving: $\text{Saving} = \text{Income} - \text{Consumption}$

• Total Wealth: Sum of savings across all periods.

Step-by-Step Guidance

1. Calculate the EPDV of investment by discounting expected profits and subtracting the cost.

2. Determine saving and consumption for each life stage (young, middle-aged, old).

3. Sum savings across all periods to find total wealth accumulation.

4. Analyze how changes in income, consumption, and financial liberalization affect saving and wealth.

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