# Homework2

```ECON 252 – Carter – Homework 2
Student Name Here
Due Friday, October 6th, 2023 at 12:00 Noon Eastern Time via Moodle. Anything submitted after that
time will be marked off 10% per 24 hours. Anything submitted 72 hours late will receive zero points.
Question 1 (1 point): You win \$10,000! You decide to save this money for retirement in the stock
market, which earns an average of 7% per year.
How long (approximately, using the Rule of 70) will it take to double your money?
How long exactly will it take to double your money? Is the rule of 70 a good approximation?
Assuming you never deposit money into or withdraw money from this account, what will be the balance
after 1 year, 2 years, 5 years, 10 years, 20 years, and 30 years?
Question 2 (1 point): Suppose total output (GDP) is given by the formula π = πΎ 0.3 π 0.7 . Over the last
year, capital increased by 3.5% and hours worked decreased by 1.6%.
How much does total output change by, rounding to the nearest tenth of a percent.
Did the increase in capital fully offset the decline in labor?
What does this question tell us about the link between unemployment and output?
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ECON 252 – Carter – Homework 2
Student Name Here
Question 3 (1 point): What is depreciation?
Why does capital depreciate?
Choose a type of business to run (not a restaurant or a farm since we used those examples in class or in
the textbook). What types of capital does your business utilize? What does depreciation look like for you
Question 4 (1 point)
What is net investment? How does it depend on the savings rate, the size of the economy, depreciation,
and current capital stock?
In the steady state with zero growth, there is zero net investment. Does this mean that all output in the
economy is used for consumption?
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ECON 252 – Carter – Homework 2
Student Name Here
Question 5 (1 point)
In the US, the savings rate is approximately 25% and the capital-output ratio is about 3. If depreciation is
7.5% per year, is the US in the steady state? (HINT: We know π π = πΏπΎ in the steady state.)
If the US is not in the steady state, what would we expect the final capital-output ratio to be in the
Question 6 (1 point)
What is the biggest difference between the Solow and Romer models of growth?
Which model of growth best explains differences between countries?
Which model of growth best describes long run growth?
Which model do you find more intuitive or interesting? Why?
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ECON 252 – Carter – Homework 2
Student Name Here
Question 7 (1 point)
Unemployment can be categorized into a few high-level types. What are frictional, structural, and
cyclical unemployment? How do these relate to the “natural rate of unemployment”?
Does the natural rate of unemployment ever change? Can the economy ever be below the natural rate
of unemployment? Can it be above the natural rate of unemployment?
Assume that the normal job separation rate is 2% and the matching rate is 25%. Using the bathtub
model, what would we expect the natural rate of unemployment to be?
Question 8 (1 point)
What is human capital?
How does human capital accumulation contribute to economic growth?
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ECON 252 – Carter – Homework 2
Student Name Here
Question 9 (1 point): You graduate college and are presented with two job offers. The first offers to
pay you \$100,000 at the end of each year for five years. The second offers you \$600,000, but it only
pays at the end of the fifth year.
What is the present discounted value of each offer, assuming a discount rate of 5%? Which offer has a
higher PDV?
What would be the present discounted value of each offer, assuming a discount rate of 15%? Which
offer has a higher PDV?
If you were deciding which offer to accept based only on PDV, which would you choose when the
discount rate is 5%? Does your answer change if the discount rate is 15%?
Are there factors you might consider beyond PDV when choosing between these offers? What are
those factors?
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ECON 252 – Carter – Homework 2
Student Name Here
Question 10 (1 point)
Using the quantity theory of money, what happens to the price level if output grows by 3%, velocity is
unchanged, and the money supply increases by 5%?
In Q2 of 2020, real GDP (output) fell by 8.35%. At the same time, the money supply increased by 22.4%.
The CPI only increased by 1.0%. What must have happened to the velocity of money? Using the quantity
theory of the price level, estimate the change in money velocity.
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