Problem Set One
Intermediate Macroeconomics – Economics 3800
J.J. Arias
1. For each time series (i) determine the growth rate of the variable, (ii) compute the next two values in the series (round off two decimal places to the right), and (iii) determine how many years it takes for the series to double in value.
(a) 500, 510, 520.2, 530.604, …
(b) 1500, 1605, 1717.35, 1837.5645, …
(c) 25, 26.25, 27.5625, 28.9406, …
2. For the consumer price index values shown, calculate the rate of inflation in each year from 1930 to 1933. What is unusual about this period, relative to recent experience?
Year: 1929 1930 1931 1932 1933
CPI : 51.3 50.0 45.6 40.9 38.3
3. Assume that Chinese real GDP per capita is approximately 12.5% of real GDP per capita in the United States. If Chinese real GDP per capita grows at 7% per year, and U.S. real GDP per capita grows at 2% annually, how many years will it take for China to catch up with the United States? What is wrong with this type of calculation? (i.e. Do you think China will actually catch up in this year?)
4. Which of the following variables are stocks and which are flows?
consumption, gross domestic product, government debt, government budget deficit, transfer payments, capital, net domestic product, inflation, price level
5. Use the household budget set and the household labor/leisure decision to graphically show the effect of the following events on employment:
(a) an ad valorem tax on labor income
(b) a lump-sum tax
(c) a lump-sum windfall (e.g. receiving an inheritance)
6. Gizmo, Inc. has the following production function.
Workers Gizmos Produced
0 0
1 8
2 15
3 21
4 26
5 30
6 33
(a) Find the MPL for each level of employment
(b) If gizmos sell for $5, how many workers will the firm hire if the (nominal) wage rate is $38? If the wage is $27? If it is $22?
(c) Graph the relationship between the firm’s labor demand and the wage.
(d) With nominal wage fixed at $38, the price of gizmos doubles from $5 to $10. What happens to labor demand and production?
7. In Year 1, a small economy had 25,000 citizens, of whom 20,000 were in the labor force. The unemployment rate was 10%. In Year 2, the economy had 30,000 citizens, of whom 25,000 were in the labor force. The unemployment rate was 12%. For each year,
(a) How many people were unemployed?
(b) What was the participation rate?
(c) What was the employment rate?
2