Macroeconomics. Chapter 3

If nominal GDP grew by 7% in year 2 relative to year 1, the price level increased by 2% during the same period and the real GDP in year 1 was $1,000, what was real GDP in year 2?

$1,050 Nominal GDP = Real GDP x Price level. Applying the second property of growth rates: growth rate of nominal GDP = growth rate of real GDP + growth rate of the price level. Growth rate of real GDP = growth rate of nominal GDP - growth rate of the price level. Growth rate of real GDP = 7% - 2% = 5%. The growth rate is the percentage change from year 1 to year 2: 5% = (real GDP in year 2 - 1,000)/1,000. Real GDP in year 2 = $1,050.

In 1994 your parents made an investment of $4,000. By 2015 the investment grew to $32,000. Assuming a constant rate of growth, what was the average annual growth rate of this investment?

10% The data above are plotted using a ratio scale. Since this is a straight line we can conclude that the growth rate is constant. We see that the investment doubles every 7 years (i.e. for 1994 - 2001 the investment grew from $4,000 to $8,000; or use formula 3.9 to verify). Therefore, we can estimate the growth rate using the rule of 70: 70/7 = 10%.

With an average annual growth rate of 5 percent per year, per capita income will increase by what factor over a century?

126 FEEDBACK: Pages 50-51. Applying the Rule of 70 implies 70/5 = 14. Thus, income will double in 14 years. In a century, per capita income will double approximately 7 times, which is 100/14. Thus, GDP per capital will increase by a factor of 27

After graduating college, you start a job making $40,000. Your earnings grow at a constant growth rate of 3 percent per year. When you retire 40 years later, you are earning approximately:

130,000. Apply formula 3.7 where y0 equals 40,000, the growth rate is .03, and t equals 40.

Costs of economic growth

Environmental pollution, breakdown of the family, isolation and alienation, urban congestion

If a variable is growing at a positive constant rate, when plotted on a ratio scale, the slope of the plot will be becoming steeper over time.

False. Straight line

Which of the following is a cost of economic growth?

Job loss in certain sectors Increased income inequality Global warming

rule for computing growth rates:

The average annual growth rate between year 0 and year t is given by g = ((yt / y0)^1/t) - 1

If population and GDP are growing at the same rates, then per capita GDP does not grow.

True

In 1990, a country's per capita income was 1,000. By the year 2000, it was 1,650. The average annual growth rate was approximately 0.05.

True, Apply formula 3.9 where yt is 1650, y0 is 1000 and t is 10.

income tomorrow

Y t+1 = Y t (1 + g)

Growth rate between period t and t+1

Y t+1 − Y t / Yt .

ratio scale

a plot where equally spaced tick marks on the vertical axis are labeled consecutively with numbers that exhibit a constant ratio, like "1, 2, 4, 8, . . ." (a constant ratio of 2) or "10, 100, 1,000, 10,000, . . ." (a constant ratio of 10).

economic growth

a steady, long-term increase in real GDP

constant growth rule

if a variable starts at some initial value y0 at time 0 and grows at a constant rate g , then the value of the variable at some future time t is given by yt = Y0 (1 + g)^t

How quickly GDP doubles will depend on:

the growth rate of GDP.

Rule of 70

Doubling time (in years) = 70/(percentage growth rate).

Chapter summary

SUMMARY 1. Viewed over the long course of history, sustained growth in standards of living is a very recent phenomenon. If the 130,000 years of human history were warped and collapsed into a single year, modern economic growth would have begun only at sunrise on the last day of the year. 2. Modern economic growth has taken hold in different places at different times. Since several hundred years ago, when standards of living across countries varied by no more than a factor of 2 or 3, there has been a "Great Divergence." Standards of living across countries today vary by more than a factor of 100. 3. Incomes in the poorest countries of the world are probably no more than twice as high as average incomes around the world a thousand years ago. 4. Since 1870, growth in per capita GDP has averaged about 2 percent per year in the United States. Per capita GDP has risen from about $3,200 in 1870 to more than $50,800 today. 5. Growth rates throughout the world since 1960 show substantial variation, ranging from negative growth in many poor countries to rates as high as 6 percent per year in several newly industrializing countries, most of which are in Asia. 6. Growth rates typically change over time. In Germany and Japan, growth picked up considerably after World War II as incomes in these countries converged to levels in the United Kingdom. Growth rates have slowed down as this convergence occurred. Brazil exhibited rapid growth in the 1950s and 1960s and slow growth in the 1980s and 1990s. China showed the opposite pattern. 7. Economic growth, especially in India and China, has dramatically reduced poverty in the world. In 1960, 2 out of 3 people in the world lived on less than $7 per day (in today's prices). By 2014, this number had fallen to only 1 in 12.