Long-Run Growth and Model of Production

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

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? Use the properties of growth rates in section 3.5 of the textbook to answer your question.

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.

Which of the following is an example of labels for equidistant tick marks on a ratio scale?

1,5,25,125,625 A ratio scale is one where the numbers exhibit a constant ratio. The ratio scale here has a constant ratio of 5.

According to figure 3.7, the fastest growing country during 1960-2014 had a level of per capita GDP approximately equal to _____of the U.S. level:

1/4

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

126 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.

If population doubles every 35 years, then the growth rate of population is

2% The Rule of 70 implies that the growth rate equals 70/35 = 2%.

If Y = AK1/3L2/3 and A grows at a rate of 1 percent per year, K grows at a rate of negative 3 percent per year and L grows at a rate of 3 percent per year, then the growth rate of Y is

2% The growth rate formula for such a production function is g(Yt) = g(At) + (1/3)*g(Kt) + (2/3)*g(Lt). The first two terms cancel and we are left with (2/3)*(3).

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?

7% 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%.

You are an economist working for the International Monetary Fund. Your boss wants to know what the total factor productivity of China is, but all you have is data on per capita GDP, y, and the per capita capital stock, k. If you assume that capital's share of GDP is one-third, what would you use to find total factor productivity?

A = y/k^(1/3)

A country that, since 1980, has shown convergence to the United States is

Japan

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

True Growth rate formulas imply that the growth rate of per capita GDP is the growth rate of GDP minus the growth rate of population, which in this example is 0.

Wages in ancient Greece and Rome were approximately equal to wages in seventeenth-century France.

True Modern economic growth is a very recent phenomenon

The law of diminishing marginal product to capital means that as we add additional units of capital:

but hold labor constant, output will increase, but at a decreasing rate.

One of the key characteristics of the Cobb-Douglas production function is:

constant returns to scale

How quickly GDP doubles will depend on:

the growth rate of GDP The Rule of 70 implies that the time it takes for a variable to double depends only on its growth rate.

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.

true When plotted on a ratio scale, constant growth appears as a straight line.