Homework #2 (Long Run Growth and Model of Production)

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

True. Page 58. 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.

Consider Figure 4.1. The shape of this production function suggests that α in the production function Y=K^alpha L^1-alpha. Look at #17. a) equal to one. b) greater than one. c) equal to zero. d) less than one. e) Not enough information is given.

d) less than one.

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? Go to #10 to look at picture. a) 7% b) 10% c) 70% d) 100%

b) 10% Pages 52-53. 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%.

If population doubles every 35 years, then the growth rate of population is a) 1 percent b) 2 percent c) 3 percent d) 4 percent

b) 2 percent Page 53. The Rule of 70 implies that the growth rate equals 70/35 = 2%.

With an average annual growth rate of 3.5 percent per year, per capita income will increase by what factor over a century? a) 16 b) 32 c) 64 d) 128

b) 32 Pages 50-51. Applying the Rule of 70 implies 70/3.5 = 20. Thus, income will double in 20 years. In a century, per capita income will double 5 times, which is 100/20. Thus, GDP per capital will increase by a factor of 2^5.

A country that, since 1980, has shown convergence to the United States is a) Japan b) China c) South Africa d) Germany

b) China Pages 54-55. Convergence is the process of a nation's economy catching up to another nation's economy.

Go to #11.

a) (b^1/2)/(d^1/2) * c^3/4

Assume that GDP per capita for two countries is displayed in plot with a ratio scale on the y-axis and a linear time scale (in years) on the x-axis. If the two times series are straight lines in this plot, then the growth rates are _____ over time. If in addition, the two lines are parallel and upward-sloping, then the income gap is ____ in absolute terms. (b) a) Equal to 0/increasing/decreasing b) Equal to 0/increasing/decreasing

a) constant b) increasing

In the Cobb-Douglas production function Y=K^alpha * L^1-alpha, if alpha = 1/3, then: a) labor's share of GDP is 2/3rds. b) labor's share of GDP is 1/3. c) capital's share of GDP is 2/3rds. d) capital's share of income is one. e) labor's share of income is three.

a) labor's share of GDP is 2/3rds.

Considering the data in Table 4.1, the explanation for the difference between the predicted and actual level of output is called ________. If you compare South Africa's observed and predicted output, this difference is equal to ________. Look at #20 for table. a) total factor productivity; 0.37 b) the Solow residual; 2.71 c) Dirac's delta; 0.14 d) capital's share of GDP; one-third e) labor's share of GDP; two-thirds

a) total factor productivity; 0.37

How quickly GDP doubles will depend on: a) the initial value of GDP b) the growth rate of GDP c) the current value of GDP d) all of these

b) the growth rate of GDP Page 51. The Rule of 70 implies that the time it takes for a variable to double depends only on its growth rate.

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. a) $1,000 b) $1,020 c) $1,050 d) $1,100

c) $1,050 Page 48; 58-60. 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? a) 1, 2, 3, 4, 5... b) 1, 3, 6, 9, 12... c) 1, 5, 25, 125, 625... d) All of these are correct

c) 1, 5, 25, 125, 625... Page 52. 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 in 2014: a) 1/16 b) 1/8 c) 1/4 d) 1/2

c) 1/4 Figure 3.7. The fastest growing country during 1960-2014 was Botswana with an average annual growth rate of above 6%. Its level of per capita GDP is slightly above 1/4 of the U.S. level.

If Y = A*K^(1/3)*L^(2/3) 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 a) 0 percent b) 1 percent c) 2 percent d) 3 percent

c) 2 percent Page 60. 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).

One of the key characteristics of the Cobb-Douglas production function is: a) increasing returns to scale. b) decreasing returns to scale. c) constant returns to scale. d) that it compacts all inputs into a single equation. e) that it is an exact replication of a firm's production function.

c) constant returns to scale.

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: a) 41,000 b) 70,000 c) 100,000 d) 130,000

d) 130,000 Page 50. Apply formula 3.7 where y0 equals 40,000, the growth rate is .03, and t equals 40.

If the production function is given by Y = K^1/4 * L^3/4 and K = 81 and L = 2.5, total output equals about: a) Y = 1 b) Y = .3 c) Y = 22.1 d) Y = 6 e) Y = 82.4

d) Y = 6

Which of the following production functions exhibits constant returns to scale? a) Y = K^alpha * L ^1 - alpha b) Y = K^1/3 * L^2/3 c) Y = K^.1 * L^.9 d) Y = K^1/4 * L^3/4 e) All of these answers are correct.

e) All of these answers are correct.

The law of diminishing marginal product to capital means that as we add additional units of capital: a) and labor, output will increase, but at a constant rate. b) and labor, output will increase, but at a decreasing rate. c) but hold labor constant, output will increase, but at an increasing rate. d) but hold labor constant, output will increase, but at a constant rate. e) but hold labor constant, output will increase, but at a decreasing rate.

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