Deck 8: Economic Growth II: Technology, Empirics, and Policy

Question 1

The Golden Rule level of the steady-state capital stock:

A)will be reached automatically if the saving rate remains constant over a long period of time.
B)will be reached automatically if each person saves enough to provide for his or her
C)retirement. implies a choice of a particular saving rate.
D)should be avoided by an enlightened government.

Answer 1

C

Question 2

In an economy with no population growth and no technological change, steady-state consumption is at its greatest possible level when the marginal product of:

A)labor equals the marginal product of capital.
B)labor equals the depreciation rate.
C)capital equals the depreciation rate.
D)capital equals zero.

Answer 2

C

Question 3

If the per-worker production function is given by y = k^1/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady-state ratio of capital to labor is:

A)1.
B)2.
C)4.
D)9.

Answer 3

D

Question 4

When f(k) is drawn on a graph with increases in k noted along the horizontal axis, the:

A)graph is a straight line.
B)slope of the line eventually gets flatter and flatter.
C)slope of the line eventually becomes negative.
D)slope of the line eventually becomes steeper and steeper.

Question 5

If the per-worker production function is given by y = k^1/2, the saving ratio is 0.2, and the depreciation rate is 0.1, then the steady-state ratio of output per worker (y) is:

A)1.
B)2.
C)3.
D)4.

Question 6

In the Solow growth model, the assumption of constant returns to scale means that:

A)all economies have the same amount of capital per worker.
B)the steady-state level of output is constant regardless of the number of workers.
C)the saving rate equals the constant rate of depreciation.
D)the number of workers in an economy does not affect the relationship between output per worker and capital per worker.

Question 7

The Solow growth model describes:

A)how output is determined at a point in time.
B)how output is determined with fixed amounts of capital and labor.
C)how saving, population growth, and technological change affect output over time.
D)the static allocation, production, and distribution of the economy's output.

Question 8

In the Solow growth model of Chapter 8, the demand for goods equals investment:

A)minus depreciation.
B)plus saving.
C)plus consumption.
D)plus depreciation.

Question 9

The change in capital stock per worker (∆k) may be expressed as a function of s = the saving ratio, f(k) = output per worker, k = capital per worker, and δ = the depreciation rate, by the equation:

A)∆k = sf(k)/δk.
B)∆k = sf(k) × δk.
C)∆k = sf(k) + δk.
D)∆k = sf(k) - δk

Question 10

Investment per worker (i) as a function of the saving ratio (s) and output per worker (f(k)) may be expressed as:

A)s + f(k).
B)s - f(k).
C)sf(k).
D)s/f(k).

Question 11

Suppose an economy is initially in a steady state with capital per worker exceeding the Golden Rule level. If the saving rate falls to a rate consistent with the Golden Rule, then in the transition to the new steady state, consumption per worker will:

A)always exceed the initial level.
B)first fall below then rise above the initial level.
C)first rise above then fall below the initial level.
D)always be lower than the initial level.

Question 12

The steady-state level of capital occurs when the change in the capital stock (∆k) equals:

A)0.
B)the saving rate.
C)the depreciation rate.
D)the population growth rate.

Question 13

If the national saving rate increases, the:

A)economy will grow at a faster rate forever.
B)capital-labor ratio will increase forever.
C)economy will grow at a faster rate until a new, higher, steady-state capital-labor ratio is reached.
D)capital-labor ratio will eventually decline.

Question 14

The Solow model shows that a key determinant of the steady-state ratio of capital to labor is the:

A)level of output.
B)labor force.
C)saving rate.
D)capital elasticity in the production function.

Question 15

If the capital stock equals 200 units in year 1 and the depreciation rate is 5 percent per year, then in year 2, assuming no new or replacement investment, the capital stock would equal units.

A)210
B)200
C)195
D)190

Question 16

Starting from a steady-state situation, if the saving rate increases, the rate of growth of capital per worker will:

A)increase and continue to increase unabated.
B)increase until the new steady state is reached.
C)decrease until the new steady state is reached.

Question 17

If an economy is in a steady state with no population growth or technological change and the marginal product of capital is less than the depreciation rate:

A)the economy is following the Golden Rule.
B)steady-state consumption per worker would be higher in a steady state with a lower saving rate.
C)steady-state consumption per worker would be higher in a steady state with a higher saving rate.
D)the depreciation rate should be decreased to achieve the Golden Rule level of consumption per worker.

Question 18

If an economy is in a steady state with no population growth or technological change and the capital stock is above the Golden Rule level and the saving rate falls:

A)output, consumption, investment, and depreciation will all decrease.
B)output and investment will decrease, and consumption and depreciation will increase.
C)output and investment will decrease, and consumption and depreciation will increase and then decrease but finally approach levels above their initial state.
D)output, investment, and depreciation will decrease, and consumption will increase and then decrease but finally approach a level above its initial state.

Question 19

If the per-worker production function is given by y = k^1/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady-state ratio of output per worker (y) is:

A)1.
B)2.
C)3.
D)4.

Question 20

If the per-worker production function is given by y = k^1/2, the saving rate (s) is 0.2, and the depreciation rate is 0.1, then the steady-state ratio of capital to labor is:

A)1.
B)2.
C)4.
D)9.

Question 21

Many policymakers are concerned that Americans do not save enough. Using the Solow growth model, with no technological change and no population growth, explain why:
a. for a given production function and depreciation rate, the saving rate determines the level of output per worker.
b. a higher saving rate will not necessarily generate more consumption per worker.
c. a higher saving rate will not produce a faster steady-state growth rate of output per worker.

Question 22

Suppose that two countries are exactly alike in every respect except that the citizens of country A have a higher saving rate than the citizens of country B.
a. Which country will have the higher level of output per worker in the steady state? Illustrate graphically.
b. Which country will have the faster rate of growth of output per worker in the steady state?

Question 23

When an economy begins above the Golden Rule, reaching the Golden Rule:

A)produces lower consumption at all times in the future.
B)produces higher consumption at all times in the future.
C)requires initially reducing consumption to increase consumption in the future.
D)requires initially increasing consumption to decrease consumption in the future.

Question 24

The initial steady-state level of capital per worker in Macroland is 5. The Golden Rule level of capital per worker in Macroland is 8.
a. What must change in Macroland to achieve the Golden Rule steady state?
b. Why might the Golden Rule steady state be preferred to the initial steady state?
c. Why might some current workers in Macroland prefer the initial steady state to the Golden Rule steady state?

Question 25

Compare and contrast the impact of a faster rate of population growth on the standard of living (output per worker) in the models by Solow, Malthus, and Kremer.

Question 26

It rains so much in the country of Tropicana that capital equipment rusts out (depreciates) at a much faster rate than it does in the country of Sahara. If the countries are otherwise identical, in which country will the Golden Rule level of capital per worker be higher? Illustrate graphically.

Question 27

Explain the two uses of saving in the steady state in the Solow model with population growth, but no technological progress.

Question 28

In the Solow growth model of an economy with population growth but no technological change, the break-even level of investment must do all of the following except:

A)offset the depreciation of existing
B)capital. provide capital for new workers.
C)equal the marginal productivity of capital (MPK).
D)keep the level of capital per worker constant.

Question 29

If an economy is in a steady state with a saving rate below the Golden Rule level, efforts to increase the saving rate result in:

A)both higher per-capita output and higher per-capita depreciation, but the increase in per-capita output would be greater.
B)both higher per-capita output and higher per-capita depreciation, but the increase in per-capita depreciation would be greater.
C)higher per-capita output and lower per-capita depreciation.
D)lower per-capita output and higher per-capita depreciation.

Question 30

Assume that a country's per-worker production is y = k^1/2, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10).
a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, and consumption per worker in the steady state? (Hint: Use sy = δk and y = k1/2 to get an equation in s, δ, k, and k1/2, and then solve for k.)
b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.6.
c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8.
d. Is it possible to save too much? Why?

Question 31

In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:

A)∆k = sf(k) + δk.
B)∆k = sf(k) - δk.
C)∆k = sf(k) + (δ + n)k.
D)∆k = sf(k) - (δ + n)k.

Question 32

If an economy is in a steady state with no population growth or technological change and the capital stock is below the Golden Rule:

A)a policymaker should definitely take all possible steps to increase the saving rate.
B)if the saving rate is increased, output and consumption per capita will both rise, both in the short and long runs.
C)if the saving rate is increased, output per capita will at first decline and then rise above its initial level, and consumption per capita will rise both in the short and long runs.
D)if the saving rate is increased, output per capita will rise and consumption per capita will first decline and then rise above its initial level.

Question 33

The economies of two countries, Thrifty and Profligate, have the same production functions and depreciation rates. There is no population growth or technological progress in either country. The economies of each country can be described by the Solow growth model. The saving rate in Thrifty is 0 3. The saving rate in Profligate is 0.05.
a. In which country is the level of steady-state output per worker larger? Explain.
b. In which country is the steady-state growth rate of output per worker larger?
c.
d. In which country is the growth rate of steady-state total output greater?

Question 34

The economy of Alpha can be described by the Solow growth model. The following are some characteristics of the Alpha economy:
saving rate (s) 0.20
depreciation rate (δ) 0.12
steady-state capital per worker (k) 4
population growth rate (n) 0.02
steady-state output per worker 20,000
a. What is the steady-state growth rate of output per worker in Alpha?
b. What is the steady-state growth rate of total output in Alpha?
c. What is the level of steady-state consumption per worker in Alpha?
d. What is the steady-state level of investment per worker in Alpha?

Question 35

One of the key distinctions made in the analysis of the Solow growth model is between changes in levels and changes in growth rates. How does an increase in the rate of population growth change the steady-state levels and growth rates of output and output per worker in the Solow model with no technological change?

Question 36

Suppose that two countries are exactly alike in every respect except that population grows at a faster rate in country A than in country B.
a. Which country will have the higher level of output per worker in the steady state? Illustrate graphically.
b. Which country will have the faster rate of growth of output per worker in the steady state?

Question 37

When an economy begins below the Golden Rule, reaching the Golden Rule:

A)produces lower consumption at all times in the future.
B)produces higher consumption at all times in the future.
C)requires initially reducing consumption to increase consumption in the future.
D)requires initially increasing consumption to decrease consumption in the future.

Question 38

Suppose an economy is initially in a steady state with capital per worker below the Golden Rule level. If the saving rate increases to a rate consistent with the Golden Rule, then in the transition to the new steady state consumption per worker will:

A)always exceed the initial level.
B)first fall below then rise above the initial level.
C)first rise above then fall below the initial level.
D)always be lower than the initial level.

Question 39

The economies of two countries, North and South, have the same production functions, depreciation rates, and saving rates. The economies of each country can be described by the Solow growth model. Population growth is faster in South than in North.
a. In which country is the level of steady-state output per worker larger? Explain.
b. In which country is the steady-state growth rate of output per worker larger?
c. In which country is the growth rate of steady-state total output greater?

Question 40

Assume that a country's production function is Y = K^1/2L^1/2.
a. What is the per-worker production function y = f(k)?
b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function?
c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)
d. If the saving rate equals the steady-state level, what is consumption per worker?

Question 41

Larger quantities of steady-state capital have both a positive and negative effect on consumption per worker in the Solow model (assume no population growth or technological progress). Explain.

Question 42

Consider two countries that are otherwise identical (have the same saving rates and depreciation rates), but the population of Country Large is 100 million, while the population of Country Small is 10 million. Use the Solow model with no technological change to compare the steady-state levels of output per worker if:
a. the population growth rates are the same in the two countries.
b. the population growth rate is higher in Country Large.