Deck 7: Economic Growth I: Capital Accumulation and Population Growth

Question 1

Unlike the long-run classical model in Chapter 3, the Solow growth model:

A)assumes that the factors of production and technology are the sources of the economy's output.
B)describes changes in the economy over time.
C)is static.
D)assumes that the supply of goods determines how much output is produced.

Answer 1

describes changes in the economy over time.

Question 2

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.

Answer 2

0.

Question 3

In the Solow growth model of Chapter 7, for any given capital stock, the determines how much output the economy produces and the determines the allocation of output between consumption and investment.

A)saving rate; production function
B)depreciation rate; population growth rate
C)production function; saving rate
D)population growth rate; saving rate

Answer 3

production function; saving rate

Question 4

Two economies are identical except that the level of capital per worker is higher in Highland than in Lowland. The production functions in both economies exhibit diminishing marginal product of capital. An extra unit of capital per worker increases output per worker:

A)more in Highland.
B)more in Lowland.
C)by the same amount in Highland and Lowland.
D)in Highland, but not in Lowland.

Question 5

In the Solow growth model of Chapter 7, where s is the saving rate, y is output per worker, and i is investment per worker, consumption per worker (c) equals:

A)sy
B)(1 - s)y
C)(1 + s)y
D)(1 - s)y - i

Question 6

If capital lasts an average of 25 years, the depreciation rate is percent per year.

A)25
B)5
C)4
D)2.5

Question 7

In the Solow model, it is assumed that a(n) fraction of capital wears out as the capital-labor ratio increases.

A)smaller
B)larger
C)constant
D)increasing

Question 8

Cause(s) the capital stock to rise, while cause(s) the capital stock to fall.

A)Inflation; deflation
B)Interest rates; the discount rate
C)Investment; depreciation
D)International trade; depressions

Question 9

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 10

(Exhibit: Capital-Labor Ratio and the Steady State) Reference: Ref 7-1 (Exhibit: Output, Consumption, and Investment) In this graph, when the capital-labor ratio is
OA, AB represents:

A)investment per worker, and AC represents consumption per worker.
B)consumption per worker, and AC represents investment per worker.
C)investment per worker, and BC represents consumption per worker.
D)consumption per worker, and BC represents investment per worker.

Question 11

In the Solow growth model the saving rate determines the allocation of output between:

A)saving and investment.
B)output and capital.
C)consumption and output.
D)investment and consumption.

Question 12

In the Solow growth model of Chapter 7, the demand for goods equals investment:

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

Question 13

In the Solow growth model of Chapter 7, investment equals:

A)output.
B)consumption.
C)the marginal product of capital.
D)saving.

Question 14

The consumption function in the Solow model assumes that society saves a:

A)constant proportion of income.
B)smaller proportion of income as it becomes richer.
C)larger proportion of income as it becomes richer.
D)larger proportion of income when the interest rate is higher.

Question 15

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 16

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

A)output per worker.
B)output per unit of capital.
C)the marginal product of labor.
D)the marginal product of capital.

Question 17

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 18

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 19

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 20

The production function y = f(k) means:

A)labor is not a factor of production.
B)output per worker is a function of labor productivity.
C)output per worker is a function of capital per worker.
D)the production function exhibits increasing returns to scale.

Question 21

A higher saving rate leads to a:

A)higher rate of economic growth in both the short run and the long run.
B)higher rate of economic growth only in the long run.
C)higher rate of economic growth in the short run but a decline in the long run.
D)large capital stock and a high level of output in the long run.

Question 22

In the Solow growth model, if investment is less than depreciation, the capital stock will and output will until the steady state is attained.

A)increase; increase
B)increase; decrease
C)decrease; decrease
D)decrease; increase

Question 23

If the per-worker production function is given by y = k1/2, 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 24

In the Solow growth model, the steady-state occurs when:

A)capital per worker is constant.
B)the saving rate equals the depreciation rate.
C)output per worker equals consumption per worker.
D)consumption per worker is maximized.

Question 25

In the Solow growth model of Chapter 7, the economy ends up with a steady-state level of capital:

A)only if it starts from a level of capital below the steady-state level.
B)only if it starts from a level of capital above the steady-state level.
C)only if it starts from a steady-state level of capital.
D)regardless of the starting level of capital.

Question 26

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.
D)decrease and continue to decrease unabated.

Question 27

Among the four countries-the United States, the United Kingdom, Germany, and Japan-the one that experienced the most rapid growth rate of output per person between
1948 and 1972 was:

A)the United States.
B)the United Kingdom.
C)Germany.
D)Japan.

Question 28

(Exhibit: Capital-Labor Ratio and the Steady State) Reference: Ref 7-2 (Exhibit: Capital-Labor Ratio and the Steady State) In this graph, starting from capital-labor ratio k , the capital-labor ratio will:
1

A)decrease.
B)remain constant.
C)increase.
D)first decrease and then remain constant.

Question 29

The formula for the steady-state ratio of capital to labor (k*), with no population growth or technological change, is s:

A)divided by the depreciation rate.
B)multiplied by the depreciation rate.
C)divided by the product of f(k*) and the depreciation rate.
D)multiplied by f(k*) divided by the depreciation rate.

Question 30

If the per-worker production function is given by y = k1/2, 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 31

If a war destroys a large portion of a country's capital stock but the saving rate is unchanged, the Solow model predicts output will grow and that the new steady state will approach:

A)a higher output level than before.
B)the same output level as before.
C)a lower output level than before.
D)the Golden Rule output level.

Question 32

If the per-worker production function is given by y = k1/2, 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.

Question 33

In the Solow growth model with no population growth and no technological progress, the higher the steady capital-per-worker ratio, the higher the steady-state:

A)growth rate of total output.
B)level of total output.
C)growth rate of output per worker.
D)level of output per worker.

Question 34

(Exhibit: Capital-Labor Ratio and the Steady State) Reference: Ref 7-2 (Exhibit: Capital-Labor Ratio and the Steady State) In this graph, capital-labor ratio k
2
Is not
The steady-state capital-labor ratio because:

A)the saving rate is too high.
B)the investment ratio is too high.
C)gross investment is greater than depreciation.
D)depreciation is greater than gross investment.

Question 35

In the steady state, the capital stock does not change because investment equals:

A)output per worker.
B)the marginal product of capital.
C)depreciation.
D)consumption.

Question 36

In the Solow growth model, if investment exceeds depreciation, the capital stock will and output will until the steady state is attained.

A)increase; increase
B)increase; decrease
C)decrease; decrease
D)decrease; increase

Question 37

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 38

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 39

If the per-worker production function is given by y = k1/2, 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 40

An economy in the steady state will have:

A)investment exceeding depreciation.
B)no depreciation.
C)saving equal to consumption.
D)no change in the capital stock.

Question 41

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 42

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 43

In the Solow growth model, increases in capital output and the amount of output used to replace depreciating capital.

A)increase; increase
B)increase; decrease
C)decrease; increase
D)decrease; decrease

Question 44

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.

Question 45

Examination of recent data for many countries shows that countries with high saving rates generally have high levels of output per person because:

A)high saving rates mean permanently higher growth rates of output.
B)high saving rates lead to high levels of capital per worker.
C)countries with high levels of output per worker can afford to save a lot.
D)countries with large amounts of natural resources have both high output levels and high saving rates.

Question 46

To determine whether an economy is operating at its Golden Rule level of capital stock, a policymaker must determine the steady-state saving rate that produces the:

A)largest MPK.
B)smallest depreciation rate.
C)largest consumption per worker.
D)largest output per worker.

Question 47

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 48

(Exhibit: Steady-State Consumption II) Reference: Ref 7-4 (Exhibit: Steady-State Consumption II) The Golden Rule level of steady-state investment per worker is:

A)AC.
B)AB.
C)BC.
D)DE.

Question 49

The Golden Rule level of capital accumulation is the steady state with the highest level of:

A)output per worker. capital
B)per worker. savings per
C)worker. consumption per
D)worker.

Question 50

In the Solow growth model, with a given production function, depreciation rate, no technological change, and no population growth, a higher saving rate produces a:

A)higher MPK in the new steady-state.
B)higher steady-state growth rate of output per worker.
C)higher steady-state growth rate of total output.
D)higher steady-state level of output per worker.

Question 51

A reduction in the saving rate starting from a steady state with more capital than the Golden Rule causes investment to in the transition to the new steady state.

A)increase
B)decrease
C)first increase, then decrease
D)first decrease, then increase

Question 52

If an economy with no population growth or technological change has a steady-state MPK of 0.1, a depreciation rate of 0.1, and a saving rate of 0.2, then the steady-state capital stock:

A)is greater than the Golden Rule level.
B)is less than the Golden Rule level.
C)equals the Golden Rule level.
D)could be either above or below the Golden Rule level.

Question 53

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 54

The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is:

A)c* = f(k*) - δk*.
B)c* = f(k*) + δk*.
C)c* = f(k*) ÷ dk*.
D)c* = k* - δf(k)*.

Question 55

Assume two economies are identical in every way except that one has a higher saving rate. According to the Solow growth model, in the steady state the country with the higher saving rate will have level of total output and rate of growth of output per worker as/than the country with the lower saving rate.

A)the same; the same
B)the same; a higher
C)a higher; the same
D)a higher; a higher

Question 56

With a per-worker production function y = k1/2, the steady-state capital stock per worker (k*) as a function of the saving rate (s) is given by:

A)k* = (s/δ)2.
B)k* = (δ/s)2.
C)k* = s/δ.
D)k* = δ/s.

Question 57

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 retirement.
C)implies a choice of a particular saving rate.
D)should be avoided by an enlightened government.

Question 58

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 59

If an economy with no population growth or technological change has a steady-state MPK of 0.125, a depreciation rate of 0.1, and a saving rate of 0.225, then the steady-state capital stock:

A)is greater than the Golden Rule level.
B)is less than the Golden Rule level.
C)equals the Golden Rule level.
D)could be either above or below the Golden Rule level.

Question 60

(Exhibit: Steady-State Consumption II) Reference: Ref 7-4 (Exhibit: Steady-State Consumption II) The Golden Rule level of steady-state consumption per worker is:

A)AC.
B)AB.
C)BC.
D)DE.

Question 61

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

Question 62

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 63

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. In which country is the growth rate of steady-state total output greater?

Question 64

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 65

The economy of Alpha can be described by the Solow growth model. The following are some characteristics of the Alpha economy:
saving rate (s) .20 depreciation rate (δ) .12 steady-state capital per worker (k) 4 population growth rate (n) .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 66

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 67

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 68

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 69

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 70

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 71

If the production function exhibits increasing returns to scale in the steady state, an increase in the rate of growth of population would lead to:

A)growth in total output and growth in output per worker.
B)growth in total output but no growth in output per worker.
C)growth in total output but a decrease in output per worker.
D)no growth in total output or in output per worker.

Question 72

If the production function exhibits decreasing returns to scale in the steady state, an increase in the rate of population would lead to:

A)growth in total output and growth in output per worker.
B)growth in total output but no growth in output per worker.
C)growth in total output but a decrease in output per worker.
D)no growth in total output or in output per worker.

Question 73

Assume that a country's production function is Y = K1/2L1/2. 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 74

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.

Question 75

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 76

Assume that a country's per-worker production is y = k1/2, 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?