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Name Testbank Chapter 7: Economic Growth I

Description Question pool for Testbank Chapter 7: Economic Growth I

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Question

The Solow growth model describes:

Answer how output is determined at a point in time.

how output is determined with fixed amounts of capital and labor.

how saving, population growth, and technological change affect output over time.

the static allocation, production, and distribution of the economy's output.

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Question

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

Answer assumes that the factors of production and technology are the sources of the economy's

output.

describes changes in the economy over time.

is static.

assumes that the supply of goods determines how much output is produced.

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Question

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

Answer all economies have the same amount of capital per worker.

the steady-state level of output is constant regardless of the number of workers.

the saving rate equals the constant rate of depreciation.

the number of workers in an economy does not affect the relationship between output per

worker and capital per worker.

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Question

The production function y = f(k) means:

Answer labor is not a factor of production.

output per worker is a function of labor productivity.

output per worker is a function of capital per worker.

the production function exhibits increasing returns to scale.

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Question

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

Answer graph is a straight line.

slope of the line eventually gets flatter and flatter.

slope of the line eventually becomes negative.

slope of the line eventually becomes steeper and steeper.

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Question

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

denotes:

Answer output per worker.

output per unit of capital.

the marginal product of labor.

the marginal product of capital.

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Question

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:

Answer more in Highland.

more in Lowland.

by the same amount in Highland and Lowland.

in Highland, but not in Lowland.

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Question

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

Answer constant proportion of income.

smaller proportion of income as it becomes richer.

larger proportion of income as it becomes richer.

larger proportion of income when the interest rate is higher.

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Question

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

Answer minus depreciation.

plus saving.

plus consumption.

plus depreciation.



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Question

In the Solow growth model of Chapter 7, the saving rate determines the allocation of output between:

Answer saving and investment.

output and capital.

consumption and output.

investment and consumption.

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Question

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:

Answer sy.

(1 – s)y.

(1 + s)y.

(1 – s)y – i.

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Question

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

Answer output.

consumption.


saving.

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Question

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.

Answer saving rate; production function

depreciation rate; population growth rate

production function; saving rate

population growth rate; saving rate

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Question

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

Answer Inflation; deflation

Interest rates; the discount rate

Investment; depreciation

International trade; depressions




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Question

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

expressed as:

Answer s + f(k).

s – f(k).

sf(k).

s/f(k).

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Question

In this graph, when the capital-labor ratio is OA, AB represents:

Answer investment per worker, and AC represents consumption per worker.

consumption per worker, and AC represents investment per worker.

investment per worker, and BC represents consumption per worker.

consumption per worker, and BC represents investment per worker.

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Question

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

Answer 25

5

4

2.5

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Question

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

ratio increases.

Answer smaller

larger

constant

increasing

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Question

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 —the depreciation rate, by the equation:

Answer ∆k = sf(k) ÷ k.

∆k = sf(k) × k.

∆k = sf(k) + k.

∆k = sf(k) – k.

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Question

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

Answer 0.

the saving rate.

the depreciation rate.

the population growth rate.

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Question

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



depreciation.

consumption.

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Question

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

Answer only if it starts from a level of capital below the steady-state level.

only if it starts from a level of capital above the steady-state level.

only if it starts from a steady-state level of capital.

regardless of the starting level of capital.

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Question

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

Answer capital per worker is constant.

the saving rate equals the depreciation rate.

output per worker equals consumption per worker.

consumption per worker is maximized.

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Question

Exhibit: Capital-Labor Ratio and the Steady State

In this graph, capital-labor ratio k2 is not the steady-state capital-labor ratio because:

Answer the saving rate is too high.

the investment ratio is too high.

gross investment is greater than depreciation.

depreciation is greater than gross investment.

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Question

Exhibit: Steady-State Capital-Labor Ratio




In this graph, the capital-labor ratio that represents the steady-state capital-labor ratio is:

Answer k0.

k1.

k2.

k3.

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Question

Exhibit: The Capital-Labor Ratio

In this graph, starting from capital-labor ratio k1, the capital-labor ratio will:

Answer decrease.

remain constant.

increase.

first decrease and then remain constant.

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Question

In the Solow growth model, if investment exceeds depreciation, the capital stock will ______ and output

will ______ until the steady state is attained.

Answer increase; increase

increase; decrease

decrease; decrease

decrease; increase

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Question

In the Solow growth model, if investment is less than depreciation, the capital stock will ______ and

output will ______ until the steady state is attained.


increase; decrease




decrease; decrease

decrease; increase

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Question

An economy in the steady state will have:

Answer investment exceeding depreciation.

no depreciation.

saving equal to consumption.

no change in the capital stock.

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Question

In the Solow growth model of an economy with no population growth and no technological progress,

the higher the steady capital-per-worker ratio, the higher the steady-state:

Answer growth rate of total output.

level of total output.

growth rate of output per worker.

level of output per worker.

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Question

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

change, is s:

Answer divided by the depreciation rate.

multiplied by the depreciation rate.

divided by the product of f(k*) and the depreciation rate.

multiplied by f(k*) divided by the depreciation rate.

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Question

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:

Answer 1.

2.

4.

9.

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Question


, the saving ratio is 0.3, and the depreciation

rate is 0.1, then the steady-state ratio of capital to labor is:




Answer 1.

2.

4.

9.

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Question



rate is 0.1, then the steady-state ratio of output per worker (y) is:

Answer 1.

2.

3.

4.

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Question



rate is 0.1, then the steady-state ratio of output per worker (y) is:

Answer 1.

2.

3.

4.

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Question

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:

Answer a higher output level than before.

the same output level as before.

a lower output level than before.

the Golden Rule output level.

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Question

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:

Answer the United States.

the United Kingdom.

Germany.

Japan.

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Question

If the national saving rate increases, the:

Answer economy will grow at a faster rate forever.

capital-labor ratio will increase forever.

economy will grow at a faster rate until a new, higher, steady-state capital-labor ratio is

reached.

capital-labor ratio will eventually decline.

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Question

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

worker will:

Answer increase and continue to increase unabated.

increase until the new steady state is reached.

decrease until the new steady state is reached.

decrease and continue to decrease unabated.

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Question

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

Answer level of output.

labor force.

saving rate.

capital elasticity in the production function.

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Question

A higher saving rate leads to a:

Answer higher rate of economic growth in both the short run and the long run.

higher rate of economic growth only in the long run.

higher rate of economic growth in the short run but a decline in the long run.

large capital stock and a high level of output in the long run.

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Question

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.

Answer the same; the same

the same; a higher

a higher; the same

a higher; a higher

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Question

In the Solow growth model of an economy, with a given production function, depreciation rate, no

technological change, and no population growth, a higher saving rate produces a:

Answer higher MPK in the new steady state.

higher steady-state growth rate of output per worker.

higher steady-state growth rate of total output.

higher steady-state level of output per worker.

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Question

Examination of recent data for many countries shows that countries with high saving rates generally

have high levels of output per person because:

Answer high saving rates mean permanently higher growth rates of output.

high saving rates lead to high levels of capital per worker.

countries with high levels of output per worker can afford to save a lot.

countries with large amounts of natural resources have both high output levels and high

saving rates.

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Question

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


capital per worker.

savings per worker.

consumption per worker.

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Question

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

investment per worker is:

Answer c* = f(k*) – k*.

c* = f(k*) + k*.

c* = f(k*) ÷ dk*.

c* = k* – f(k)*.

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Question

In the Solow growth model, increases in capital ______ output and ______ the amount of output used

to replace depreciating capital.


increase; decrease

decrease; increase

decrease; decrease




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Question

Exhibit: Steady-State Consumption I

The Golden Rule level of the capital-labor ratio is:

Answer k*A.

above k*A but below k*

B.

k*B.

above k*B.

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Question

Exhibit: Steady-State Consumption II

Reference: Ref 7-1




(Exhibit: Steady-State Consumption II) The Golden Rule level of steady-state consumption per worker

is:

Answer AC.

AB.

BC.

DE.

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Question

Exhibit: Steady-State Consumption II

Reference: Ref 7-1

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

Answer AC.

AB.

BC.

DE.

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Question

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:

Answer labor equals the marginal product of capital.

labor equals the depreciation rate.

capital equals the depreciation rate.

capital equals zero.

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Question

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

Answer will be reached automatically if the saving rate remains constant over a long period of time.

will be reached automatically if each person saves enough to provide for his or her

retirement.

implies a choice of a particular saving rate.

should be avoided by an enlightened government.

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Question

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:

Answer the economy is following the Golden Rule.

steady-state consumption per worker would be higher in a steady state with a lower

saving rate.

steady-state consumption per worker would be higher in a steady state with a higher

saving rate.

the depreciation rate should be decreased to achieve the Golden Rule level of

consumption per worker.

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Question

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:

Answer is greater than the Golden Rule level.

is less than the Golden Rule level.

equals the Golden Rule level.

could be either above or below the Golden Rule level.

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Question

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:

Answer is greater than the Golden Rule level.

is less than the Golden Rule level.

equals the Golden Rule level.

could be either above or below the Golden Rule level.

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Question

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:

Answerk* = (s/ )

2.

k* = ( /s)2.

k* = s/ .




k* = /s.

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Question

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:

Answer largest MPK.

smallest depreciation rate.

largest consumption per worker.

largest output per worker.

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Question

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:

Answer output, consumption, investment, and depreciation will all decrease.

output and investment will decrease, and consumption and depreciation will increase.

output and investment will decrease, and consumption and depreciation will increase and

then decrease but finally approach levels above their initial state.

output, investment, and depreciation will decrease, and consumption will increase and

then decrease but finally approach a level above its initial state.

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Question

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:

Answer always exceed the initial level.

first fall below then rise above the initial level.

first rise above then fall below the initial level.

always be lower than the initial level.

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Question

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.

Answer increase

decrease

first increase, then decrease

first decrease, then increase

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Question

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

Answer produces lower consumption at all times in the future.

produces higher consumption at all times in the future.

requires initially reducing consumption to increase consumption in the future.

requires initially increasing consumption to decrease consumption in the future.

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Question

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:

Answer both higher per-capita output and higher per-capita depreciation, but the increase in

per-capita output would be greater.

both higher per-capita output and higher per-capita depreciation, but the increase in

per-capita depreciation would be greater.

higher per-capita output and lower per-capita depreciation.

lower per-capita output and higher per-capita depreciation.

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Question

If an economy is in a steady state with no population growth or technological change and the capital

stock is below the Golden Rule level:

Answer a policymaker should definitely take all possible steps to increase the saving rate.

if the saving rate is increased, output and consumption per capita will both rise, both in the

short and long runs.

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.

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.

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Question

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:

Answer always exceed the initial level.

first fall below then rise above the initial level.

first rise above then fall below the initial level.

always be lower than the initial level.

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Question

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

Answer produces lower consumption at all times in the future.

produces higher consumption at all times in the future.

requires initially reducing consumption to increase consumption in the future.




requires initially increasing consumption to decrease consumption in the future.

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Question

An increase in the saving rate starting from a steady state with less capital than the Golden Rule

causes investment to ______ in the transition to the new steady state.

Answer increase

decrease

first increase, then decrease

first decrease, then increase

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Question

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

equation:

Answer ∆k = sf(k) + k.

∆k = sf(k) – k.

∆k = sf(k) + ( + n)k.

∆k = sf(k) – ( + n)k.

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Question

The formula for the steady-state ratio of capital to labor (k*) with population growth at rate n but no

technological change, where s is the saving rate, is s:

Answer divided by the sum of the depreciation rate plus n.

multiplied by the sum of the depreciation rate plus n.

divided by the product of f(k*) and the sum of the depreciation rate plus n.

multiplied by f(k*) divided by the sum of the depreciation rate plus n.

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Question

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:

Answer offset the depreciation of existing capital.

provide capital for new workers.

equal the marginal productivity of capital (MPK).

keep the level of capital per worker constant.

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Question

In the Solow growth model of an economy with population growth but no technological change, if

population grows at rate n, then capital grows at rate ______ and output grows at rate ______.




Answer n ; n

n ; 0

0 ; 0

0 ; n

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Question

In the Solow growth model of an economy with population growth but no technological change, if

population grows at rate n, total output grows at rate ______ and output per worker grows at rate

______.

Answer n ; n

n ; 0

0 ; 0

0 ; n

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Question

Assume two economies are identical in every way except that one has a higher population growth rate.

According to the Solow growth model, in the steady state the country with the higher population growth

rate will have a ______ level of total output and ______ rate of growth of output per worker as/than the

country with the lower population growth rate.

Answer higher; the same

higher; a higher

lower; the same

lower; a lower

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Question

In the Solow growth model, an economy in the steady state with a population growth rate of n but no

technological growth will exhibit a growth rate of output per worker at rate:

Answer 0.

n.

.

(n + ).

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Question

In the Solow growth model, an economy in the steady state with a population growth rate of n but no

technological growth will exhibit a growth rate of total output at rate:

Answer 0.

n.

.

(n + ).

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Question

In the Solow growth model, if two countries are otherwise identical (with the same production function,

same saving rate, same depreciation rate, and same rate of population growth) except that Country

Large has a population of one billion workers and Country Small has a population of ten million

workers, then the steady-state level of output per worker will be ______ and the steady-state growth

rate of output per worker will be ______.

Answer the same in both countries; the same in both countries

higher in Country Large; higher in Country Large

higher in Country Small; higher in Country Small

higher in Country Large; higher in Country Small

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Question

In the Solow growth model of an economy with population growth but no technological progress, the

steady-state amount of investment can be thought of as a break-even amount of investment because

the quantity of investment just equals the amount of:

Answer output needed to achieve the maximum level of consumption per worker.

capital needed to replace depreciated capital and to equip new workers.

saving needed to achieve the maximum level of output per worker.

output needed to make the capital per worker ratio equal to the marginal product of

capital.

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Question

In the Solow growth model, the steady-state level of output per worker would be higher if the ______

increased or the ______ decreased.

Answer saving rate; depreciation rate

population growth rate; depreciation rate

depreciation rate; population growth rate

population growth rate; saving rate

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Question

In the Solow growth model of an economy with population growth but no technological change, a

higher level of steady-state output per worker can be obtained by all of the following except:

Answer increasing the saving rate.

decreasing the depreciation rate.

increasing the population growth rate.

increasing the capital per worker ratio.

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Question

In the Solow growth model of an economy with population growth but no technological change, which

of the following will generate a higher steady-state growth rate of total output?




Answer a higher saving rate

a lower depreciation rate

a higher population growth rate

a higher capital per worker ratio

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Question

The Solow growth model of an economy with population growth but no technological progress can

explain:

Answer persistent growth in output per worker.

persistent growth in total output.

persistent growth in consumption per worker.

persistent growth in the saving rate.

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Question

In the Solow growth model of an economy with a given production function, depreciation rate, saving

rate, and no technological change, higher rates of population growth produce:

Answer higher steady-state ratios of capital per worker.

higher steady-state growth rates of output per worker.

higher steady-state growth rates of total output.

higher steady-state levels of output per worker.

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Question

In the Solow growth model of an economy with a given production function, depreciation rate, saving

rate, and no technological change, lower rates of population growth produce:

Answer lower steady-state ratios of capital per worker.

lower steady-state growth rates of output per worker.

lower steady-state growth rates of total output.

lower steady-state levels of output per worker.

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Question

The Solow model of an economy with population growth but no technological change cannot explain

persistent growth in standards of living because:

Answer total output does not grow.

depreciation grows faster than output.

output, capital, and population all grow at the same rate in the steady state.

capital and population grow, but output does not keep up.

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Question

With population growth at rate n but no technological change, the Golden Rule steady state may be

achieved by equating the marginal product of capital (MPK):

Answer net of depreciation to n.

to n.

net of depreciation to the depreciation rate plus n.

to the depreciation rate.

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Question

In the Solow growth model of an economy with population growth but no technological progress, in the

Golden Rule steady state, the marginal product of capital minus the rate of depreciation equals:

Answer 0.

the population growth rate.

the saving rate.

output per worker.

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Question

In the Solow growth model of an economy with population growth but no technological progress, if in

the steady state the marginal product of capital equals 0.10, the depreciation rate equals 0.05, and the

rate of population growth equals 0.03, then the capital per worker ratio ______ the Golden Rule level.

Answer is above

is below

is equal to

moves to

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Question

In the Solow growth model of an economy with population growth but no technological progress,

increases in capital have a positive impact on steady-state consumption per worker by ______, but

have a negative impact on steady-state consumption per worker by ______.

Answer increasing the capital to worker ratio; reducing saving in the steady state

reducing investment required in the steady state; increasing saving in the steady state

increasing output; increasing output required to replace depreciating capital

decreasing the saving rate; increasing the depreciation rate

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Question

An increase in the rate of population growth with no change in the saving rate:

Answer increases the steady-state level of capital per worker.

decreases the steady-state level of capital per worker.

does not affect the steady-state level of capital per worker.

decreases the rate of output growth in the short run.

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Question

Analysis of population growth around the world concludes that countries with high population growth

tend to:

Answer have high income per worker.

have a lower level of income per worker than other parts of the world.

have the same standard of living as other parts of the world.

tend to be the high-income-producing nations of the world.

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Question

According to Kremer, large populations:

Answer require the capital stock to be spread thinly, thereby reducing living standards.

place great strains on an economy's productive resources, resulting in perpetual poverty.

are a prerequisite for technological advance and higher living standards.

are not a factor in determining living standards.

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Question

According to Malthus, large populations:





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Question

According to the Solow growth model, large populations:





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Question

The Malthusian model that predicts mankind will remain in poverty forever:

Answer underestimated the possibility for technological progress.

failed to predict that scarcity would be eliminated in the modern world.

assumed that prosperity would lead to declining human fertility.

recognized that the ability of natural resources to sustain humans is far greater than the

power of population to consume resources.

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Question

According to the Kremerian model, large populations improve living standards because:

Answer crowded conditions put more pressure on people to work hard.

there are more people who can make discoveries and contribute to innovation.

more people have the opportunity for leisure and recreation.

most people prefer to live with many other people.

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Question

If Y = K0.3

L0.7

, then the per-worker production function is:

Answer Y = F(K/L).

Y/L = (K/L)0.3

.

Y/L = (K/L)0.5

.

Y/L = (K/L)0.7

.

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Question

If y = k1/2

, there is no population growth or technological progress, 5 percent of capital depreciates

each year, and a country saves 20 percent of output each year, then the steady-state level of capital

per worker is:

Answer 2.

4.

8.

16.

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Question

If y = k1/2

, the country saves 10 percent of its output each year, and the steady-state level of capital per

worker is 4, then the steady-state levels of output per worker and consumption per worker are:

Answer 2 and 1.6, respectively.

2 and 1.8, respectively.



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Question

Assume that two countries both have the per-worker production function y = k1/2

, neither has population

growth or technological progress, depreciation is 5 percent of capital in both countries, and country A

saves 10 percent of output whereas country B saves 20 percent. If A starts out with a capital-labor ratio

of 4 and B starts out with a capital-labor ratio of 2, in the long run:




Answer both A and B will have capital-labor ratios of 4.

both A and B will have capital-labor ratios of 16.

A's capital-labor ratio will be 4 whereas B's will be 16.

A's capital-labor ratio will be 16 whereas B's will be 4.

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Question

Assume that a war reduces a country's labor force but does not directly affect its capital stock. Then the

immediate impact will be that:

Answer total output will fall, but output per worker will rise.

total output will rise, but output per worker will fall.

both total output and output per worker will fall.

both total output and output per worker will rise.

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Question

Assume that a war reduces a country's labor force but does not directly affect its capital stock. If the

economy was in a steady state before the war and the saving rate does not change after the war, then,

over time, capital per worker will ______ and output per worker will grow ______ than it did before the

war.

Answer decline; faster

increase; faster

decline; more slowly

increase; more slowly

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Question

If a larger share of national output is devoted to investment, then living standards will:

Answer always decline in the short run but rise in the long run.

always rise in both the short and long runs.

decline in the short run and may not rise in the long run.

rise in the short run but may not rise in the long run.

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Question

If a larger share of national output is devoted to investment, starting from an initial steady-state capital

stock below the Golden Rule level, then productivity growth will:

Answer increase in the short run but not in the long run.

increase in the long run but not in the short run.

increase in both the short run and the long run.

not increase in either the short run or the long run.

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Question

If the U.S. production function is Cobb-Douglas with capital share 0.3, output growth is 3 percent per

year, depreciation is 4 percent per year, and the Golden Rule steady-state capital-output ratio is 4.29,

to reach the Golden Rule steady state, the saving rate must be:

Answer 17.5 percent.

25 percent.

30 percent.

42.9 percent.

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Question

If all wage income is consumed, all capital income is saved, and all factors of production earn their

marginal products, then:

Answer the economy will reach a steady-state level of capital stock below the Golden Rule level.

the economy will reach a steady-state level of capital stock above the Golden Rule level.

wherever the economy starts out, it will not grow.

wherever the economy starts out, it will reach a steady-state level of capital stock equal to

the Golden Rule level.

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Question

If an economy moves from a steady state with positive population growth to a zero population growth

rate, then in the new steady state total output growth will be ______ and growth of output per person

will be ______.

Answer lower; lower

lower; the same as it was before

higher; higher than it was before

higher; lower

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Question

If the production function exhibits decreasing returns to scale in the steady state, an increase in the

rate of population would lead to:

Answer growth in total output and growth in output per worker.

growth in total output but no growth in output per worker.

growth in total output but a decrease in output per worker.

no growth in total output or in output per worker.

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Question

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:

Answer growth in total output and growth in output per worker.

growth in total output but no growth in output per worker.

growth in total output but a decrease in output per worker.




no growth in total output or in output per worker.

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Question

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

L1/2

.

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?

Answer a. y = k1/2

.

b. Y = 20,000; Y/L = 2; y = 2; yes

c. s = 0.2.

d. Consumption per worker will be 1.6.

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Question

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 = k and y = k1/2

to get

an equation in s, , 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?

Answer a. k = 16; y = 4; consumption per worker is 2.4.

b. k = 36; y = 6; consumption per worker is 2.4.

c. k = 64; y = 8; consumption per worker is 1.6.

d. Yes. If the capital stock gets so big that the extra output produced by more capital is less

than the extra saving needed to maintain it, extra capital reduces consumption per worker. The

saving rate exceeds the Golden Rule rate.

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Question

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?




Answer a. Country A will have the higher level of output per worker.

b. In the steady state, the growth rate of output per worker will be zero in both country A and

country B.

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Question

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?

Answer a. Country B will have the higher level of output per worker.

b. In the steady state, the growth rate of output per worker will be zero in both Country A and

Country B.

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Question

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.

Answer The Golden Rule level of capital per worker will be higher in Sahara.

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Question

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 ( ) 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?

Answer a. In the steady state, capital per worker is constant, so output per worker is constant. Thus,

the growth rate of steady-state output per worker is 0.

b. In the steady state, population grows at a 2 percent rate (0.02). Capital must grow at a rate

of 2 percent in order to maintain a constant capital per worker ratio in the steady state;

therefore, given the constant returns to scale production function, total output must increase at

a 2 percent rate.

c. If the saving rate is 20 percent, then the consumption rate is 80 percent (1 – 0.2).

Steady-state consumption per worker is 16,000, which is 80 percent of steady-state output per

worker.

d. In the steady state, investment per worker equals saving per worker, which is 20 percent of

steady-state output per worker. Thus, steady-state investment per worker is 4,000.

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Question

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?

Answer a. The saving rate in Macroland must be increased to achieve the higher capital per worker

ratio of the Golden Rule steady state.

b. Consumption per worker is higher in the Golden Rule steady state than in the initial steady

state.

c. In the transition from the initial steady state to the Golden Rule steady state, the level of

consumption per worker must initially decrease to accumulate the additional capital required

for the Golden Rule steady state. Thus, workers who do not want to sacrifice current

consumption for future consumption may prefer the initial steady state.

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Question

The economies of two countries, North and South, have the same production functions, depreciation

rates, and saving rates. The economy 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?

Answer a. North will have a higher level of steady-state output per worker because the population

growth is faster in South. The same saving in both countries means that investment in both

countries will be the same. However, capital will be spread more thinly per worker in the

South, where the population is growing more rapidly. Given the same production functions,

output per worker will be higher in the North because it has a higher capital per worker ratio

than the South.

b. In the steady state in both countries, capital per worker is constant, so output per worker is

constant. The growth rate of output per worker is zero in both North and South.

c. In the steady state, total output grows at the rate of population growth. Since South has a

higher rate of population growth, the growth rate of total output will be higher in South than in

North.

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Question

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

0.5. The saving rate in Profligate is 0.3.

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?

Answer a. Thrifty will have the higher level of steady-state output per worker. With a higher saving rate

in Thrifty, there will be more saving, more investment, and, consequently, a higher

steady-state capital per worker ratio. For the same production function, the higher capital per

worker ratio will produce a higher level of steady-state output per worker.

b. In the steady state in both countries, capital per worker is constant, so output per worker is

constant. The growth rate of output per worker is zero in both Thrifty and Profligate.

c. Since there is no population growth or technological change in the steady state, total output

will be constant in both countries. The growth rate of total output will be zero in both Thrifty

and Profligate.

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Question

Many policymakers are concerned that Americans do not save enough. Using the Solow growth model

of an economy 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.

Answer a. The saving rate is the proportion of output that is saved and the proportion of output

allocated to investment. A larger amount of investment can maintain a larger ratio of capital

per worker and, therefore, a higher level of output per worker can be produced than with a

smaller saving rate.

b. If a high rate of saving generates a level of capital per worker greater than the Golden Rule

level of capital per worker, then consumption per worker will be smaller than at the Golden

Rule level, with a lower saving rate.

c. In the steady state, the capital per worker ratio is constant, so output per worker is constant.

The steady-state growth rate of output per worker is zero regardless of the saving rate.

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Question

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?

Answer The increase in the population growth rate will increase the steady-state level of output and

the steady-state growth rate of output (which will grow at a rate equal to the new higher growth

rate of population). The increase in the population growth rate will not change the steady-state

growth rate of output per worker which in the long run is zero.

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Question

Explain the two uses of saving in the steady state in the Solow model of an economy with population

growth but no technological progress.

Answer Saving supplies (1) the investment to replace the depreciating capital and (2) the investment

to equip new workers with the same amount of capital as existing workers in the economy so

that the steady-state capital per worker ratio does not change.

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Question

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.

Answer In the Solow growth model, a faster rate of population growth reduces output per worker

because capital must be spread more thinly over the supply of workers. In Malthus's model,

faster population growth exhausts the supply of food and leads to a lower standard of living. In

Kremer's model, faster rates of population growth increase the pool from which new ideas and

innovations can be drawn and thereby improves the standard of living.

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Question

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.

Answer a. The steady-state levels of output per worker will be the same in both countries because the

assumption of constant returns to scale means that the absolute size of the economy,

measured by number of workers, does not affect output.

b. The steady-state level of output per worker will be lower in Country Large, because with the

same saving rate but a faster growing population, Country Large will not be able to maintain

as high a capital per worker ratio as Country Small.

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Question

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.

Answer Larger quantities of steady-state capital increase the capital per worker ratio and increase the

quantity of output; therefore, a greater quantity of output is available for consumption per

worker. Large quantities of steady-state capital generate more depreciation which must be

replaced from output in order to maintain the steady state, thus reducing the amount of output

available for consumption per worker.

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