Chapter 8: Capital Accumulation and Population Growth
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:
Output, investment, and depreciation will decrease, and consumption will increase and then decrease but finally approach a level above its initial state
The Solow growth model with population growth but no technological progress can explain:
Persistent growth in total output
According to Malthus, large populations:
Place great strains on an economy's productive resources, resulting in perpetual poverty
In the Solow growth model of Chapter 9, the demands for goods equals investment:
Plus consumption
When an economy begins above the Golden Rule, reaching the Golden Rule:
Produces higher consumption at all times in the future
In the Solow growth model of Chapter 8, for any given capital stock, the _____ determines how much output the economy produces and the _____ determines the allocation of output between consumption and investment.
Production function; Saving rate
In the Solow growth model of Chapter 8, the economy ends up with a steady-state level of capital:
Regardless of the starting level of capital
When an economy begins below the Golden Rule, reaching the Golden Rule:
Requires initially reducing consumption to increase consumption in the future
In the Solow growth model of Chapter 8, investment equals:
Saving
The Solow model shows that a key determinant of the steady-state ratio of capital to labor is the:
Saving rate
In the Solow growth model, the steady state level of output per worker would be higher if the _____ increased or the _____ decreased.
Saving rate; Depreciation rate
If y = k^1/2, the country saves 10% of its output each year, and the steady-state level of capital per worker is 4, then steady-state levels of output per worker and consumption per worker are:
2 and 1.8, respectively
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:
3
Analysis of population growth around the world concludes that countries with high population growth tend to:
Have a lower level of income per worker than other parts of the world
Examination of recent data for many countries shows that countries with high saving rates generally have high levels of output per person because:
High saving rates lead to high levels of capital per worker
In the Solow growth model, with a given production function, depreciation rate, saving rate, and no technological change, higher rates of population growth produce:
Higher steady-state growth rates of total output
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:
Higher steady-state level of output per worker
In the Solow growth model 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:
Increasing the population growth rate
In the Solow growth model the saving rate determines the allocation of output between:
Investment and Consumption
_____ cause(s) the capital stock to rise, while _____ cause(s) the capital stock to fall.
Investment; Depreciation
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:
Is less than the Golden Rule level
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:
Japan
A higher saving rate leads to a:
Larger capital stock and a higher level of output in the long run
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:
Largest consumption per worker
An economy in the steady state with no population growth or technological change will have:
No change in the capital stock
The Solow model with population growth but no technological change can't explain persistent growth in standards of living because:
Output, capital, and population all grow at the same rate in the steady state
If an economy is in a steady state with no population growth or technological change and the marginal product of a capital is less than the depreciation rate:
Steady-state consumption per worker would be higher in a steady state with a lower saving rate
When f(k) is drawn on a graph with increases in k noted along the horizontal axis, the slope of the line denotes:
The marginal product of capital
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:
Level of output per worker
In the Solow growth model, with a given production function, depreciation rate, saving rate, and no technological change, lower rates of population growth produce:
Lower steady-state growth rates of total output
(Exhibit: Steady-State Consumption II) The Golden Rule level of steady-state consumption per worker is:
AB
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:
Always exceed the initial level
According to Kremer, large populations:
Are a prerequisite for technological advances and higher living standards
(Exhibit: Steady-State Consumption II) The Golden Rule level of steady-state investment per worker is:
BC
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:
Both higher per-capita output and higher per-capita depreciation, but the increase in per capita output would be greater
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:
Capital equals the depreciation rate
Assume that a country's production function is Y = (K^1/2)(L^1/2). d. If the saving rate equals the steady-state level, what is consumption per worker?
Consumption per worker will be 1.6
If a larger share of national output is devoted to investment, then living standards will:
Decline in the short run and may not rise in the long run
The Solow growth model describes:
How saving, population growth, and technological change affect output over time
In the Solow growth model of Chapter 8, where s is the saving rate, y is output per worker, and i is investment per worker, consumption per worker (c) equals:
(1 - s) y
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:
4
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:
0
The steady-state level of capital occurs when the change in the capital stock (Δk) equals:
0
If y = k^1/2, there is no population growth or technological progress, 5% of capital depreciates each year, and a country saves 20% of output each year, then the steady-state level of capital per worker is:
16
If the capital stock equals 200 units in year 1 and the depreciation rate is 5% per year, then in year 2, assuming no new or replacement investment, the capital stock would equal _____ units.
195
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:
2
If the U.S. production function is Cobb-Douglas with capital share 0.3, output growth is 3% per year, depreciation is 4% per year, and the Golden Rule steady-state capital-output ratio is 4.29, the saving rate must be:
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 capital to labor is:
9
In the Solow growth model with population growth, but no technological change, which of the following will generate a higher steady-state growth rate of total output?
A higher population growth rate
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 output per person and _____ rate of growth of output per worker as/than the country with the lower saving rate.
A higher; The same
Assume that countries both have the per-worker production function y = k^1/2, neither has population growth or technological progress, depreciation is 5% of capital in both countries, and country A saves 10% of output whereas country B saves 20%. 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:
A's capital-labor ratio will be 4 whereas B's withh be 16
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, the, over time, capital per worker will _____ and output per worker will _____ as it returns to the steady state.
Decline; Increase
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.
Decrease
In the Solow growth model, if investment is less than depreciation, the capital stock will _____ and output will _____ until the steady state is attained.
Decrease; Decrease
An increase in the rate of population growth with no change in the saving rate:
Decreases the steady-state level of capital per worker
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:
Growth in total output and growth in output per worker
If the production function exhibits decreasing returns to scale in the steady state, an increase in the rate of population would lead to:
Growth in total output but a decrease in output per worker
If an economy is in a steady state with no population growth or technological change and the capital stock is below the Golden Rule:
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
The Golden Rule level of the steady-state capital stock:
Implies a choice of a particular saving rate
(Exhibit: The Capital-Labor Ratio) In this graph, starting from capital-labor ratio k1, the capital-labor ratio will:
Increase
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.
Increase
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:
Increase in the short run but not in the long run
Starting from a steady-state situation, if the saving rate increases, the rate of growth of capital per worker will:
Increase until the new steady state is reached
In the Solow growth model, if investment exceeds depreciation, the capital stock will _____ and output will _____ until the ready state is attained.
Increase; Increase
In the Solow growth model, increases in capital _____ output and _____ the amount of output used to replace depreciation capital.
Increase; Increase
In the Solow growth model 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 _____.
Increasing output; Increasing output required to replace depreciating capital
In the Solow growth model 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, the the capital per worker ratio _____ the Golden Rule level.
Is below
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 output per person and ______ rate of growth of output per worker as/than the country with the lower population growth rate.
Lower; The same
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 _____.
Lower; The same as it was before
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:
More in Lowland
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:
Multiplied by f(k*) divided by the sum of the depreciation rate plus n
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):
Net of depreciation to n
The production function y = f(k) means:
Output per worker is a function of capital per worker
When f(k) is drawn on a graph with increases in k noted along the horizontal axis, the:
Slope of the line eventually gets flatter and flatter
In the Solow growth model, the assumption of constant returns to scale means that:
The number of workers in an economy does not affect the relationship between output per worker and capital per worker
In the Solow growth model with population growth, but no technological progress, in the Golden Rule steady state, the marginal product of capital minus the rate of depreciation will equal:
The population growth rate
If all wage income is consumed, all capital income is saved, and all factors of production earn their marginal products, then:
Wherever the economy starts out, it will reach a steady-state level of capital stock equal to the Golden Rule level
Assume that a country's production function is Y = (K^1/2)(L^1/2). 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?
Y = 20,000 Y/L = 2 y =2 Yes
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% of capital depreciates per year (= 0.10). d. Is it possible to save too much? Why?
Yes. If the capital stock gets so big that the extra output produced by more capital is less than the extra savings needed to maintain it, extra capital reduces consumption per worker. The saving rate exceeds the Golden Rule rate.
The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is:
c* = f(k*) - δk*
(Exhibit: Output, Consumption, and Investment) In this graph, when the capital - labor ratio is OA, AB represents:
investment per worker, and BC represents consumption per worker
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% 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?
k = 16 y = 4 Consumption per worker is 2.4
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% of capital depreciates per year (= 0.10). c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8.
k = 64 y = 8 Consumption per worker is 1.6
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% of capital depreciates per year (= 0.10). b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.6.
k =36 y = 6 Consumption per worker is 2.4
(Exhibit: Steady-State Consumption I) The Golden Rule level of the capital-labor ratio is:
k*
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:
k* = (s/δ)^2
(Exhibit: Steady-State Capital-Labor Ratio) In this graph, the capital-labor ratio that represents the steady-state capital-ratio is:
k2
The formula for the steady-state ratio of capital to labor (k*), with no population growth or technological change, is s:
multiplied by f(k*) divided by the depreciation rate
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:
n
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 _____.
n; 0
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 _____.
n; n
Assume that a country's production function is Y = (K^1/2)(L^1/2). c. Assume that 10% of capital depreciates each year. What gross saving rate is necessary to make the given capital - labor ratio the steady - state capital - labor ratio?
s = 0.2
Investment per worker (i) as a function of the saving ratio (s) and output per worker (f(k)) may be expressed as:
sf(k)
Assume that a country's production function is Y = (K^1/2)(L^1/2). a. What is the per-worker production function y = f(k)?
y = k^1/2
In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:
Δk = sf(k) - (δ + n)k
The change in capital stock per worker (Δk) may be expressed as a function s = the saving ration, f(k) = output per worker, k = capital per worker, and δ = the depreciation rate, by the equation:
Δk = sf(k) - δk
According to the Solow growth model, high population growth rates:
Force the capital stock to be spread thinly, thereby reducing living standards
In the Solow growth model 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:
Capital needed to replace depreciated capital and to equip new workers
In the Solow growth model, the steady-state occurs when:
Capital per worker is constant
In the Solow model, it is assumed that a(n) _____ fraction of capital wears out as the capital - labor ratio increases.
Constant
The consumption function in the Solow model assumes that society saves a:
Constant proportion of income
The Golden Rule level of capital accumulation is the steady state with the highest level of:
Consumption per worker
In the steady state with no population growth or technological change, the capital stock does not change because investment equals:
Depreciation
(Exhibit: Capital - Labor Ratio and the Steady State) In this graph, capital-labor ration k2 is not the steady-state capital-labor ration because:
Depreciation is greater than gross investment
Unlike the long-run classical model in Chapter 3, the Solow growth model:
Describes changes in the economy over time
If the national saving rate increases, the:
Economy will grow at a faster rate until a new, higher, steady-state capital-labor ratio is reached
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:
Equal the marginal productivity of capital (MPK)
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:
Equals the Golden Rule level
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 the transition to the new steady state consumption per worker will:
First fall below then rise above the initial level
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 1 billion workers and Country Small has a population of 10 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 ______
The same in both countries; The same in both countries
If a war destroys a large portion of a country's capital stock but the saving rate is unchanged, the Solow model predicts that output will grow and that the new steady state will approach:
The same level of output per person as before
According to the Kremerian model, large populations improve living standards because:
There are more people who can make discoveries and contribute to innovation
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:
Total output will fall, but output per worker will rise
The Malthusian model that predicts mankind will remain in poverty forever:
Underestimated the possibility for technological progress
If y = (K^0.3)(L^0.7), then the per-worker production function is:
Y/L = (K/L)^0.3
