Econ 102 Chapter 8
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
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.
The Golden Rule level of the steady-state capital stock:
implies a choice of a particular saving rate.
Exhibit: The Capital-Labor Ratio
increase
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.
The production function y = f(k) means:
output per worker is a function of capital per worker.
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
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
In the Solow model, it is assumed that a(n) ______ fraction of capital wears out as the capital-labor ratio increases.
constant
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
According to the Solow growth model, high population growth rates:
force the capital stock to be spread thinly, thereby reducing living standards.
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, no technological change, and no population growth, a higher saving rate produces a:
higher steady-state level of 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.
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 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.
Exhibit: Steady-State Capital-Labor Ratio
k2
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.
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
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
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:
A's capital-labor ratio will be 4 whereas B's will be 16.
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 Y = K0.3L0.7, then the per-worker production function is:
Y/L = (K/L)0.3.
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
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.
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.
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 ______ as it returns to the steady state.
decline; decrease
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
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 in the transition to the new steady state consumption per worker
first fall below then rise above the initial level.
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 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.
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
The Solow model with population growth but no technological change cannot 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 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.
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
Investment per worker (i) as a function of the saving ratio (s) and output per worker (f(k)) may be expressed as:
sf(k).
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.
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.
In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:
∆k = sf(k) - (δ + n)k.
The steady-state level of capital occurs when the change in the capital stock (∆k) equals:
0
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
Exhibit: Steady-State Consumption II The Golden Rule level of steady-state consumption per worker is:
AB
Exhibit: Steady-State Consumption II The Golden Rule level of steady-state investment per worker is:
BC
______ cause(s) the capital stock to rise, while ______ cause(s) the capital stock to fall.
Investment; depreciation
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
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.
The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per wo
c* = f(k*) - δk*.
The Solow growth model describes
how saving, population growth, and technological change affect output over time.
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 the saving rate determines the allocation of output between:
investment and consumption.
Exhibit: Steady-State Consumption I The Golden Rule level of the capital-labor ratio is:
k*A
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.
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 8, the demand 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.
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, 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.
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.
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:
16
If the capital stock equals 200 units in year 1 and the depreciation rate is 5 percent per year, then in year 2, assuming no new or replacement investment, the capital stock would equal _____ units.
190
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:
2 and 1.8, respectively.
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.
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 steady state is attained.
increase; increase
In the Solow growth model, increases in capital ______ output and ______ the amount of output used to replace depreciating capital.
increase; increase
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.
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.
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, then the capital per worker ratio ____ the Golden Rule level.
is below
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.
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
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.
An economy in the steady state with no population growth or technological change will have:
no change in the capital stock.
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.
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:
steady-state consumption per worker would be higher in a steady state with a lower saving rate.
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:
∆k = sf(k) - δk.
