Macroeconomics chapter 8 and 9
? cause(s) the capital stock to rise over time, while ? cause(s) the capital stock to fall over time.
Investment; depreciation
If Y = K^0.3L^0.7, then the per worker production function is:
Y/L = (K/L)^0.3
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.
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
An increase in the rate of population growth with no change in the saving rate:
decreases the steady-state level of capital per worker.
In the Solow growth model with population growth and technological change, the breakeven level of investment must cover:
depreciating capital, capital for new workers, and capital for new effective workers.
Exhibit: Capital Labor Ratio and the Steady State In this graph, capital-labor ratio k2 is not the steady state capital labor ratio because:
depreciation is greater than gross investment.
The number of effective workers takes into account the number of workers and the:
efficiency of each worker.
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 will:
first fall below then rise above the initial level.
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.
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.
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.
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 long run but not in the short run.
In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:
k = sf(k) - ( + n)k.
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:
k = sf(k) - k.
Assuming that technological progress increases the efficiency of labor at a constant rate is called:
labor augmenting technological progress.
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 output per worker.
Endogenous growth theory rejects the assumption of exogenous:
technological change.
According to the Solow model, persistently rising living standards can only be explained by:
technological progress.
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, 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.
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 saving rate.
International data suggest that economies of countries with different steady states will converge to:
their own steady state.
Conditional convergence occurs when economies converge to:
their own, individual steady states.
The steady state level of capital occurs when the change in the capital stock (k) equals:
0.
The Golden Rule level of the capital-labor ratio is:
*Ak .
If the perworker 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, the steady state occurs when:
- capital per worker is constant.
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.
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.
If y = k^1/2, 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 1.6, respectively.
If the per worker production function is given by y = k^1/2, the saving ratio is 0.2, and the depreciation rate is 0.1, then the steady state ratio of output per worker (y) is:-
2.
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:
30 percent.
If y = k^1/2, 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:
4.
If the labor force is growing at a 3 percent rate and the efficiency of a unit of labor is growing at a 2 percent rate, then the number of effective workers is growing at a rate of:
6 percent.
With a per worker production function y = k^1/2, the steady state capital stock per worker (k*) as a function of the saving rate (s) is given by
: - k* = (s/)^2
If the per worker production function is given by y = k ^1/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady state ratio of output per worker (y) is
:- 2.
If the per worker production function is given by y = k^1/2, the saving rate (s) is 0.2, and the depreciation rate is 0.1, then the stead -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:-
AC.
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.
Assume that two countries both have the per worker production function y = k^1/2, 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:
both A and B will have capital-labor ratios of 4.
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.
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:
both total output and output per worker will fall.
The formula for steady state consumption per worker (c*) as a function of output per worker and investment per worker is
c* = f(k*) - k*.
The Solow residual measures the portion of output growth that cannot be explained by growth in
capital and labor.
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.
The Golden Rule level of capital accumulation is the steady state with the highest level of:
capital per worker.
In this graph, starting from capital labor ratio k1, the capital labor ratio will:
increase.
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.
increase; decrease
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 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 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.
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
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.
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 steady state of 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
Schumpeter's thesis of "creative destruction" is an explanation of economic progress resulting from:
new product producers driving incumbent producers out of business.
In the Solow growth model with population growth, but no technological progress, the steady state amount of investment can be thought of as a breakeven amount of investment because the quantity of investment just equals the amount of:
output needed to make the capital per worker ratio equal to the marginal product of capital.
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, the demand for goods equals investment:
plus consumption.
In the Solow growth model, the steady state level of output per worker would be higher if the ? increased or the ? decreased.
population growth rate; depreciation rate
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
When an economy begins below the Golden Rule, reaching the Golden Rule:
requires initially reducing consumption to increase consumption in the future.
Exhibit: Steady State Capital Labor Ratio In this graph, the capital labor ratio that represents the steady
state capital ratio is- k2.
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 Solow model predicts that two economies will converge if the economies start with the same:
steady states.
If two economies are identical (with the same population growth rates and rates of technological progress), but one economy has a lower saving rate, then the steady state level of income per worker in the economy with the lower saving rate:
will be at a lower level than in the steady state of the high-saving economy.
If two economies are identical (including having the same saving rates, population growth rates, and efficiency of labor), but one economy has a smaller capital stock, then the steady state level of income per worker in the economy with the smaller capital stock:
will be at the same level as in the steady state of the high capital economy.
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
Unlike the long run classical model in Chapter 3, the Solow growth model:
✅- describes changes in the economy over time.
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.-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, if investment is less than depreciation, the capital stock will ? and output will ? until the steady state is attained.
✅decrease; decrease
In the steady state with no population growth or technological change, the capital stock does not change because investment equals:
✅depreciation.
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, 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.
The Solow growth model describes:
✅how saving, population growth, and technological change affect output over time.
In the Solow growth model, if investment exceeds depreciation, the capital stock will ? and output will ? until the steady state is attained.
✅increase; increase
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.
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
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 production function y = f(k) means:
✅output per worker is a function of capital per worker.
In the Solow growth model of Chapter 8, investment equals:
✅saving.
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.
