Econ 4999 Final Exam

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

0.

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.

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 / )2.

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.

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.

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).

The Solow growth model describes:

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

In the Solow growth model, investment equals:

saving.

In a steady-state economy with a saving rate s, population growth n, depreciation rate , and labor-augmenting technological progress g, the formula for the steady-state ratio of capital per effective worker (k*), in terms of output per effective worker (f (k*)), is

sf (k) / ( + n + g).

In the Solow growth model, 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

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 model with technological progress, the steady-state growth rate of capital per effective worker is:

0.

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

Investment; depreciation

Exhibit: Steady-State Consumption I The Golden Rule level of the capital-labor ratio is:

K*a

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 that 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 compared to the country with the lower saving rate.

a higher; the same

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*.

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.

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.

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.

When does a steady state occur?

an unchanging condition, system or physical process that remains the same even after transformation or change.

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.

The efficiency of labor:

depends on the knowledge, health, and skills of labor.

In the Solow growth model with population growth and labor-augmenting technological change, the break-even level of investment must cover:

depreciating capital, capital for new workers, and capital for new effective workers.

Exhibit: Capital per Worker and the Steady State In this graph, capital-labor ratio k2 is not the steady-state because:

depreciation is greater than gross investment.

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 and then rise above the initial level.

In the Solow model with technological progress, the steady-state growth rate of output per worker is:

g.

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 countries with low population growth.

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.

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

Starting from a steady-state situation, if the saving rate increases, capital per worker will:

increase until the new steady state is reached.

Exhibit: The Capital-Labor Ratio In this graph, starting from capital-labor ratio k1, the capital-labor ratio will:

increase.

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

Exhibit: Output, Consumption, and Investment In this graph, when the capital stock per worker 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.

Assume that 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 compared to 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.

In the Solow model with technological progress, the steady-state growth rate of total output is:

n + g.

The production function y = f (k) means:

output per worker is a function of capital per worker.

Suppose that an economy is in its steady state and the capital stock is above the Golden Rule level. Assuming that there are no population growth or technological change, if 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 the demand for goods equals investment:

plus consumption.

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

regardless of the starting level of capital.

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

results in higher consumption at all times in the future.

According to the Solow model, persistently rising living standards can only be explained by:

technological progress.

What is the marginal product of capital (MPK), as shown with the Solow model?

the additional production a company experiences by adding one unit of capital.

The rate of labor-augmenting technological progress (g) is the growth rate of:

the efficiency of labor.

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

the marginal product of capital.

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, 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 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

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.

What is the difference between convergence and conditional convergence with respect to predictions of the Solow growth model? Explain.

Convergence applies to economies with the same saving rate, population growth rate, depreciation rate, rate of technological progress, and production function. Conditional convergence applies to economies with different saving rates, population growth rates, depreciation rates, rates of technological progress, and/or production functions.

If the saving rate increases, the:

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

The number of effective workers takes into account the number of workers and the:

efficiency of each worker.

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 the Solow model with technological change, the Golden Rule level of capital is the steady state that maximizes:

consumption per effective worker.

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

consumption per worker.

Exhibit: Steady-State Capital-Labor Ratio In this graph, the steady-state capital-labor ratio is:

k2.

The assumption that technological progress increases the efficiency of labor is called:

labor-augmenting technological progress.

A higher saving rate leads to a:

larger capital stock and a higher level of output in the long run.

With population growth at rate n and labor-augmenting technological progress at rate g, the Golden Rule steady state requires that the marginal product of capital (MPK):

net of depreciation be equal to n + g.

When an economy's capital is below the Golden Rule level, reaching the Golden Rule level:

requires initially reducing consumption to increase consumption in the future.

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 with population growth but no technological progress, when the economy finds itself at the Golden Rule steady state, the marginal product of capital minus the rate of depreciation will equal:

the population growth rate.

Define Golden Rule level of capital.

the rate of savings which maximizes steady state level or growth of consumption

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, the steady-state growth rate of output per effective worker is ______, and the steady-state growth rate of output per actual worker is ______.

zero; the rate of technological progress

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 approximately at a rate of:

5 percent.

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 in the steady state grows at rate ______, and output per worker grows at rate ______ in the steady state.

n; 0

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).

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 model with technological progress, the steady-state growth rate of output per effective worker is:

0.

In the Solow growth model of an economy with population growth but no technological change, if population grows at rate n, then capital in the steady state grows at rate ______, and output grows at rate ______ in the steady state.

n; n