Homework 7

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 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 the Solow growth model the saving rate determines the allocation of output between:

investment and consumption

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 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

A higher saving rate leads to a:

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

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 = 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

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.

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

Investment; depreciation

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

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

capital per worker is 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.

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 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.

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

describes changes in the economy over time.

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 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, 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.

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.

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.

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 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.

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

0.

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

The production function y = f(k) means:

output per worker is a function of capital per worker.

The change in capital stock per worker (Δk) 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:

Δk = sf(k) - δk.

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.

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, 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