HW5

If the capital stock is above the steady-state level, then investment: A. is smaller than depreciation. B. is larger than depreciation. C. is equal to depreciation. D. could be higher than, lower than, or equal to depreciation.

A (The correct answer is: is smaller than depreciation. Since the capital stock is above its steady-state level, it must be falling. This occurs when investment is smaller than depreciation. See Section 8-1)

In the Solow growth model, if investment exceeds depreciation, the capital stock will ______ and output will ______ until the steady state is attained. A. increase; increase B. increase; decrease C. decrease; decrease D. decrease; increase

A

In the Solow growth model, the steady-state occurs when: A. capital per worker is constant. B. the saving rate equals the depreciation rate. C. output per worker equals consumption per worker. D. consumption per worker is maximized.

A

The Malthusian model that predicts mankind will remain in poverty forever: A. underestimated the possibility for technological progress. B. failed to predict that scarcity would be eliminated in the modern world. C. assumed that prosperity would lead to declining human fertility. D. recognized that the ability of natural resources to sustain humans is far greater than the power of population to consume resources.

A

The consumption function in the Solow model assumes that society saves a: A. constant proportion of income. B. smaller proportion of income as it becomes richer. C. larger proportion of income as it becomes richer. D. larger proportion of income when the interest rate is higher.

A

The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is: A. c* = f(k*) - δk*. B. c* = f(k*) + δk*. C. c* = f(k*) ÷ δk*. D. c* = k* - δf(k)*.

A

The steady-state level of capital occurs when the change in the capital stock (Δk) equals: A. 0. B. the saving rate. C. the depreciation rate. D. the population growth rate.

A

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: A. k* = (s/δ)2. B. k* = (δ/s)2. C. k* = s/δ. D. k* = δ/s.

A

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: A. 2 and 1.6, respectively. B. 2 and 1.8, respectively. C. 4 and 3.2, respectively. D. 4 and 3.6, respectively.

B

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: A. sy B. (1 - s)y C. (1 + s)y D. (1 - s)y - i

B

Starting from a steady-state situation, if the saving rate increases, the rate of growth of capital per worker will: A. increase and continue to increase unabated. B. increase until the new steady state is reached. C. decrease until the new steady state is reached. D. decrease and continue to decrease unabated.

B

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: A. 1. B. 2. C. 3. D. 4.

B

An economy starts off in a steady state with less capital than at the Golden Rule level. Now the saving rate changes to the level that will achieve the Golden Rule. What is the path of consumption during the transition to the Golden Rule steady state? A. It is lower, then higher than in the initial steady state. B. It is higher, then lower than in the initial steady state. C. It is always lower than in the initial steady state. D. It is always higher than in the initial steady state.

A (The saving rate must rise to achieve the Golden Rule. This will reduce consumption immediately, but will raise it in the long run. See Figure 8.10 in Section 8-2)

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. A. increase B. decrease C. first increase, then decrease D. first decrease, then increase

B

According to Malthus, large populations: A. require the capital stock to be spread thinly, thereby reducing living standards. B. place great strains on an economy's productive resources, resulting in perpetual poverty. C. are a prerequisite for technological advances and higher living standards. D. are not a factor in determining living standards.

B

An increase in the rate of population growth with no change in the saving rate: A. increases the steady-state level of capital per worker. B. decreases the steady-state level of capital per worker. C. does not affect the steady-state level of capital per worker. D. decreases the rate of output growth in the short run.

B

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: A. a higher level of output per person than before. B. the same level of output per person as before. C. a lower level of output per person than before. D. the Golden Rule level of output per person.

B

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: A. is greater than the Golden Rule level. B. is less than the Golden Rule level. C. equals the Golden Rule level. D. could be either above or below the Golden Rule level.

B

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: A. always exceed the initial level. B. first fall below then rise above the initial level. C. first rise above then fall below the initial level. D. always be lower than the initial level.

B

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: A. more in Highland. B. more in Lowland. C. by the same amount in Highland and Lowland. D. in Highland, but not in Lowland.

B

Unlike the long-run classical model in Chapter 3, the Solow growth model: A. assumes that the factors of production and technology are the sources of the economy's output. B. describes changes in the economy over time. C. is static. D. assumes that the supply of goods determines how much output is produced.

B

When an economy begins above the Golden Rule, reaching the Golden Rule: A. produces lower consumption at all times in the future. B. produces higher consumption at all times in the future. C. requires initially reducing consumption to increase consumption in the future. D. requires initially increasing consumption to decrease consumption in the future.

B

f Y = K^0.3 * L^0.7, then the per-worker production function is: A. Y = F(K/L). B. Y/L = (K/L)^0.3. C. Y/L = (K/L)^0.5. D. Y/L = (K/L)^0.7.

B

The change in the capital stock is equal to: A. investment. B. investment - depreciation. C. investment - inflation. D. investment - depreciation - inflation.

B (Investment is the amount of new capital added each period, depreciation is the amount of capital that wears out each period. See Section 8-1)

If the population growth rate decreases in an economy described by the Solow growth model, the line representing population growth and depreciation will: A. pivot counterclockwise. B. pivot clockwise. C. stay the same. D. shift upwards.

B (The correct answer is: pivot clockwise. Decreasing the rate of population growth shifts the line downward. See Figure 8.12 in Section 8-3)

The Solow growth model assumes that the production function exhibits: A. decreasing returns to scale. B. constant returns to scale. C. increasing returns to scale. D. increasing marginal product.

B (The production function used in the Solow growth model exhibits constant returns to scale. See Section 8-1)

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. A. higher; the same B. higher; a higher C. lower; the same D. lower; a lower

C

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. the same; the same B. the same; a higher C. a higher; the same D. a higher; a higher

C

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: A. is greater than the Golden Rule level. B. is less than the Golden Rule level. C. equals the Golden Rule level. D. could be either above or below the Golden Rule level.

C

If the national saving rate increases, the: A. economy will grow at a faster rate forever. B. capital-labor ratio will increase forever. C. economy will grow at a faster rate until a new, higher, steady-state capital-labor ratio is reached. D. capital-labor ratio will eventually decline.

C

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: A. 1. B. 2. C. 4. D. 9.

C

If the per-worker production function is given by y = k1/2, the saving rate is 0.3, and the depreciation rate is 0.1, then the steady-state ratio of output per worker (y) is: A. 1. B. 2. C. 3. D. 4.

C

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: A. labor equals the marginal product of capital. B. labor equals the depreciation rate. C. capital equals the depreciation rate. D. capital equals zero.

C

In the Solow model, it is assumed that a(n) ______ fraction of capital wears out as the capital-labor ratio increases. A. smaller B. larger C. constant D. increasing

C

In the steady state with no population growth or technological change, the capital stock does not change because investment equals: A. output per worker. B. the marginal product of capital. C. depreciation. D. consumption.

C

Investment per worker (i) as a function of the saving ratio (s) and output per worker (f(k)) may be expressed as: A. s + f(k). B. s - f(k). C. sf(k). D. s/f(k).

C

The Golden Rule level of the steady-state capital stock: A. will be reached automatically if the saving rate remains constant over a long period of time. B. will be reached automatically if each person saves enough to provide for his or her retirement. C. implies a choice of a particular saving rate. D. should be avoided by an enlightened government.

C

The Solow growth model describes: A. how output is determined at a point in time. B. how output is determined with fixed amounts of capital and labor. C. how saving, population growth, and technological change affect output over time. D. the static allocation, production, and distribution of the economy's output.

C

The Solow model with population growth but no technological change cannot explain persistent growth in standards of living because: A. total output does not grow. B. depreciation grows faster than output. C. output, capital, and population all grow at the same rate in the steady state. D. capital and population grow, but output does not keep up.

C

The production function y = f(k) means: A. labor is not a factor of production. B. output per worker is a function of labor productivity. C. output per worker is a function of capital per worker. D. the production function exhibits increasing returns to scale.

C

An economy is in a steady state with capital higher than the Golden Rule level. Now the saving rate falls to a level that will achieve the Golden Rule capital stock in the long run. What will happen to the level of consumption between the initial and new steady states? A. It will rise gradually. B. It will fall instantly and then will rise gradually. C. It will rise instantly and then will fall gradually. D. It will rise instantly and then will remain constant.

C (As shown in Figure 8.9, the level of consumption rises instantly and then falls gradually until it reaches its Golden Rule level)

The Golden Rule level of capital accumulation is defined as the level of the capital stock that achieves a steady state with the: A. highest rate of savings. B. highest level of income. C. highest level of consumption. D. lowest level of depreciation.

C (For a discussion of the Golden Rule level of capital accumulation, see Section 8-2)

If an economy is initially in a steady state and it experiences an increase in its saving rate, then the steady-state capital stock will: A. fall. B. stay the same. C. rise. D. rise only if depreciation also rises.

C (If the saving rate rises, the steady-state level of the capital stock will also rise. See Section 8-1)

A war has wrecked the economy of Baloneya: both the capital stock and the work force have been reduced by 50 percent. If the economy's production function has constant returns to scale, how will the postwar level of output per worker compare to the prewar level? A. It will be lower. B. It will be higher. C. It will be the same. D. It could be higher or lower.

C (Output per worker depends only on the level of capital per worker. Since capital per worker does not change in this case, neither does the level of output per worker. See Section 8-1)

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: A. output, consumption, investment, and depreciation will all decrease. B. output and investment will decrease, and consumption and depreciation will increase. C. output and investment will decrease, and consumption and depreciation will increase and then decrease but finally approach levels above their initial state. D. output, investment, and depreciation will decrease, and consumption will increase and then decrease but finally approach a level above its initial state.

D

In an economy with population growth at rate n, the change in capital stock per worker is given by the equation: A. Δk = sf(k) + δk. B. Δk = sf(k) - δk. C. Δk = sf(k) + (δ + n)k. D. Δk = sf(k) - (δ + n)k.

D

In the Solow growth model of Chapter 8, investment equals: A. output. B. consumption. C. the marginal product of capital. D. saving.

D

In the Solow growth model the saving rate determines the allocation of output between: A. saving and investment. B. output and capital. C. consumption and output. D. investment and consumption.

D

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: A. growth rate of total output. B. level of consumption per worker. C. growth rate of output per worker. D. level of output per worker.

D

In the Solow growth model, the assumption of constant returns to scale means that: A. all economies have the same amount of capital per worker. B. the steady-state level of output is constant regardless of the number of workers. C. the saving rate equals the constant rate of depreciation. D. the number of workers in an economy does not affect the relationship between output per worker and capital per worker.

D

The Golden Rule level of capital accumulation is the steady state with the highest level of: A. output per worker. B. capital per worker. C. savings per worker. D. consumption per worker.

D

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: A. Δk = sf(k)/δk. B. Δk = sf(k) × δk. C. Δk = sf(k) + δk. D. Δk = sf(k) - δk.

D

The formula for the steady-state ratio of capital to labor (k*), with no population growth or technological change, is s: A. divided by the depreciation rate. B. multiplied by the depreciation rate. C. divided by the product of f(k*) and the depreciation rate. D. multiplied by f(k*) divided by the depreciation rate.

D

If two economies are identical except for their rates of population growth, then the economy with the higher rate of population growth will have: A. higher steady-state output per worker. B. higher steady-state capital per worker. C. higher steady-state consumption per worker. D. lower steady-state output per worker.

D (As discussed in Section 8-3, an economy with a higher rate of population growth will have lower steady-state levels of capital, output, and consumption per worker)

At the Golden Rule level of capital accumulation, the marginal product of capital equals the: A. real interest rate. B. depreciation rate. C. savings rate. D. marginal product of labor.

D (For a discussion of the Golden Rule level of capital accumulation, see Section 8-2)

Which of the following is not assumed by the Solow growth model? A. constant returns to scale in production B. output depends only on capital, labor, and technology C. diminishing marginal products of labor and capital D. output is constant

D (In the Solow growth model, output varies if capital, labor, or technology changes. See Section 8-1)

Suppose that the production function is y = k^0.5, s = 0.40, and the depreciation rate δ = 0.10. What is the steady-state level of capital? A. 2 B. 4 C. 10 D. 16

D (In the steady state: sy = δk. So 0.4 × k0.5 = 0.1 × k. This formula can be rearranged to yield sqrt(k) = (0.4/0.1). Thus, k = 16. See Section 8-1)

Suppose that the capital stock is 100, the depreciation rate is 10 percent per year, and output is 25. What must the saving rate be to keep the capital stock constant? A. 2.5 percent B. 10 percent C. 25 percent D. 40 percent

D (Total depreciation is 10 units per year. If the saving rate is 40 percent, total investment will also be 10 units per year, and the capital stock will be constant. See Section 8-1)