Chapter 9 Macro Econ

The Golden Rule with population growth

c*=y*-i* = f (k*) - (δ+n)k*for i*= (δ+n)k* at the steady state

In the basic endogenous growth model, income can grow forever—even without exogenous technological progress—because:

capital does not exhibit diminishing returns.

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 two-sector endogenous growth model, income growth persists because the:

creation of knowledge in universities never slows down.

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 model, which two variables have similar effects on the capital stock per worker?

depreciation and population growth

In the Solow model, which two variables have similar effects on the capital stock per worker?

depreciation and population growth

The purpose of ------ growth theory is to explain technological progress. Some of these models do so by questioning the Solow model's assumption of ------ returns to capital.

endogenous, diminishing

In the Solow model with no technological progress, the marginal product of capital at the steady state is 5%. And, the depreciation rate is 4% and the population growth rate is 2 %. Then, the economy is operating with a level of capital _____ than the Golden Rule level of capital, and it must _____ the saving rate to reach the Golden Rule level of capital.

more; decrease

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

technological progress.

In the two-sector endogenous growth model, the steady-state stock of physical capital is determined by _____, and the growth in the stock of knowledge is determined by _____.

the saving rate; the fraction of labor in universities

How do the long-run predictions of the Solow growth model and endogenous growth model compare?

the slow model predicts an eventual SS equilibrium, and the endogenous growth model allows for continued growth

Population Growth Changes in the Solow Model

Assume that population and the number of workers grow at the same rate of n.

Maximizing c* in (2) with respect to k yields:

Atk*gold ,MPK=δ+n

Various specifications for the prod' in for knowledge The Two sector model:

G&S producing sector Reseurch sector producing, knowledge that increases labor efficiency in G&S sector. (n) G&S production function: (3) Y-FIX,(-W)EL] where u - fraction of labor in research E - labor efficiency, increasing with knowledge (b) Knowledge production function: (4) AE = g(u)E E is not subject to diminishing returns.

Possibility of sustained higher growthAssume that g(u) follows increasing returns from existing knowledge production.

If u ↑, new discoveries (ΔE > 0)→ increases the stock of knowledge→ more new discoveries (ΔE > 0)→ ↑ stock of knowledge → further discovery ... (ii) With ↑ E, ↑ productivity of labor →y↑ → As more discoveries increase technological progress, the growth of y speeds up. => output growth can "take off" or be ever-increasing or explosive.

A change in weather patterns increases the depreciation rate.

Shifts the (δ+n)k down

Better birth control methods reduce the rate of population growth.

Shifts the (δ+n)k up

A one-time permanent improvement in technology increases the amount of output that can be produced from any given amount of labor and capital.

Shifts the sf(k) curve down

A change in consumer preferences increases the saving rate.

Shifts the sf(k) curve up

Endogenous growth theory:

The growth rate of productivity (or, technological change) is endogenous. Explains a possibility of persistent rise in living standards. Knowledge is a type of capital and is not subject to diminishing returns.

Many variants of endogenous growth theory predicts that:

an increase in population or an increase in the share of people working in the knowledge sector will increase economic growth. Implications on the role of n: • the Solow model where technological changes are exogenous, an 1 in population growth (n) leads to capital dilution lowering the living standards. • In the endogenous growth of technology, an 1 in n improves living standards in the long ryn.

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

According to Thomas Malthus, large populations:

place great strains on an economy's productive resources, resulting in perpetual poverty.

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

In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:

Δk = sf (k) - (𝛿 + n) k.

With population growth, the equation of motion for k is:

Δk = sf(k) - (δ+n)k