ECON 510 Final Review

An increase in the saving rate leads to:

higher output in the long run faster growth temporarily but not faster steady-state growth

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.

An increase in savings rate results in:

leads to higher k* and y*, which raises c* reduces consumption's share of income (1-s), which lowers c*.

If capital Stock is above the Golden Rule level,

as capital increases. The increase in output is smaller than the increase in depreciation, so consumption falls. As k rises, the gap between the two curves grows.

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.

Capital per worker (k)

k = (K/L)

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/δ)2.

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 Solow model with population growth but no technological change cannot explain persistent growth in standards of living because:

output, capital, and population all grow at the same rate in the steady state

Change in capital stock (Δk)

Change in capital stock = investment -depreciation Δk = i - δk, Since i = sf(k) , this becomes: Δk = s f(k) - δk

Output per worker (y)

y = (Y/L)

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.

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

Population growth

= n = (ΔL/L) exogenous variable

National Income Identity

Y = C+I

Production Function

Y = F(K,L)

Y = K0.3L0.7, then the per-worker production function is

Y/L = (K/L)0.3

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 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

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

0

Consumption per person (c)

c = (1-s)f(k) or = (1-s)y

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

What does the Solow show about the savings rate?

Higher s (savings rate) = Higher k* (steady state capital) Higher k* (steady state capital) = Higher y* (steady state income) The Solow model predicts that countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run

The formula for steady-state consumption per worker (c*) as a function of output per worker and investment per worker is:

c = f(k) - δk*.

c* in terms of k*

c* = y* − i* = f (k*) − i* = f (k*) − δk* In the steady state: i* = δk* or sf(k*)= δk* because Δk = 0

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.

An increase in population growth results in:

causes an increase in break-even investment, leading to a lower steady-state level of k.

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

The Solow growth model describes:

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

Investment per person (i)

i = s*f(k) or = s*y

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.

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

The Solow growth model with population growth but no technological progress can explain

persistent growth in total output.

The Solow growth model shows that, in the long run, a country's standard of living depends:

positively on its saving rate negatively on its population growth rate

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

produces higher consumption at all times in the future

If the economy has more capital than the Golden Rule level, then:

reducing saving will increase consumption at all points in time, making all generations better off.

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, the steady state level of output per worker would be higher if the _____ increased or the _____ decreased.

saving rate; depreciation rate

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.

Break-even investment

the amount of investment necessary to keep k constant = (δ + n)k

the saving rate (s)

the fraction of income that is saved (s is an exogenous parameter) s: MPS and (1-S):MPC

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 population growth rate.

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 all wage income is consumed, all capital income is saved, and all factors of production earn their marginal products, then:

wherever the economy starts out, it will reach a steady-state level of capital stock equal to the Golden Rule level.

National Income Identity (per worker terms)

y = c+i y:income per person c: consumption per person i: investment per person c = y-i (what we don't save or invest will be consumed)

Per Worker Production Function (Income per person) (y)

y = f(k)

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

Saving per person

= y-c, which = y-(1-s)y, which = sy i = sy = s*f(k)

Depreciation per worker

= δk (= the fraction of the capital stock that wears out each period)

Equation of motion for k (using population growth)

The change in capital stock per person (k) is actual investment (i) minus the break-even investment. Δk = sf(k) - (δ + n)k

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.

If capital Stock is below the Golden Rule level,

an increase in the capital stock raises output more than depreciation, so consumption raises. As k rises, the gap between the two curves grows.

Golden Rule level of capital

denoted as k*gold; the steady state value of k* that maximizes consumption.

What happens if capital per worker is greater than the steady state? (k > k*)

depreciation will exceed investment, and capital per worker (k) will continue to decrease toward the steady state (k*)

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).

What does the Solow model predict about population growth?

higher population growth (n) means lower steady-state level of k (k*). Lower k* means lower levels of capital and income per worker (y*). The Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run

In the Solow growth model, if investment exceeds depreciation, the capital stock will ______ and output will ______ until the steady state is attained.

increase; increase

If the economy has less capital than the Golden Rule level, then:

increasing saving will increase consumption for future generations, but reduce consumption for the present generation.

What happens if capital per worker is less than the steady state? (k < k*)

investment will exceed depreciation, and capital per worker (k) will continue to grow toward the steady state (k*)

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.

The formula for the steady-state ratio of capital to labor (k*), with no population growth or technological change, is s:

multiplied by f(k*) divided by the depreciation rate.

With population growth at rate n but no technological change, the Golden Rule steady state may be achieved by equating the marginal product of capital (MPK):

net of depreciation to n.

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

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:

4

The Steady State (k*)

If investment is just enough to cover depreciation [sf(k) = δk ], then capital per worker will remain constant: Δk = 0

Capital Accumulation: basic idea

Investment increases the capital stock, depreciation reduces it

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

Investment; depreciation