นโยบายการคลังกับการขยายตัวเศรษฐกิจ : การสะสมทุน (Capital Accumulation)

1This lecture drawn heavily from Mankiw, Macroeconomics, 5th edition, 2003

นโยบายการคลังกบการขยายตัวเศรษฐก�จ:

การสะสมทุ�น (Capital Accumulation)

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เสถี�ยรภาพกบการขยายตัวเศรษฐก�จ

• นโยบายการคลังเพ� อการรกษาเสถี�ยรภาพมกหมายถี#งการลัดการขาดด�ลัการคลังซึ่# งการบร�หารนโยบายดงกลั&าวมกตั'องม�ตั'นทุ�นในร)ปของโอกาสการขยายตัวในระยะยาว (เพราะตั'องเส�ยทุรพยากรในการรกษาเสถี�ยรภาพของระบบเศรษฐก�จ เช่&นการลัดการใช่'จ&ายเป,นตั'น)

• ดงน-นในการออกแบบนโยบายการรกษาเสถี�ยรภาพจ#งตั'องค/าน#งถี#งการขยายตัวของเศรษฐก�จด'วย

• ตัวอย&าง: public capital declined suggest lower of economic investment.

• การรกษาเสถี�ยรภาพกบการขยายตัวเศรษฐก�จตั'องการการจดการด'านอ�ปสงค0ทุ� ม�&งเพ� อส&งเสร�มการเพ� มของStabilization and growth requires that demand management policies be complemented by policies aimed at increasing potential output.

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•นโยบายการคลังเพ� อการขยายตัวเศรษฐก�จแลัะการพฒนาตั'องค/าน#งถี#งความส/าคญขององค0ประกอบแลัะประส�ทุธิ�ภาพ ของมาตัรการโดยเฉพาะด'านการใช่'จ&าย รวมทุ-งบทุบาทุของนโยบายทุ� มาจากทุางด'านอ�ปทุานด'วย (supply side)

เสถี�ยรภาพกบการขยายตัวเศรษฐก�จ

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ทุ/าไมการขยายตัวเศรษฐก�จจ#งม�ความส/าคญ

• ป6จจยทุ� ม�ผลัตั&อการขยายตัวเศรษฐก�จในระยะยาวแม'จะเป,นเพ�ยงเลั8กน'อยจะส&งผลัตั&อค�ณภาพช่�ว�ตัในระยะยาว

1,081.4%243.7%85.4%

624.5%169.2%64.0%

2.5%

2.0%

100 ป:50 ป:25 ป:

% การเพ� มข#-นของดช่น�มาตัรฐานค�ณภาพช่�ว�ตั

อตัราการขยายตัวเศรษฐก�จ

ตั&อหวประช่ากร

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ทุ� มาของการขยายตัวเศรษฐก�จ• ผลั�ตัภณฑ์0ภาคการผลั�ตั (Productivity)

• ป6จจยการผลั�ตั (Factors of Production)

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ผลั�ตัภณฑ์0ภาคการผลั�ตั PRODUCTIVITY: บทุบาทุแลัะการก/าหนด

ขนาด• ผลั�ตัภณฑ์0ภาคการผลั�ตัม�บทุบาทุส/าคญในการ

ก/าหนดค�ณภาพช่�ว�ตัของประช่าช่นในทุ�กๆ ประเทุศ ตัวอย&าง เวลัาทุ� ใช่'ในการทุ/างานทุ� ลัดลัง การด/ารงช่�ว�ตัทุ� ด�ข#-น เป,นตั'น

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ทุ/าไมผลั�ตัภณฑ์0ภาคการผลั�ตัจ#งม�ความส/าคญ•ผลั�ตัภณฑ์0ภาคการผลั�ตั Productivity หมายถี#งจ/านวนส�นค'าแลัะบร�การทุ� แรงงานสามารถีผลั�ตัได'ในแตั&ลัะช่&วงเวลัา (ช่ วโมง)

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การจ/าแนกแลัะก/าหนดผลั�ตัภณฑ์0การผลั�ตั• The inputs used to produce goods and

services are called the factors of production.

• The factors of production directly determine productivity.

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ผลั�ตัภณฑ์0ภาคการผลั�ตั

• The Factors of Production– Physical capital– Human capital– Natural resources– Technological knowledge

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• Physical Capital– is a produced factor of production.

• It is an input into the production process that in the past was an output from the production process.

– is the stock of equipment and structures that are used to produce goods and services.

• Tools used to build or repair automobiles.• Tools used to build furniture.• Office buildings, schools, etc.

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• Human Capital– the economist’s term for the knowledge and

skills that workers acquire through education, training, and experience

• Like physical capital, human capital raises a nation’s ability to produce goods and services.

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• Natural Resources– inputs used in production that are provided by

nature, such as land, rivers, and mineral deposits.

• Renewable resources include trees and forests.• Nonrenewable resources include petroleum and

coal.

– can be important but are not necessary for an economy to be highly productive in producing goods and services.

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• Technological Knowledge– society’s understanding of the best ways to

produce goods and services. – Human capital refers to the resources

expended transmitting this understanding to the labor force.

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FYI: The Production Function

• Economists often use a production function to describe the relationship between the quantity of inputs used in production and the quantity of output from production.

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• Y = A F(L, K, H, N) – Y = quantity of output– A = available production technology– L = quantity of labor– K = quantity of physical capital– H = quantity of human capital– N = quantity of natural resources– F( ) is a function that shows how the inputs

are combined.

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• A production function has constant returns to scale if, for any positive number x,

xY = A F(xL, xK, xH, xN)xY = A F(xL, xK, xH, xN)

• That is, a doubling of all inputs causes the amount of output to double as well.

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• Production functions with constant returns to scale have an interesting implication.– Setting x = 1/L,– Y/ L = A F(1, K/ L, H/ L, N/ L)Y/ L = A F(1, K/ L, H/ L, N/ L)

Where:

Y/L = output per worker

K/L = physical capital per worker

H/L = human capital per worker

N/L = natural resources per worker

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• The preceding equation says that productivity (Y/L) depends on physical capital per worker (K/L), human capital per worker (H/L), and natural resources per worker (N/L), as well as the state of technology, (A).

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The production function• In aggregate terms: Y = F (K, L)

• Define: y = Y/L = output per worker k = K/L = capital per worker

• Assume constant returns to scale:zY = F (zK, zL ) for any z > 0

• Pick z = 1/L. Then Y/L = F (K/L, 1) y = F (k, 1) y = f(k) where f(k) = F(k, 1)

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The production functionOutput per worker, y

Capital per worker, k

f(k)

Note: this production function exhibits diminishing MPK.

Note: this production function exhibits diminishing MPK.

1MPK = f(k +1) – f(k)

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The national income identity

• Y = C + I (remember, no G )

• In “per worker” terms: y = c + i where c = C/L and i = I /L

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The consumption function

• s = the saving rate, the fraction of income that is saved

(s is an exogenous parameter)

Note: s is the only lowercase variable that is not equal to

its uppercase version divided by L

• Consumption function: c = (1–s)y (per worker)

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Saving and investment

• saving (per worker) = y – c

= y – (1–s)y

= sy

• National income identity is y = c + i

Rearrange to get: i = y – c = sy

(investment = saving)

• Using the results above, i = sy = sf(k)

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Output, consumption, and investment

Output per worker, y


f(k)

sf(k)

k1

y1

i1

c1

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DepreciationDepreciation per worker, k


k

= the rate of depreciation

= the fraction of the capital stock that wears out each period

= the rate of depreciation

= the fraction of the capital stock that wears out each period

1

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Capital accumulation

Change in capital stock = investment – depreciation

k = i – k

Since i = sf(k) , this becomes:

k = s f(k) – k

The basic idea: Investment increases the capital stock, depreciation reduces it.

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The equation of motion for k

• The Solow model’s central equation

• Determines behavior of capital over time…

• …which, in turn, determines behavior of all of the other endogenous variables because they all depend on k. E.g.,

income per person: y = f(k)

consumption per person: c = (1–s) f(k)

k = s f(k) – k

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การขยายตัวเศรษฐก�จกบนโยบายรฐECONOMIC GROWTH AND PUBLIC POLICY

• รฐบาลัสามารถีออกแบบนโยบายทุ� จะเป,นการเพ� มผลั�ตัภาพ (productivity) แลัะค�ณภาพช่�ว�ตั (living standards) ของประช่าช่นได'อย)&ตัลัอดเวลัา

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การขยายตัวเศรษฐก�จกบนโยบายรฐ

• Government Policies That Raise Productivity and Living Standards– Encourage saving and investment.– Encourage investment from abroad– Encourage education and training.– Establish secure property rights and maintain

political stability.– Promote free trade.– Promote research and development.

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The steady state

If investment is just enough to cover depreciation [sf(k) = k ],

then capital per worker will remain constant: k = 0.

This occurs at one value of k, denoted k*, called the steady state capital stock.

k = s f(k) – k

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An increase in the saving rate

Investment and

depreciation

k

k

s1 f(k)

*k1

An increase in the saving rate raises investment…

…causing k to grow toward a new steady state:

s2 f(k)

*k2

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Prediction:

• Higher s higher k*.

• And since y = f(k) , higher k* higher y* .

• Thus, 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.

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International evidence on investment rates and income per person

100

1,000

10,000

100,000

0 5 10 15 20 25 30 35

Investment as percentage of output

Income per person in

2000 (log scale)

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The Golden Rule: Introduction• Different values of s lead to different steady states.

How do we know which is the “best” steady state?

• The “best” steady state has the highest possible consumption per person: c* = (1–s) f(k*).

• An increase in s – leads to higher k* and y*, which raises c*

– reduces consumption’s share of income (1–s), which lowers c*.

• So, how do we find the s and k* that maximize c*?

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The Golden Rule capital stock

the Golden Rule level of capital, the steady state value of k

that maximizes consumption.

*goldk

To find it, first express c* in terms of k*:

c* = y* i*

= f (k*) i*

= f (k*) k* In the steady state:

i* = k* because k = 0.

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Then, graph f(k*) and k*, look for the point where the gap between between them is biggestthem is biggest.

Then, graph f(k*) and k*, look for the point where the gap between between them is biggestthem is biggest.

The Golden Rule capital stocksteady state output and

depreciation

steady-state capital per worker, k*

f(k*)

k*

*goldk

*goldc

* *gold goldi k

* *( )gold goldy f k

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The Golden Rule capital stock

c* = f(k*) k*

is biggest where the slope of the production function

equals the slope of the depreciation line:

c* = f(k*) k*

is biggest where the slope of the production function

equals the slope of the depreciation line:

steady-state capital per worker, k*

f(k*)

k*

*goldk

*goldc

MPK =

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The transition to the Golden Rule steady state

• The economy does NOT have a tendency to move toward the Golden Rule steady state.

• Achieving the Golden Rule requires that policymakers adjust s.

• This adjustment leads to a new steady state with higher consumption.

• But what happens to consumption during the transition to the Golden Rule?

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Starting with too much capital

then increasing c* requires a fall in s.

In the transition to the Golden Rule, consumption is higher at all points in time.

then increasing c* requires a fall in s.

In the transition to the Golden Rule, consumption is higher at all points in time.

If goldk k* *

timet0

c

i

y

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Starting with too little capital

then increasing c* requires an increase in s.

Future generations

enjoy higher consumption, but the current one experiences an initial drop in consumption.

then increasing c* requires an increase in s.

Future generations

enjoy higher consumption, but the current one experiences an initial drop in consumption.

If goldk k* *

timet0

c

i

y

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Population growth

• Assume that the population (and labor force) grow at rate n. (n is exogenous.)

• EX: Suppose L = 1,000 in year 1 and the population is growing at 2% per year (n = 0.02).

• Then L = n L = 0.02 1,000 = 20,so L = 1,020 in year 2.

Ln

L

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Break-even investment

• ( + n)k = break-even investment, the amount of investment necessary to keep k constant.

• Break-even investment includes: k to replace capital as it wears out

– n k to equip new workers with capital

(Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers.)

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The equation of motion for k• With population growth,

the equation of motion for k is

break-even investment

actual investment

k = s f(k) ( + n) k

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The Solow model diagramInvestment, break-even investment


sf(k)

( + n ) k

k*

k = s f(k) ( +n)k

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The impact of population growthInvestment, break-even investment


sf(k)

( +n1) k

k1*

( +n2) k

k2*

An increase in n causes an increase in break-even investment,

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

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Prediction:

• Higher n lower k*.

• And since y = f(k) , lower k* lower y*.

• Thus, 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.

49

International evidence on population growth and income per person

100

1,000

10,000

100,000

0 1 2 3 4 5Population Growth

Income per Person

in 2000 (log scale)

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The Golden Rule with population growth

To find the Golden Rule capital stock, express c* in terms of k*:

c* = y* i*

= f (k* ) ( + n) k*

c* is maximized when MPK = + n

or equivalently, MPK = n

In the Golden Rule steady state, the marginal product

of capital net of depreciation equals the population growth rate.

In the Golden Rule steady state, the marginal product

of capital net of depreciation equals the population growth rate.

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Supply-side Effectsof Fiscal Policy

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Supply-side Effects of Fiscal Policy

• From a supply-side viewpoint, the marginal tax rate is of crucial importance:– A reduction in marginal tax rates increases

the reward derived from added work, investment, saving, and other activities that become less heavily taxed.

• High marginal tax rates will tend to retard total output because they will: – discourage work effort and reduce the

productive efficiency of labor, – adversely affect the rate of capital formation

and the efficiency of its use, and,– encourage individuals to substitute less

desired tax-deductible goods for more desired non-deductible goods.

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Supply-side Effects of Fiscal Policy

• So, changes in marginal tax rates, particularly high marginal rates, may exert an impact on aggregate supply because the changes will influence the relative attractiveness of productive activity in comparison to leisure and tax avoidance.

• Impact of supply-side effects: – Usually take place over a lengthy time period. – There is some evidence that countries with high taxes

grow more slowly—France and Germany versus United Kingdom.

– While the significance of supply-side effects are controversial, there is evidence they are important for taxpayers facing extremely high tax rates – say rates of 40 percent or above.

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AD1

• What are the supply-side effects of a cut in marginal tax rates?

Supply Side Economics and Tax RatesPriceLevel

LRAS1

YF2YF1

AD2

Goods & Services(real GDP)

With time, lower tax ratespromote more rapid growth (shifting LRAS and SRASout to LRAS2 and SRAS2).

SRAS1

P0

SRAS2

E1

LRAS2

E2

• Lower marginal tax rates increase the incentive to earn and use resources efficiently. AD1 shifts out to AD2, and SRAS & LRAS shift to the right.

• If the tax cuts are financed by budget deficits, AD may expand by more than supply, bringing an increase in the price level.

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Share of Taxes Paid By the Rich

• The share of personal income taxes paid by the top one-half percent of earners is shown here.

• During the last four decades, the share of taxes paid by these earners has increased as the top tax rates have declined. This indicates that the supply side effects are strong for these taxpayers.

30 %

28 %

26 %

24 %

22 %

20 %

18 %

1960

16 %

14 %

Share of personal income taxes paid by top ½ % of earners

199519901980197519701965 1985

1964-65Top rate cut from

91% to 70%

1981Top rate cut from

70% to 50%

1986Top rate cut from

50% to 30%

1997Capital gainstax rate cut

2000

1990-93Top rate raised from

30% to 39%

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Have Supply-siders Found a Way to Soak the Rich?

• Since 1986 the top marginal personal income tax rate in the United States has been less than 40% compared to 70% or more prior to that time.

• Nonetheless, the top one-half percent of earners have paid more than 25% of the personal income tax every year since 1997.

• This is well above the 14% to 19% collected from these taxpayers in the 1960s and 1970s when much higher marginal personal income tax rates were imposed on the rich.

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นโยบายการคลังกับการขยายตัวเศรษฐกิจ : การสะสมทุน (Capital Accumulation)