Chapter 7:

Economic Growth

Supply of Goods

Production Function: Y = F(K, L)

Assume constant returns to scale: zY = F(zK, zL)

Express in labor units: z = 1/L:

Y/L = F(K/L, 1) or

y = f(k)

Supply of Goods

Production Function: y = f(k)

Output per worker, y

f(k)

MPK

1

Capital per worker, k

Demand for Goods

Express Y = C + I in per unit of labor:

Y/L = C/L + I/L

y = c + I = (1-s)y

Where (1-s) = MPC and s = MPS

y = (1-s)y + i

i = y- (1-s)y = sy = sf(k)

This is Investment = Saving

Demand Components

f(k) = (1-s)f(k) + sf(k)

Investment, Depreciation

f(k)

Output per worker

Consumption per worker

sf(k)

Investment per worker

k*

Capital per worker

Capital Depreciation

Capital depreciation = δk where δ>0 is depreciation rate

Depreciation

Depreciation, δk

Capital per worker, k

Steady State Equilibrium

Steady state of capital accumulation

is achieved when sf(k) = δk

Investment, Depreciation

δk

Depreciation

sf(k)

Depreciation>Investment

Capital per worker

k1

k*

k2

Stability of Steady State Equilibrium

Once k*, steady state level of capital per worker, is

achieved, it will remain stable.

At k1 < k*, investment exceeds depreciation. So,

investment increases to raise k1 to k*

At k2 > k*, depreciation exceeds investment. So,

investment decreases to lower k2 to k*

Increase is Saving

An increase in saving results in a higher level of capital per worker.

Investment, Depreciation

δk

s2f(k)

s1f(k)

Capital per worker

k1*

k2*

Income per capita vs. Investment

The Golden Rule Level of Capital

A steady state level of capital per worker at which

consumption per worker is maximized.

Above the Golden Rule steady state level, increases in

steady state capital per worker reduce consumption per

worker

The Golden Rule Level of Capital

A steady state equilibrium at which consumption per worker is maximized

Investment, Depreciation

δk

sf(k)

k1

k*

k2 Capital per worker

Labor Force Growth

Define n as the rate of labor force growth

The amount of capital per worker required to offset

depreciation and population growth is (δ + n)k

Steady state equilibrium condition is f(k*) = (δ + n)k*

Population growth shifts (δ + n)k up reducing the level of

capital per worker

Impact of Labor Force Growth

Labor force growth results in a lower

level of capital per worker.

Investment, Depreciation

(δ+n2)k

(δ+n1)k

sf(k)

k2*

k1*

Capital per worker

Income Per Capita vs. Population Growth

Economic Efficiency

Rewrite production function as Y = F(K, LE), where E is

an indicator of the efficiency of labor

Divide by (LE) to get y = f(k)

where y = Y / (L E) and k = K / (L E)

Define n = rate of labor force growth and g = rate of

efficiency improvement

Steady State Equilibrium

Steady state of capital accumulation is achieved when sf(k) = (δ+n+g)k

Investment, Depreciation

(δ + n + g)k

sf(k)

k*

Capital per worker

Determinants of Economic Growth

Investment in physical capital

Proper maintenance of physical capital

Investment in human capital

– Decrease labor force growth

– Increases worker efficiency

Investment in technological advancement

Investment in infrastructure

Reasons for Recent Slow Growth

Measurement problem of inflation as quality improvement

is not taken into account

Fluctuating oil prices

Reduced worker quality

Depletion of Ideas

Economic Growth

Supply of Goods

Production Function: Y = F(K, L)

Assume constant returns to scale: zY = F(zK, zL)

Express in labor units: z = 1/L:

Y/L = F(K/L, 1) or

y = f(k)

Supply of Goods

Production Function: y = f(k)

Output per worker, y

f(k)

MPK

1

Capital per worker, k

Demand for Goods

Express Y = C + I in per unit of labor:

Y/L = C/L + I/L

y = c + I = (1-s)y

Where (1-s) = MPC and s = MPS

y = (1-s)y + i

i = y- (1-s)y = sy = sf(k)

This is Investment = Saving

Demand Components

f(k) = (1-s)f(k) + sf(k)

Investment, Depreciation

f(k)

Output per worker

Consumption per worker

sf(k)

Investment per worker

k*

Capital per worker

Capital Depreciation

Capital depreciation = δk where δ>0 is depreciation rate

Depreciation

Depreciation, δk

Capital per worker, k

Steady State Equilibrium

Steady state of capital accumulation

is achieved when sf(k) = δk

Investment, Depreciation

δk

Depreciation

sf(k)

Depreciation>Investment

Capital per worker

k1

k*

k2

Stability of Steady State Equilibrium

Once k*, steady state level of capital per worker, is

achieved, it will remain stable.

At k1 < k*, investment exceeds depreciation. So,

investment increases to raise k1 to k*

At k2 > k*, depreciation exceeds investment. So,

investment decreases to lower k2 to k*

Increase is Saving

An increase in saving results in a higher level of capital per worker.

Investment, Depreciation

δk

s2f(k)

s1f(k)

Capital per worker

k1*

k2*

Income per capita vs. Investment

The Golden Rule Level of Capital

A steady state level of capital per worker at which

consumption per worker is maximized.

Above the Golden Rule steady state level, increases in

steady state capital per worker reduce consumption per

worker

The Golden Rule Level of Capital

A steady state equilibrium at which consumption per worker is maximized

Investment, Depreciation

δk

sf(k)

k1

k*

k2 Capital per worker

Labor Force Growth

Define n as the rate of labor force growth

The amount of capital per worker required to offset

depreciation and population growth is (δ + n)k

Steady state equilibrium condition is f(k*) = (δ + n)k*

Population growth shifts (δ + n)k up reducing the level of

capital per worker

Impact of Labor Force Growth

Labor force growth results in a lower

level of capital per worker.

Investment, Depreciation

(δ+n2)k

(δ+n1)k

sf(k)

k2*

k1*

Capital per worker

Income Per Capita vs. Population Growth

Economic Efficiency

Rewrite production function as Y = F(K, LE), where E is

an indicator of the efficiency of labor

Divide by (LE) to get y = f(k)

where y = Y / (L E) and k = K / (L E)

Define n = rate of labor force growth and g = rate of

efficiency improvement

Steady State Equilibrium

Steady state of capital accumulation is achieved when sf(k) = (δ+n+g)k

Investment, Depreciation

(δ + n + g)k

sf(k)

k*

Capital per worker

Determinants of Economic Growth

Investment in physical capital

Proper maintenance of physical capital

Investment in human capital

– Decrease labor force growth

– Increases worker efficiency

Investment in technological advancement

Investment in infrastructure

Reasons for Recent Slow Growth

Measurement problem of inflation as quality improvement

is not taken into account

Fluctuating oil prices

Reduced worker quality

Depletion of Ideas

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