# Intermediate macroeconomics chapt07

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

is achieved when sf(k) = δk

Investment, Depreciation

δk
Depreciation
sf(k)
Depreciation>Investment

Capital per worker
k1

k*

k2

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, LE), where E is
an indicator of the efficiency of labor
Divide by (LE) 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 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 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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