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Economic Growth (Check Development Economic Readings) Notes

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Long run characterised by steady state growth in which output and employment grow at constant proportional rates and in which net saving (and investment) is a constant share of output. o In S-S model, without technological progress, output and employment grow at the same rate in the steady state, which implies that the level of output per worker remains constant
 So growth rate of output per capita is zero in the steady state
 A rise in savings (and investment) share of output shifts the economy to a new steady state characterised by higher output per worker (output per worker is rising during shift from one steady state to another) - so economic growth in the sense of growth in output per worker is only a transitional process.

This doesn't fit with evidence so necessary to introduce technology

Growth and the growth rate o Notation:
 is the rate of change of output (it is the continuous time equivalent of ) i.e.

[rate of change, discrete time]

[rate of change, continuous time]
 (Proportional) rate of growth is defined in discrete time as:

[growth rate, discrete time]

[growth rate, continuous time]
o Growth rates, exponential and log functions
 Growth rate in discrete time is the same as in continuous time when the time period is short enough e.g. t and t+∆t where ∆t is small.
 Growth rate can be expressed in several equivalent ways:

 Logs


The growth rate of the ratio of 2 variables is equal to the difference between the two growth rates: gX/Y = gX - gY o E.g. the growth rate of output per worker is equal to the growth rate of output minus the growth rate of workers.

The growth rate of the product of 2 variables is equal to the sum of their growth rates o Useful definitions for growth theory
 Growth rate can be calculated via the log difference method as follows:

o Where t is the number of years, Y0 is the base level of output and Yt is the final year level

The Solow-Swan model o What is capital in this model
 Capital is productive but it does not need to be productive all the time
 Capital is itself created from existing resources in the income - so trade off between consuming resources today or transforming them into capital which will potentially produce more resources tomorrow (i.e. Investment)
 Capital earns a return, assumed that capital can be rented at real rate R
 Capital depreciates (at the constant rate, δ), where real IR, r = R - δ
 Capital is a rival good - usage of one unit of capital by an individual means that no one else can use it. o Aggregation of capital
 Difficult - think apples and pears
 Only under very special circumstances is aggregation mathematically warranted

o The production function
 Y = F(K,L)
 MPK and MPL are positive and diminishing
 Production function exhibits CRS

i.e. F(θK, θL) = θF(K,L)

allows us to define output and capital in intensive form (i.e. per worker terms) so y = Y/K and k = K/L
 so:

 CRS implies that returns to each factor depend only on the factor ratio i.e. K/L

So APK and MPK are decreasing functions of K/L and APL and MPL are increasing functions of K/L o APK = f(k)/k and APL = f(k) o MPK = f'(k) and MPL = f(k) - f'(k)k

If we assume Cobb Douglas production function: o o o o How labour and capital inputs change over time
 Assume labour force grows at constant positive exponential growth rate, n:

Growth rate of capital: o o Steady state or balanced growth
 If we take a constant n, then when the capital stock is growing at the same rate the KL ratio will be constant - known as the steady state K-L ratio, k*
 Hence, steady state growth requires

Which implies: o
[Domar's formula]
o So far:
 In steady state growth, output and capital grow at the same rate as the exogenously given n. No growth in output per capita in the steady state.
 The capital output ratio in the steady state is higher, the higher is the savings rate and the lower are the labour force growth rate and depreciation. o Dividing by L:

 Note that
 Multiplying each side by K/L gives
 Substituting gives Fundamental Solow Equation of Motion:

o First term shows extent to which I is adding to the capital stock per worker o Second term shows amount of I needed to offset depreciation (δk) and to equip additions to labour force at existing levels of capital per head (nk) o If s = 0, i.e. no savings, capital per head would be falling under pressures of an increasing population and capital depreciation o If capital per worker increases because I per head is > reduction in capital per head due to increasing population and depreciation o FIGURE 13.3

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