Economic Growth (Check Development Economic Readings) Notes
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ECONOMIC GROWTH (CHECK DEVELOPMENT ECONOMIC READINGS) 'Macroeconomics' Carlin & Soskice 2006 CHAPTER 13 - EXOGENOUS GROWTH THEORY
• 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 • If • 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 K- L 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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