Solow-Swan Model

Key behavioural assumption of the Solow-Swan Model

• Savings in each period is equal to a constant fraction (s) of output

• In a closed economy, investment per period is equal to savings

• Consumption, assuming the first two things, is equal to one minus the constant fraction of savings multiplied by output

• Savings and consumption are not dynamic household decisions

• Basic prediction: an economy should grow faster when it is far below its steady state and slower when it is close to steady state

Capital accumulation in terms of Aggregate production function

• The net change in capital between two periods is equal to investment in that period less capital depreciation

• Investment is equal to Aggregate production function multiplied by savings fraction

• When investment is greater than depreciation, capital is increasing, etc.

• Investment is a logarithmic function whereas depreciation is a line

Steady-State Capital K*, Output Y* and Consumption C*

• Occurs when capital doesn’t change, or when the amount of investment is equal to the amount of depreciation

• Using Cobb Douglas, K* increase when savings rate, productivity or Labour increases, and decreases when depreciation rate increases

• Find steady state output with K*, find steady state consumption with Y*

Diminishing Returns to K implications — Transitional Dynamics

• In the short-run, if capital is less than stead-state, the marginal product is relatively high and the economy grows, but at a decreasing rate, until it reaches zero

• Permanent increase in savings rate shifts up the investment curve, exceeding depreciation upon impact, but over time diminishing returns set in and growth slows to zero

• Increasing the savings rate increases the levels of capital and output in the long run but has no long run effect on growth (visual as a logarithmic shift)

• Only a shift up in A allows more output at any given level of capital per worker

Labour-augmenting Productivity and effective worker

• Assuming that total factor productivity reasons that with better technology/innovation, the labour force expands

• We then get y and k, which are output and capital per effective worker

• Intensive form of the production function gives use F(capital per effective worker, 1)

• Capital accumulation per effective worker is given by the change in capital per effective worker multiplied by the growth of total factor productivity and labour, equal to savings rate multiplied by production function minus the depreciation and growth multiplied by capital per effective worker

• effective investment > effective depreciation means capital per effective worker is increasing

• steady state output and consumption per effective worker can then be found

Balanced Growth

• steady state capital and output per effective worker are constant

• when k=k*, aggregate capital and output grow at the same rate as effective labour (balanced growth path)

• The long run growth rates of capital per worker and out per worker are equal to the total factor productivity growth rate

Convergence hypothesis

• if growth rates slow when reaching steady state, poor economies should hypothetically catch up to rich economies in the Long Run

• conditional convergence is what Solow-Swan predicts, or that only economies with the same parameters will have the same long run output per worker

Growth Accounting

• Can infer productivity through observed input and output growths

• Supposing alpha is a third

• inferred productivity growth

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