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- Solow-Swan exogenous growth model and its limitations (recap)
- Romer's endogenous growth model
- Convergence in the international setting
Solow ModelAims to explain disparities in wealth between countries. Technological change is exogenous
o Assume decreasing marginal returns, concave production function
One good, 'output', is produced
Constant savings rate 's'
o Full employment, so savings = investment
Production function is Cobb-Douglas, so constant returns to scale
Diminishing marginal returns to capital per workerYt =K αt ( A t Lt )1−α
Cobb douglas production function: use 1/3 and 2/3 commonly because this is proportion of firm expenditure on capital and labour respectively. Assume payment
= marginal productivity
A = labour productivity,
o C and I are consumption
This is the resource constraint - shows dropping savings doesn't change output, only the growth of output. Savings is a trade-off between C and I
K t +1=K t +s Y t−d K t
Gives capital accumulation.
Proposes that capital accumulation is key to growthYt =K αt ( A t Lt )1−α∆ K ( t+ 1 )=It−d Kt [capital accumulation]
Lt +1=Lt ( 1+n)
At +1= A t ( 1+ g )
C t + I t=Y t
I t=s Y t--
o s is investment rate
d is capital depreciate rate
Lbar is labour force
Kbar0 is initial capital stock
Steady state exists where sY=dK, so dK and sY mapped on the same graph of investment/depreciation, the point at which they cross is the steady state. Capital accumulation is zero
Occurs because investment yields diminishing returns but capital depreciation yields constant returns, so investment at any given rate will continue to increase capital stocks until the investment yields an increase in capital equal to the depreciation rate
( 13 )
-> Y =
d 2 3
1 2 o----So production is dependent on investment rate, capital depreciation rate and TFP
Combining production and Solow: y = =
o So wealth is explained through differences in investment rate and the TFP (A)
Will increasing savings rate lead to growth? Yes in the short-run, no in the long-run. The smaller alpha, the faster the short-term growth would fade away, alpha is the curvature of the graph in the Solow model.
No long run growth in Solow that can be explained endogenously - doesn't match reality.
Growth must be driven by exogenous increases in A
Growth in labour force: causes growth in aggregate growth but not per capita growth
o Grow when below steady state, steady state may be extremely distant so always approaching
The greater the difference between capital stock and steady state capital, the more growth there is
Savings rate change:
o Drop in the savings rate: reduced per capita output because lower steady state of capital per person. Positive effect on consumption because Y = sY + C, so C = Y(1-s).
positive and negative effect here from s going down and Y going down, if depreciation rate very low, lower savings changes output a lot so first effect dominates. If d very high, positive effect dominates because amount of capital hasn't actually changed very much
Population growth rate change: if population growth drops, growth of per capita income increases.
o Example: UK harshens policy on immigrants, so less can arrive in the future. This represents a permanent shock to the population growth rate. Output and capital per capita increase, but overall output will grow at a lesser rate. However, ends up on a growth path (at this new, lower slope) that's higher than if you just rotated the growth line at the point of the shock, as output level higher because each worker has more capital attached to them, so savings higher, so overall balanced growth path at a higher output level but lower growth rate.
Short-run upwards effect and long-run downwards effect which may or may not cancel out the upwards short-run effect.
Given Solow, expect poor countries to grow quicker than rich countries. Works in OECD
countries well, but growth quite slow, not really a catch up. Doesn't match with growth rates globally, so some reason why steady states in poor countries are vastly different
All growth has to happen in exogenous variables related to labour supply and productivity.
Assuming constant labour supply, we get growth equal to growth in A
o Focus on investment and capital, ignoring TFP
o Does not explain why countries have different investment rates
Does not explain why there's growth. In Solow steady state, there is no long run growth
Main move Solow makes is from a leontieff to a Cobb-Douglas production function: Leontieff doesn't have diminishing marginal returns, because no substitution between factors.
Can you permanently increase growth rate: yes, if there aren't diminishing returns to production of ideas, then if you put more resources into producing ideas, growth in ideas can be permanently higher
Theories of endogenous growth to add to Solow:
o Growth of ideas
o Human capital: schooling increases human capacity to produce things
Tech progress either capital saving, labour saving or neutral
Technical transfer - stealing ideas
Augmented Solow Model: Slightly more complex, with endogenous growth
So growth rate of output per work growing at rate g, which is positive, because productivity is growing. Wiggly lines over parameter = productive worker / efficiency unit of labour
Endogenous growth aims to:
1. Explain g within the model, in such a way that g can be changed by policy
2. Overcome decreasing returns (add at least one input with constant returns)
o There can be endogenous growth in the long run because there's a growth rate of A
greater than zero, which offsets the decreasing marginal returns of capital
Endogenous Growth Models
Simplest endogenous model = AK
The linear production function is what gives us constant returns to scale, so there can be an explanation for long run growth. But as in diagram, saving is always above depreciation therefore growth will b predicted at an unrealistically fast rate. Also might lead to bad policy suggestion of saving more to increase growth, Japan and
USSR had very high savings rates but this was due to overinvestment in dubious industries
Knowledge Externalities Assumes that any improvements in knowledge lead to externalities to the whole economy, it's a model of pure externalities. Assumed balanced growth path, if growth rate of capital was more than growth rate of output itself, then all of additional output and more would be going into new capital stock - doesn't make sense o
Assumption that there is no depreciation of human capital within the law of motion is an exaggeration. Resultant growth rate also totally dependent on resources dedicated to training and learning.
Ideas: Productive Knowledge
Romer and Jones - basic property if ideas is that they are non-rival
But also partially excludable = patents
Knowledge not an externality
IRS are incompatible with perfect competition
Because ideas are non-rivalrous, powers in the production function are not just about distribution, therefore they don't have to add up to 1. The wage rate and capital rental rates can't be unequal if there's perfect competition?
Romer ModelKey: ideas are non-rivalrous
Objects are finite and rivalrous eg. Capital and labour, private goods
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