Download Economics Response 8 economic growth

What makes economies grow?
Suggested Response
The following response sets out in note-form what I consider to be the key points of the activity –
you may have presented your answers differently, focused on other aspects of the problem or
included relevant material which is not presented below.
Introduction
• Long-run economic growth is growth in the potential output of the economy:
o This can be understood as the theoretical maximum output of the economy.
o It is also known as aggregate supply or the production possibility frontier.
• In the short-run actual output (aggregate demand) may deviate from potential output:
o This occurs when factors of production are unused (due to unemployment etc.)
o The extent of these deviations, their causes and the appropriate policy response
are the subject of controversy between classical and Keynesian economists.
• Factors typically thought to impact on potential output of an economy (known as supplyside factors) include the following:
o Quantity and quality of factors of production (i.e.
 Number of workers and their skills
 Amount of capital stock (plant) and its quality
 Availability of natural resources
 Number of entrepreneurs)
o Available technology
o Economic organisation of the country
• Growth theory attempts to study these factors in a more formal method
The Solow Model
• The Solow Model (otherwise known as the neoclassical or exogenous model) of
economic growth is a key model in the historical evolution of growth models.
• The Solow Model has the following key characteristics:
o A (classical) production function which exhibits
 Constant Returns to Scale (CRS)
 Diminishing marginal returns to specific factors of production
o Two factors of production – capital (K1) and labour (L)
o Exogenous labour-augmenting technological change
o Exogenous increases in the labour rate
o Capital is accumulated through saving (Saving=Investment)
o Capital depreciates at a constant rate δ
• Let us consider the production function first of all:
o A production function describes how inputs (K,L) transform into output Y:
1
o
The production function is CRS, which means that doubling both inputs leads to
doubling in output, that is:
o
Diminishing marginal returns to specific factors
 This means that marginal increases in either factor ceteris paribus leads
to increases in output but the size of the increases progressively decrease
Capital is generally denoted by K from the German Kapital as in Marx’s Das Kapital

In calculus, this can be represented as
The intuition behind this is that adding more of one factor while leaving the
other factor fixed will be less effective as the fixed factor becomes over
worked (for example adding more machines will be useless if there are not
sufficient workers to use these extra machines)
The technological change is exogenous and labour-augmenting2
 The Solow model does not explain the source of technology – it is
conventionally said to be ‘mana from heaven’. It is exogenous because it
happens at a fixed rate (g) independent of the remainder of the model.
 Technology is labour-augmenting because it makes each unit of labour
more productive (i.e. each worker can produce more)
The treatment of population and the workforce in the model is simple
 The workforce is a fixed proportion of the population
 This allows us to rewrite the production function in a normalised form

where small letter variables are expressed in per-capita
(i.e. per person form3)
 The population increases at a fixed exogenous rate n
The capital stock is determined within the model
 Output per-capita y can either be invested (saved) in capital or consumed
 Denote the savings rate as s and consumption per-capita consumption as
c such that

 Capital per-capita depreciates (i.e. gets worn out) in each period by
 The capital accumulation relationship is thus

o
o
o


o
Where
The dynamics of the model are as follows4:

When
such that
 The model is in a steady-state - the capital stock does not change
 Output and consumption per-capita therefore grows at g (the rate
of growth in technology)

When
such that
 The capital stock increases over time
 Output and consumption per-capita grows faster than g

When
such that
 The capital stock decreases over time
 Output and consumption per-capita grows slower than g

Note the capital stock converges on

o
2
(capital per-unit of technology-enhanced labour)
where the level of
- The savings rate (increases in it increase
)

- (increases in these decrease )
The policy implications of the model are these
 When in a steady-state, increases in per-capita consumption are driven by
increases in the rate of growth of technology (or productivity we would
say) –
This is called Harrod-neutral technological change.
For the mathematically inclined, the assumptions we made about F makes this possible
4
Note these properties depends on the assumptions we made about F.
3
depends on
o
 Increasing this is the only way to increase long term prosperity
 Policy should focus on increasing invention and innovation5
 Increases in the savings rate, increase in per-capita growth through a
greater capital stock but they reduce per-capita consumption
 We should as a society choose a savings rate that maximises
consumption in the steady-state
 This is called the Golden Rule of the Solow Model
Other implications of the Solow Model
 We should expect to see convergence between different countries over
time –
 Poor countries must be below their steady states, while richer
countries must be at their steady states
 Poor countries should therefore grow faster than rich countries
 This leads to convergence
 Do we see convergence?
 This is a controversial question in the literature
 Reasons why we might not see convergence include
• Different technology in different countries
• Different production functions in different countries
Endogenous Growth
• Endogenous growth models try to explain the causes of technological growth in the
model
o Growth derives not only from an Exogenous process of discovery; but also
o From spill-over type effects which can lead to sustained growth in the long-run
• A simple example of an Endogenous Growth Model is the AK model
o This has a production function of the form
(a normalisation has been
made for labour to abstract from that side of the model)
o The production function is thus linear in the capital stock (there are no diminishing
marginal returns to capital as there are in the Solow Model)
o This means that there can be perpetual growth in output per-capita even with no
technological growth –
 Growth is thus endogenous explained without “mana from heaven”
 There is no steady state
 The growth rate is equal to the rate of growth in the capital stock + the
rate of growth in technology
o The implications of the AK model are
 Increases in the savings rate (increasing capital accumulation) lead to
significant increases in the rate of growth
 Convergence is not implied – because if different countries start off with
different capital stocks the one with more can perpetual grow faster than
the other
o A production function linear in the capital stock can be explained by
 The idea that capital also includes human capital (i.e. skills etc.)
 The idea that knowledge has spill-over effects (externalities)
• Most other Endogenous Growth Models are more involved
o They have more than one sector of production (such as
 A final goods output sector
 A knowledge or R&D sector)
o Ideas captured by these models include
 Learning by doing –
• A larger capital stock has a positive externality on productivity
5
Invention refers to the creation of new technology; innovation refers to its adoption.
This is explained by the notion that the workforce learns from their
experience with working for capital
• This model has an implicit market failure deriving from the
externality –
o Since in any market equilibrium there will be
underinvestment in capital
o The solution is said to be government intervention
Research Spillovers
• A larger research sector leads to greater than proportionately
faster than research – again owing to an externality from research
Technology transfers
• Trade between countries leads to the transfer of technology
between countries – perhaps creating a mechanism for
convergence?
•


Conclusion
• Growth theory is important for economic policy in several ways
• Understanding the causes of long-run growth are vital if the large increases in human
welfare that have continued through the 20th century are to be repeated in the 21st
• Understanding the causes of growth are vital if the problems of poverty and economic
development are to be tackled correctly
• This activity has only been an introduction to economic growth and we have not looked at
the statistical evidence for convergence – if you continue with Economics at university
you will have an opportunity to pose such questions which are so important to both North
and South