The Solow Growth Model with one Endogenous Growth Model

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Compare and contrast the Solow Growth Model with one Endogenous Growth

Model

In order to compare two models of economic growth, I will look at the

primary model of exogenous growth, the Solow model, and ArrowÂ’s

endogenous growth theory, based on research and development generated

within the system. I will define the models and identify their

similarities and differences.

The Solow model, or Neoclassical growth model as it is sometimes

known, is an example of exogenous growth models. This is to say that

the level of economic growth depends on externally determined rates of

growth in certain variables. The Solow model was devised to show the

relationship between the inputs of labour (L), capital (K) and

knowledge (A) on the output level (Y). these are modelled as a

function of time, which does not directly feature in the model:[IMAGE].

Therefore an example of this would be the Cobb Douglas function

F(K,AL) = Kα(AL)1-α, 0<α<1

Output will only change if the values of the inputs change. For

instance, given a fixed level of capital and labour, output will only

grow if there is technical progress, that is the value of

technological change, A, changes. Because technology is introduced

into the function as multiplying L, it is known as labour augmenting

or Harrod neutral. This is distinct from capital augmenting: Y(t) =

F[A(t)K(t),L(t)] and Hicks Neutral: AY(t) = F[K(t),L(t)].

Some assumptions are made concerning this function. Firstly, AL is

defined as effective labour; this will become an important concept

later. The economy is assumed large enough so that all improvements

from specialisation have been exhausted, and the only inputs that are

of any importance are labour, capital and labour. Combining these

assumptions, the nature of the production function is such that it

exhibits constant returns to scale. The production function can now be

illustrated in its intensive form

[IMAGE]

Inputting the Cobb Douglas function mentioned earlier, the intensive

form of the production function is [IMAGE].

The variables k and y are not of interest in their own right; instead,

they help us gain an idea into how the main variables interact. This

method is akin to dividing the economy into AL pieces. As a result, we

can look at the quantity of capital per unit of effective labour and

its impact on output per unit of effective labour, as opposed to being

overly concerned with the overall size of the economy.

f(k) is assumed to satisfy that f(0) = 0, f’(k)> 0 and f”(k) <0.

this means that the marginal product of capital is positive, but it

declines as the level of capital rises , i.e. there is diminishing

marginal product of capital.

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