Question

How are the three versions of the Solow Growth Model different?

Why do you think we need three different versions of the same model? (Hint: Steady-state growth rates)

What is convergence and conditional convergence? Give examples.  

Answer 1

Solow model is a neoclassical economics model which states the economic growth in the long run.It explains the economic growth by looking into different variables like capital accumulation,labour turnover ,technological advancement etc.Mathematically it consists of a non linear differential equation. There are theree versions of the model as it assumes that income can increase due to three facrors which are capital(both physical and human),investment and ideas . He also introduced the three states of the growth those are catching up rate , this rate is for poorer countries and they use capital and investment to reach to point of maximisation .Steady rate at this point the output is steady or we can say it is a state of zero output . Cutting down rate ,it is prevelant in economically wealthy nations and it requires the use of new and innovative ideas to increase technological output to further maximize their steady rate.

1. Physical capital and diminishing returns - It means that as we invest more and more capital into the function the marginal output of each input of capital diminishes.This happens because when there is less capital invested it becomes easy to grow from the base and eventually there is high marginal growth.Lets assume a function which shows the relation between capital and income be so this justifies that as more capital will be invested the marginal output decreases.

2.The Solow Model and the Steady State - It assumes that depreciation increases at a constant rate as the investment increases.The more the capital is the more is the rate of depreciation .As we know that we either consume the money from income or we invest it .If we invest the 40% of the income ,so as we add initial unit of capital we get more output and so we get more investment as this have a direct propotionality but as we add more and more unit of outputs the marginal rate of invetmment and income decreases significantly . As discussed earlier   and investment =I so which gives into which we should increase a situation that let the depreciation (d)increase in a rate of 20% of investment , so .

So now we have two equations  

&

and we can conclude that a situation will occur when D will be equal to I and significantly it will be more than investment as we add more and more capital and the point where D=I is steady state of capital it ia point where all the capital is being used to repair and replace the existing machienery and after this steady state the situation arises where capital stock starts shrinking .

3 Human Capital & Conditional Convergence - It is the version of the model it has been defined that like every other capital the human capital also depriciates .It also assumes that the poor countries grow faster than the rich countries and as because of initial increase in output of physical as well as human capital but the sondition which is applied is that both contries should have similar social structure.This will lead the poor countries to give more and more output and therefore will converge with rich countries of same social structure.

4. Solow model of ideas - It explaines how countries go through cutting edge growth .Solow explained when there is optimum utilization of capital which is both physical and human then the ideas can give growth to the economy .It increases the output of worker across the economies. It increase the rate of output which increases the rate of investment and due to the reason that depreciation holds in a same rate so the steady state moves ahead and so its income doesnt stop .

ANS 2

Convergence means that poorer economies who have their resources unutilized moves at a greater speed than the economically wealthier countries and later their output converge with the outputs of wealthier countries .Like if a country X is economically strong and country Y is economically weak but due to convergence they will have similar outputs after few years but this doesnt happen in the real world economy it requires a condition to be true because if this would be true then the output of USA would be same as output of India ,the condition is that the countries who converge should have similar social structure .for eg switzerland and spain have similar social structure and due to which spain was a weaker economy but its growth has been relative faster than switzerland due to which their output has converged.