Question

Question 1: Solow Model 

i. In 3-4 pages, in your own words, delve into a detailed discussion of the three variations of the Solow growth model (the basic Solow model, Solow model with population growth and the Solow model with technological progress). Be sure to explain the relevant equations that form the foundation of each model as well as the predictions for the three variations of the model. 

ii. In your judgement, how useful (or not) is the Solow model as an analytic tool for understanding the differences in developing and developed countries? (1-2 pages)

Answer 1

i)

Solow Model is an exogenous growth model in which the variables which are used in the model are not explained by the models. The variables are just taken from outside the model and are not explained within the model. The assumptions of solow model are -

1. Labour force is growing at a constant exogenous rate, let's say "n".

2. There are just two factors of production, labour and capital. Thus, Y = f ( K, L)

3. There are diminihsing returns to individual factors, but constant returns to scale of production. There is also perfect substituteability of factors.

4. The savings are reinvested and there is no independent investment function. S = I = sY

The Solow model can be dervived using the Cobb-Douglas function as -

Y = AKaLb

here, a + b = 1 -> b = 1-a

Therefore, Y = AKaL1-a

Dividing by L on both sides, we get -

Y/L = AKaL-a

y = A (K/L)a .........(y = Y/L)

If k = K/L, then -

y = A ka

Solow model lays more emphasis on capital. The above equation obtained is the production function for the solow growth model.

Diagramatically, it can be explained as follows -

In the diagram, the production curve is y = A ka which is the mirror image of the savings (investment) curve. There is diminishing returns to capital as the marginal product of capital is less than zero.

The savings curve is also increasing at a diminishing rate which is sY. There is depreciation in the capital and the rate of this deprciation is measured as dK

The x-axis measures the capital-labour ratio (independent variable) and the y-axis measures the output-labour ratio (dependent variable).

Now, according to solow model, an economy reaches steady state shown by R*, and beyond this, there is no increase in capital as the depreciation rate is more than the growth rate and the output will not increase any more. It will remain unchanged at y. Thus, lower the capital endowment of nations, higher will be the rate of GDP growth.

Now consider if the savings increase, there is increase in capital stock from R1 to R2 becasue of the investment in capital and capital accumulation. Increase in savings shifts the savings curve upwards from sY to sY', and hence the output curve also shifts from y1 to y2. Ths shift from A to B is known as the levels effect. This growth of output due to increase in savings is for the short run only and in the long run the level of output is again stabilised.

Growth in Population

Now, if there is population growth, which is "n", the depreciation shifts upwards from dk to dk+n. This is becasue both depreciation and population growth now affects capital stock. It is a dual effect. The output falls from y1 to y2 because of fall in capital from R1 to R2.

Technological Progress

In this factor, the assumptions we mentoned earlier leaves the technological change to happen. Now, this leads to long term growth in the economy. Technological progress brings efficiency in the production frontier. Efficiency can be achieved by two things -

1. same level of output with lesser inputs

2. same level of inputs for higher output

Now, solow model did not descrive that where the technogical progress happens form. He has taken it as an exogenous variable and has not defined it. In the function y = A ka, A is the technogical constraint, which is exogenously defined. In the diagram below, the levels of technology as A3 > A2 > A1.

The production function shifts due to technogical development giving higher levels of growth.

ii)

Robert Solow developed the neo-classical theory of economic growth and Solow won the Nobel Prize in Economics in 1987. He has made a huge contribution to our understanding of the factors that determine the rate of economic growth for different countries.

Growth comes from adding more capital and labour inputs and also from ideas and new technology. Developing countries are now the engine driving the global economy, accounting for around two-thirds of global growth

There are many differences across countries but there are some common elements to countries that have grown continuously. They have stable governments that pursue prudent economic policies, provide essential infrastructure and services, and take a long-term perspective. They use the opportunities provided by global markets and they have a dynamic and competitive private sector"