# Assignment 1: The Solow Growth Model

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ASSIGNMENT 1: THE SOLOW GROWTH MODEL 6

Assignment 1: The Solow Growth Model

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Assignment 1: The Solow Growth Model

1. Discuss the three (3) basic assumptions of the Solow Growth Model and analyze their compatibility with real-world economic conditions.

Just like other models in economics, Solows Model operates on certain assumptions. These are statements that are put in place in order to make a model work. When such assumptions are absent, other economists question the correctness of the given model. The assumptions of Solows economic model are outlined below.

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There is a constant growth rate of labor force in the economy. The model assumes that the labor within a given economy grows in a continuous manner. This assumption means that as a given economy grows, its labor force reaches a certain level in terms of quantity. Then with time, the economy goes on growing. Similarly, the labor force increases on a constant basis. According to the assumption, there should not be a change of any kind in the growth rate of labor.

Another assumption is that one good is made with an unchanging technology. In order to make the Solow Model work, it is assumed that there is a single good within the economy. This merchandise is made with a similar technology; the technology for production of the good remains the same.

The third Solow models assumption to be discussed is that all factors of production are fully employed. There are three factors of production: labor, capital, and land. The Solow model can only be said to work if the factors of production are put into use without excluding any of them. All the factors of production are equally vital in a growing economy. They therefore have to be considered in the application of the Solow Growth Model. The study of the problems of growth in economics reveals that all the production factors are important and none can be excluded.

2. Analyze the effects of an increase in population growth on the growth rate of capital per worker. Population growth in the economy has the effect of increasing consumption. Increase in the population will lead to an automatic increase in demand. Assuming that the level of technology remains the same, the supply cannot satisfy the increased demand. Again, capital remains constant. Therefore, the capital per worker reduces.

Labor is a vital factor of production. Increase in population directly spearheads increased labor force, which leads to upward shift in labor. The upward change in the labor force may result from factors like absence of crisis and problems such as draught, floods, famines, and epidemics of fatal diseases among others. However, the growth of population does not result in a similar increase in capital, which is the other production factor. Capital means the facilities, which bring about production like machinery, finances, plants, and so on. As the level of technology does not change, the efficiency per worker goes down with population increase.

The truth is that capital rate of growth is not related to the amplified population advance. The degree of advance in population rises at a rate that is upper than capital advance. The first labor force diminishes the preceding capital per worker. This is demonstrated below:

Let the initial population be n, and the initial capital be k; we assume that the population increases from n by a constant c. The new population will be n+c while the capital remains constant at k. The capital per worker will reduce since it can be calculated as k/n+c which is lower than the original k/n.

3. Describe the effects of a decline in the labor participation ratio on the growth rate of capital per worker with the population growth rate held constant. Solow model reveals that economic growth in short term is controlled by labor availability, population growth, and capital accumulation. In the long-run growth of economy, technological advancement is a necessity and has to be checked to see that it is in place. Solow model makes proper use of neo classical economics.

Neoclassical economics is a school of thought that believes that economic growth is driven by forces of demand and supply. The three factors identified by the Solow model, i.e. labor, capital accumulation, and population growth, have a direct relationship with demand and supply. Solow model uses mathematical approaches to calculate economic growth, and this makes it reliable due to the objectivity of the scientific method.

Solow model shows that the economic growth in the short run is regulated by labor amongst other factors mentioned above. When labor force increases, it will steer up the growth of economy while the reverse is true holding other factors constant.

When labor participation declines, short-term growth declines as well. Long-term growth will also be inhibited, because the economy transit from labor intensive to capital intensive. Long-term growth is propelled by technological advancement which cannot come into being without the labor force. The lack of labor participation may also lead to the use of more capital as shown by Cobb Douglas model.

However, this is assumed to happen in a closed economy since in an open economy, labor can be imported if the local labor is unwilling to participate or is inadequate in terms of population and competencies. This is common in countries like Saudi Arabia, Qatar, and Bahrain that are rich in natural resources such as oil, gas, and gold.

Mathematical Representation Let n be advance in the labor force. As it grows, k = K/L deteriorates (due to the increase in L), and y = Y/L also declines (also due to the increase in L).

Thus, as L grows?, the change in k is the following:

Dk = s*f(k) d*k n*k,

where n*k represents the decrease in the capital stock per unit of labor from having more labor. The steady state condition is now as follows: s*f(k) = (d+n) * k: 4. Analyze the effects of a positive technology growth rate on the growth rate of capital per worker.

There is a correlation between technology change and capital growth. Technology is not a static but a dynamic phenomenon. Each and every day, technology keeps on changing, and this is a factor we cannot ignore in production. There have been rapid improvements in technology leading to better methods of production. For example, countries like the USA, Japan, and China have better products which they introduce in the market as a result of better technology. An improvement in technology leads to higher efficiency.

A positive technology growth rate will increase the capital per worker. This is a consequence of the enhanced efficiency per worker as result of the improved technology. Using a better technology, each worker will increase the rate of growth in his capital. Usually, the capital rate of growth will rise with time, just as the technology goes up. For example, the technology of producing cars may change in a positive way to help a company like the Toyota increase its efficiency. Let us say the company produced five hundred units a year before the acquisition of a better technology and had two hundred employees. After a positive change in its production technology, the company is able to produce two million cars, still having the same number of employees. It follows that the capital growth rate per worker improves due to this change in technology. This example shows that each employee could make a positive contribution to the companys growth thanks to the technology that has been improved.