The Solow Model

Contents

1 Introduction

2 Background
2.1 Economic Growth
2.1.1 Relevance of Economic Growth
2.1.2 Historical Overview
2.2 Models
2.3 Robert M. Solow

3 The Solow Model
3.1 Background
3.2 Assumptions
3.3 Dynamics
3.4 Implications

4 Conclusion

5 The Bibliography

1 Introduction

This paper briefly examines the concept of economic growth and focuses on one of its most important theories: The Solow Growth Model. I will start of with a short insight to the importance of economic growth and its historical development and then move on to the theoretical aspects and implications of the model itself. It can well be argued that the Solow Model is one of the most influential works regarding growth theory. Also it does not account for every factor today believed to have influence on economic development it basic principles are of empirical relevance and can be observed in the real economic world. Economists following Robert Solow have added to the model as well as criticised it, thereby giving much material for academic discussion and thinking. However this article will stick with the basic theory proposed by Solow himself and try to lay out the way it depicts and explains the process of economic growth. In order to give Solow’s theories a place in the development of economic thinking, I will give a short overview on his predecessors in the subject. Section 2 is dedicated to the latter purpose, while section 3 goes into the detailed examination of Solow’s work.

2 Background

2.1 Economic Growth

2.1.1 Relevance of Economic Growth

”Once one starts to think about them, it is hard to think about anything else.”, said Robert E. Lucas¹ in 1988, referring to the consequences of economic growth for human welfare.

This sentence shows the considerable impact the issue has on the economic world, but what is the relevance of the mentioned questions outside the scientific community? The first hint to answer this questions was given by Mr. Lucas himself. The above quotations was of course taken out of a larger context, in which he points out the difference in growth rates between India, which was then a very underdeveloped country, and Indonesia, which was one of the ”asian tigers”. He also brought up the question if India can influence its growth rate to gain similar economic development. And if so, how such

As a short example I will examine the growth performance of the United States in comparison with other nations². The average annual growth rate of the US for roughly the last century has been around 1.8 percent and it has led them to the second-highest level of per capita gross domestic product (GDP) worldwide in 2000. Also their GDP now is approximately ten times greater than in 1870. Under the assumption that the US would have grown only one percent less since 1870, roughly at the average rate of Pakistan, its GDP in 2000 would be less than a third of the actual level. This would put the US on rank 45 out of 150 instead of second, right along with Mexico and Poland. The consequences from another viewpoint are also startling: The average growth rate for Bangladesh after 1945 is 1.4 percent and if it continues to grow at this rate, it will take roughly 200 years for the country to reach the current US-GDP level. But if it manages to speed growth up to 5 percent, as some ”growth miracle” countries have done, the length of the adaption process would be reduced to about 50 years.

This shows the enormous influence of economic growth on a country’s prosperity and human welfare. Although this is especially important for developing countries, it also concerns the ”rich” nations, as growth is also essential for continuous wealth and the economic security of future genera- tions.

2.1.2 Historical Overview

In the previous section the huge importance of economic growth and its implications for modern economics has been laid out. But the questions why and how a economy grows, thus increasing the corresponding nations wealth, and why some countries do get richer and some don’t, is not a new one. Since the early modern times (roughly 16th to 18th century) researchers have been interested in the mechanics of economic growth, its causes and the possibilities to manipulate it. The latter was probably the starting point of the interest in the first place, as a major goal of any state was and is the accumulation of wealth and therefore power.

The first ”scientific” work about growth came from the scholars of the mercantile period, who believed the opulence of nations to be determined through the total amount of spicie (precious metals), which was used as medium of payment, under state-control. Hence, they thought that the indi- cator for growth was an increase in its quantity. This idea led to protection- istic policies and trade controls, in order to keep bullion inside the nation. It also encouraged imperialism, as cheap raw materials could be acquired from the colonies and after refining in the home-country, be sold to increase the wealth of the state.

The modern view of economic growth and thereby the rejection of the mercantilist ideas emerged in the 18th century through the scottish enlight- enment, especially promoted by Adam Smith (1776) and his famous work ”The Wealth of Nations”. Smith believed capital accumulation to be the key to both prosperity and growth of a nation and put great emphasis on the importance of saving and investment. His reasoning was that a nation had to increase its productivity in order to prosper. But as the amount of available labour is limited it can only do so by investing in means of production to enhance the output of the existing work force, e.g. machines. He also ad- vocated free markets, private property and laissez faire policies to facilitate economic growth.

Another idea of some impact on the concept of growth was the ”compar- ative advantage” notion of David Ricardo (1817), which promoted speciali- sation of production and free trade between nations. Through this countries could complement each others produce, benefit mutually, contrary to the mercantilistic believe of a ”zero-sum-economy”, and thus grow. Further as- pects to the conception of economic growth have been provided by Thomas Malthus (1798), who investigated the interrelation of population growth, food supply and actual welfare benefits and by Joseph Schumpeter (1934), who promoted the idea of entrepreneurship and its innovative effect on technical progress being crucial for the economic development of a society.

The basics of Adam Smiths approach to growth made their way into modern economics and are, although somewhat adapted, still relevant today. The current theories of growth also consider the accumulation of capital an important agent of economic growth and pay great attention to saving, invest- ment and productivity levels. However, there is a major difference between Smith’s way of addressing economic questions and the methods of modern economists. Since the 18th century a change in methodology has taken place, which slowly began with the works of Ricardo and developed to the present day. While Smith’s approach to assessing certain issues was largely based on a combination of theory and historical description, later scientists de- veloped their theories around a central core of simplifying assumptions and mathematical equations. They came to work with something we call today ”economic models”.

2.2 Models

In this section I will give a brief insight to the principles and purposes of models as applied in modern economics³.

A model is a theoretical framework representing certain economic pro- cesses and relationships using mathematical equations, simplified assump- tions and variables. They are necessary, because the world as it stands is too complex and too unpredictable to analyse it without simplifying it. Each model deals with a particular feature of the reality, assesses a specific ques- tion and uses more or less restrictive and ”unrealistic” assumptions. When pointing out this apparent defect, one has to be aware that the purpose is not to be realistic, but to explain the problem the model was designed for. In this case simplification is a virtue, as it makes it possible to understand a certain feature by segregating the issue of interest. Simplification in this context means mainly to chose the few most relevant factors from the vast number influencing the matter in reality. The art of modeling is to decide which factors can be ignored and which not. Assumptions may cause in- correct answers in general, but are acceptable when they provide accurate information about the question they have been formulated to address. An- other important feature of models are the two different kinds of variables used: exogenous and endogenous. The first come from ”outside” the model and are taken as constants. These input variables have an effect on the sec- ond type, which are ”inside” the model and are the objects of interest. The purpose of the model is to explain the endogenous variables dependent upon the exogenous elements.

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¹ Robert E. Lucas, *1937, American economist at the University of Chicago influence could look like and if not, what in the ”nature” of India prevents it. This can equally be applied on any other developing country’s pursuit of prosperity. What sounds quite trivial on the first hand, proves to be of great importance to the development of countries. To have knowledge about the mechanics and influence factors of growth would enable governments to affect their population’s well-being, as small differences in long-term growth can mean an immense alteration of the eventual outcome and thus have influence on a nations wealth and standard of living.

² cp. Barro, pg. 1f[4] (see References); Romer, pg. 5ff[3]

³ cp. Romer, pg. 14[3] ; Mankiw, pg. 8f[6]; Wikipedia(en) ”Economic Model”