Brief Biographical Sketch of Robert Solow

Brief Biographical Sketch of Robert Solow

Robert Solow was born on 23rd August 1924 in Brooklyn, New York, United States. Robert is known across the world as a prolific American economist due to his major contributions in the fields of Economics and got awarded the Nobel Prize in 1987 (Solow 1990). The Nobel Prize in Economic sciences resulted due to his significant contributions to theories of economic growth.

As for his education, in 1947 and 1949, Solow received a B.A. as well as an M.A before pursuing further studies and getting a PH.D. from Harvard University in 1951. After this, he proceeded to teach economics at the Massachusetts Institute of Technology (MIT) in 1949 (Solow 1990). He then became a professor of economics at the institution in 1958 before becoming a Professor Emeritus. In his capacity, he also served as the council of economic advisers between 1961 and 1962 as well as serving as a consultant in the same institution.

In an article in 1957 called ‘Technical change and the aggregate production function,’ Solow noticed that half all economic growth could not be accounted for by an increase in labor and capital. It was then that he derived the standard neoclassical microeconomics as well as Keynesian macroeconomics (Solow 1990). He argued that half of the economic growth could not be represented by virtual increases in labor and capital. The unaccounted part of economic growth could be represented as what he called Solow`s residual, which occurs due to technological innovation. The new growth model factored in the known aspects of technology since it was always improving, which meant that new capital had a higher value as compared to the old capital.

The productivity paradox

In 1987 Solow observed that the new computer age and information technologies had not resulted in productivity growth. The aspect was known as ‘the productivity paradox.’ He explained that the paradox could happen due to the time lag between time of introducing new technology and the effect that technology has on economic growth (Aghion and Howitt 2003). The other explanation could be that there is a transition occurring between the old economy and automation that has grown at the expense of labor, which is not being reabsorbed in other sectors of the economy to affect productivity growth.

Solow`s contribution to Philip`s curve development

Solow also attempted to answer the questions regarding unemployment, inflation, and the selection of appropriate economic policies. In analyzing the causes of inflation, he offered modifications to the classic Philips curve after he replaced changes in rates of nominal wages with the rate of inflation (Aghion and Howitt 2003). In such a Philips curve one could illustrate the link between rate of inflation and rate of unemployment. According to Solow, stable price levels could only be achieved when the unemployment rate stood at 5%.

Other contributions

Solow also analyzed the challenge of unemployment and the labor market and concluded that unemployment was an involuntary position (Assaf 2017). He concluded that the labor market was distinct to other markets due to social patterns as well as principles of appropriate behavior, for instance, household management and unemployment assistance.

Introduction

Most scientists might fail to recognize that they owe a huge debt of gratitude to Robert Solow than all other Nobel prize winners in science. Solow made a huge contribution to economics by formulating a theory of economic growth, which showed the critical significance of technology. He indicated that technology, which is summed up as the application of new knowledge to production processes, is the chief reason why economies expand in the long run, which is higher than the increases that occur in labor and capital (Broughel and Thierer 2019). Thanks to Robert Solow, the equation of research=investment has been constantly quoted nowadays. Solow was selected amongst other candidate to be honoured by the Royal Swedish Academy of Sciences for the contributions he made to the growth model. In addition, he was able to analytically demonstrate the theory. Solow`s growth model has a framework in which modern macroeconomic theories can get structured.

Modern industrial-based economies have multiple dynamics that are characterized by rapid innovation and transformation in the use of technological knowledge, which tends to impact factors such as economic growth (De la Grandville 2007). Economics theorists such as Schumpeter 1934 offered an explanation of the phenomenon using the theory of innovation, which is the major factor that impacts long-term economic growth. However, economists such as Solow developed different neoclassical growth models who took a different direction. They did not offer a theory that could explain innovation and technological change but rather recognized the role that technological change plays in growth. The theories derived were based on capital accumulation, and the neoclassical growth model aims to explain how rises in per capita income occur. This has been the trend in most money market economies since the era of World War II (Gagnon 2019). According to the neoclassical growth model, production occurs in light of competition, with capital accumulation being the main engine fuelling output growth.

What fuels the economic engine according to Robert Solow

One might ask what contributes to steady growth in a country`s economy. Before Solow derived his growth mode. It was assumed that sustained growth in the economy required for the perfect coordination of factors such as rate of savings, capital-output ratio, and rate of growth in the labor market. The three factors had to be balanced within a narrow wedge and using unstable parameters on what Solow referred to a ‘knife-edge.’ If the factors were not kept within stable parameters, then the economic engine, just like an internal combustion engine, would begin to cough and sputter.

Solow found the knife-edge equilibrium growth model to be very inflexible as well as being remote from absolute reality. According to Solow (1956), it was impossible for most economies to have an equilibrium growth path. In such a framework, the history of capitalist economies would be such that there is an alternation of long durations of worsening unemployment and then followed by long periods of a labor shortage.

Besides, the then accepted theory of growth suggested that in order to double the rate of economic growth in a labor surplus, participants in the economy had to double the savings rate. This meant that the countries that had higher savings could grow more quickly as compared to poor countries, which could only save little and hence could not attain the higher growth rates (Broughel and Thierer 2019). The model sounded implausible to Solow especially due to the expanding industrial economies in the 1950s and that developing nations at the time were experiencing rapid economic expansion despite their lower savings rate. It was at the time that Solow offered a more flexible theory that could explain economic growth and which could demonstrate how the various growth components, which include technical change, could be measured.

Robert Solow`s growth model

In 1956, Robert Solow published his article called ‘A contribution to the theory of economic growth,’ which documented a mathematical model which was based on a differential equation that describes how increases in capital stock generated a much higher per capita production level (Solow 1956). In the growth model, Solow indicates that society saved a certain constant level of their incomes. In the model, the population growth rate and supply of labor all grew at a constant rate. Besides, the capital intensity which is the capital levels per employee were all regulated. The production factor prices determined the capital intensity (capital per individual employed). Due to the law of diminishing returns, any additional rise in the capital (increasing capital intensity) made smaller changes and contributions to production.

Based on the model, in the long term and when there is no technological progress, the economy will attain a stable growth path in the vent capital, output, and labor grows at the same level. The model assumes that the output and capital per worker remains constant in the model as the economy achieves an identical growth rate for labor, capital and total production (Gagnon 2019). Hence, in the model, a rise in the levels of saved income cannot cause permanent rises in the growth rates. In the model, the lack of technological progress means the growth rate will remain constant (despite the savings level share) and will depend solely on the rise in the levels of labor supply.

According to Solow (1956), the findings from his article ‘Technical change and the aggregate production function’ deduced that about seven out of eight of the double gross output per worker in the United States was as a result of technical changes. It also included improvements in the education levels of the employees. He concluded that only one of eight resulted from a rise in the injection of capital. In some instances, increases in capital yielded diminishing output returns (Bianovsky and Hoover 2009). In his model, Solow managed to show us that in the long run, a rise in quantity was not significant. What really mattered was how better technology caused an increase in quality as a result of increased efficiency. The findings as well as Solow`s philosophical position have stimulated other economics and theorists to publish hundreds of empirical articles on the same. It has found itself as the common fund of knowledge in economic theory and thought. Besides, from Solow`s findings, a new specialty emerged, which is growth accounting (Bianovsky and Hoover 2009). The model had a significant impact on economic analysis and shaped the manner in which economists, researchers, and scholars alike approached economics as well as the entire macroeconomics field.

Solow`s neoclassical growth model

Solow (1956) is critical of the Keynesian Harrod Domar long term growth model since he makes an assumption that production occurs based on the condition of fixed proportions. In such a model, the fixed proportions will result in economic growth having varied dysfunctional aspects. Such factors include prolonged inflation as well as rising unemployment levels.

The neoclassical growth model by Solow (1956) offered a new model that could demonstrate how long-run growth is sustained in economies. The model accepted Harrod-Domar`s assumption except for the assumption that production was caused by fixed proportions. The model considers the aspect of labor and capital substitution in which any changes occurring in the production techniques were in response to the shifts in the relative price of capital and labor. Hence, Solow (1956) derived a production function at the center of his growth model (Mauro and Kevin 2009).

The theory has the following hypotheses, which include the following:

1. There exists declining marginal returns
2. The economies with initial conditions converge (De la Grandville 2007)
3. Markets remain in balance as a result of the market-clearing mechanism
4. There is zero long-term growth rate that corresponds to an exogenous increase in technical progress rates.

The Neoclassical model has exogenous variables that include savings rate, technical progress growth rates, and the growth rate of the population. The change that occurs on the factors of production capital (K) and labor (L) occurs because of changes in investments and well as an increase in population growth. Besides, the market remains in a perfect competition position (Aghion and Howitt 2003).

The representation of the model is as follows:

To determine the level of technological possibilities, we begin with the aggregate production function. Which is given as

1. Y= F (K, L)

In the model, the output is represented by Y (net output after deducting the depreciation of capital); K and L represent the physical units of capital and labor (De la Grandville 2007). The equation indicates the aggregate production function, which satisfies several technical conditions such as a display of constant return to scale, a display of each factor`s decreasing marginal returns, and an increase in the two arguments.

The Cobb-Douglas production function satisfied the premises and assumes that the function F demonstrates constant returns to scale of the factors F and L. It also linearly homogeneous.

The stock of capital is also illustrated in the Solow model. The capital stock (K) t assumes a form where there exists an accumulation of the composite commodity (Schiliro 2017). The net investments (I) t are derived as the increase in the rate of the capital stock dK/dt. Hence, from the model we have a basic identity as indicated.

2. dK/dt = K= I (t)

The third element of Solow`s model is the investment and savings functions. The assumption is that it takes a Keynesian nature. In a closed economy, the savings and investments are a constant function of income Y (t) such that:

3. S(t) = I (t) = sY (t)

Inserting equation to equation one gives

4. K = sF (K, L)

Due to exogenous population growth, the rate in the growth of labor will increase at a constant rate of n. In the model, Solow makes an assumption that the lack of technological change will correspond to the Harrod-Domar natural rate of growth.

5. L (t) = Long

The full set of equations in 4 and 5 are

∂F(K, L) / ∂L = w

This is called the marginal productivity equation, which indicates the real wage rates.

From equation 4, we can deduce that L represents the total employment level, while in equation 5, L indicates the total available labor supply (Broughel and Thierer 2019). Solow makes an assumption that full employment levels are only reached when one can identify the variables.

By inserting equation five into the equation, we can get the following:

6. K= sF (K, L)

The equation indicates the capital accumulation time path, which must be followed for all the labor to become employed. The differentiation of equation 6 gives the time profile that the available capital stock in the country to result in full employment.

In the model, Solow offers a brief explanation of the process of capital accumulation by indicating that ‘at any moment, since the factors will adjust to result in the full employment of capital and labor it is possible to make use of the production function to indicate the current output rates (Broughel and Thierer 2019). The propensity to save also offers us a detailed explanation of the net output that can get invested and saved. Hence, Solow indicates the possible growth paths after making an analysis of the capital accumulation path that is consistent with labor force growth.

In the model, a new variable is introduced by r = K/L, which indicates the ratios of labor to capital. We have the following.

K = rL = Loe

The differentiation with respect to time gives

7. K = Loent + nr Loent

By making a substitution of equation 7 to equation 6 we can divide both varibles in F using

L = Loent

We will obtain the following (r+nr) Loent = s Loent F (K/ Loent , 1)

A division of the common factor Loent derives the following function

8. r = sF(r,1) – nr

The eighth equation offers a representation of the rate of changes in capital and labor, which indicates a difference in the terms. The function of F (r,1) shows the total product curve in which the varying amounts are representing how an amount of r will be employed using one labor unit (Solow 1956). In the event r = 0, the labor and capital ratio remains constant, with the capital stock being expanded at the same rate as the labor force n. It gives the warranted rate of growth. It is the rate at which the real rate of return to capital will equal the natural rate. The marginal product associated with an additional unit of capital will decline as a result of diminishing returns. In the model, Solow details that growth will occur as a result of capital accumulation (Prescott 1988). The highest growth levels will be realized as the countries begin to accumulate the relevant capital. In the assumption, the assumption stands out that the per capita growth in output will only occur as the economy moves towards a steady state. When the economy is at a steady-state, no growth in y can occur. The output of the economy will increase at a rate of n.

In conclusion, Solow`s model offers a significant contribution to economic theory by offering a model for economic growth, While it fails to explain all the factors that influence the rate of economic growth. From the conclusion, we can deduce that the accumulation of capital is not the most significant factor impacting growth. Several criticisms have been leveled against the neoclassical growth model (Aghion and Howitt, 2003). The critics emphasize that by treating human capital as an exogenous variable makes it hard to analyze how the critical factor of production and how various policies impact the factor. Besides, the Solow model has been criticized for lacking micro-foundations. One scenario, this element comes out is that households make decisions on their consumption and savings mechanically. This means that s does not occur due to a utility maximization problem, and equilibrium might be inefficient.

The relevance of Robert Solow`s growth model

Before the formulation of Solow`s neoclassical growth model, only fixed coefficient growth models existed. However, Solow`s model introduced a new substitution effect between labor and capital (Schiliro, 2017). The growth model offers economic growth facts but does away with the instability that was the knife-edge in Harrod-Domar`s model. These factors include the following: First, the real output per worker grew at a constant rate. Second, the tangible stock of capital grew at the same rate. Third, the share of income to capital level remained constant. Fourth, the real wages and output per worker grew at the same rate on average.

Besides offering a study of growth, the model has been integral in offering guidance to subsequent economic research. In the area of public finance, the model made people ask the question of what determined the saving rate. The question was addressed by David Cess during his research on optimal savings levels (Mauro and Kevin 2009). According to his conclusion, optimal growth levels were effectively endogenized in the economy since optimal allocation helps in competitive equilibrium allocation. It also helped in drawing an important finding. That the equilibrium path converges at the steady growth path, and at that point, capital`s marginal product equals the steady-state of renting capital. It was deduced that the price of capital service depends on the tax system features (Bianovsky and Hoover 2009). The theory is a significant addition to public finance theory. The use of neoclassical growth models helped in conducting the steady-state analysis.

The neoclassical growth theory has helped to understand the growth cycle and steady-state behavior. It has been useful in understanding the fluctuations of business cycles. In this framework, several variables are analyzed, which include investment, consumption, capital and labor input, output, and factor incomes (Aghion and Howitt 2003). Various scholars and researchers analysed the aspect of optimal growth using the neoclassical growth model stochastic version. The advancement in theory, as well as parallel developments, ensured that it was possible to compute the stochastic equilibrium process in stochastic growth models with the behavior being compared to those of actual economies (Bianovsky and Hoover 2009). A comparison in that scale requires an input of decisions regarding time series as well as the statistical properties being compared. Solow`s neoclassical growth model offers some guidance on that aspect. The key business cycle is that at high frequency levels, the variations that exist in labor input will indicate a majority of variation that exists in output. In this framework, the capital stock input will account for none of the fluctuations in business cycles. The model has indicated that the observations were inconsistent with the neoclassical theory. For instance, production is more volatile as compared to final sales which indicates that there exists a highly volatile inventory investment. As the model acquires a multistage production process, the neo-classical model will show a high inventory of existing investments as well as how the inventory stocks will reduce business cycles.

Conclusion

Robert Solow can be hailed as one of the most important economists of the twentieth century. He will be remembered for his major contribution to economics through his neoclassical growth model, which has become the organizing structure in modern macroeconomics. The model replaced the IS-LM mechanism and has been adopted by economic researchers across the world. Besides, the extension of the neoclassical growth model resulted in macroeconomics being integrated into other areas of economics rather than being just one branch of economic. The integration has benefited macroeconomics and contributed to other areas such as public finance and labor economics. Robert Solow`s model has influenced nearly all areas of economic science. Besides, the model indicated that capital accumulation could not account for a lasting reason for economic growth in an economy. According to the model the most significant source of wealth in a county is the development and innovation in technology. This means that investments will take less precedence as compared to technological change. The Solow ‘residual’ indicates the rate at which technological change will occurs will explain the variations that exist between real income growth and the growth that occurs between capital and labor. Solow made significant contributions to the economic growth theory, which has expanded the technological framework of the theory. Due to the contributions of Robert Solow and his neoclassical growth model, an economist, as well as policymakers, have placed more emphasis on technical progress as well as its acceleration to help spur economic growth. Developmental economists have indicated that sustained and growing economic growth requires innovation. Economic growth is making use of technical progress and innovation to become more productive economically.