Read this article to discover Joan Robinson’s model within the neo-classical theory of economic growth.
Introduction:
Joan Robinson’s growth model addresses population growth issues in developing economies and examines how this growth affects capital accumulation and output growth rates.
The economic growth model proposed by Joan Robinson is founded on two main principles:
(i) The way income is distributed influences capital formation, and
(ii) The utilization rate of labor is determined by capital and labor supply. This model is discussed in her book, “The Accumulation of Capital,” which is grounded in capitalist principles.
Assumptions:
Robinson makes several key assumptions:
(a) Total income, when considering real values, is shared between two groups—workers and entrepreneurs.
(b) All wages earned by workers are spent on consumption, leaving no savings.
(c) Entrepreneurs save and reinvest all profits, consuming nothing. Without profits, they cannot accumulate wealth, and without accumulation, profits do not exist.
(d) Capital and labor are combined in fixed ratios to generate a specific output (this assumption was later revised), meaning there is no technological advancement. Essentially, production techniques remain constant with fixed ratios of capital to labor.
(e) Her approach focuses on the past results without considering price level changes.
(f) It assumes a closed economy with laissez-faire principles.
(g) Labor is assumed to be abundant; entrepreneurs can acquire as much labor as needed to promote steady growth. In Robinson’s structure, this growth occurs at a constant capital accumulation rate. To maintain this, there must be an appropriate profit rate, which includes the ideal condition of no excess or shortage of labor. This means that the labor force must increase at the same pace as capital.
Features:
In her dynamic two-sector model, Mrs. Robinson explores the developments that occur during the quasi-long period. She argues that in her basic model, workers spend all their earnings, while businessmen reinvest their entire profits. This leads to a crucial relationship where investment after the fact matches profits after the fact. Nonetheless, entrepreneurs face a limit to how much profit they can reinvest, dictated by the minimum real wage demands of the workers.
Within this inflationary boundary, additional barriers exist, such as financial factors, productivity limits, and the balance of payments. As the economy grows, these obstacles increase, and achieving growth becomes reliant on the drive and determination of entrepreneurs.
The growth process benefits from a steady flow of innovations, which helps to break through these barriers. The peak of this growth journey is referred to as the 'Golden Age,' where the potential growth rate mirrors Harrod’s natural growth rate, Gn. She aims to clarify the essential characteristics of economic growth based on the 'capitalist rules of the game.' To achieve this, she constructs a conceptual model while K.K. Kurihara develops a tangible model, which will follow.
The key distribution equation in her growth model is presented below.
In this context, Cn refers to the portion of wage income that workers spend (w/p.N), while SK signifies savings derived from profit income (clip_image004K). As stated in equation (i), net investment represents a rise in real capital (AK); hence, we express this as:
I = ∆K ……………………(iv)
Examining equations (iii) and (iv), we can express the relationship between S and I as:
∆K = πK ……………….(v)
Since S equals I, we can deduce that ∆K/K equals π, or alternatively, ∆K/K equates to πK/K. However, from equation (iii), we are aware that
According to J. Robinson, the growth rate of capital outlined in equation (vi) reflects what entrepreneurs can achieve by adhering to capitalist principles. The equation indicates that the capital growth rate can rise if the net return on capital (P-w/P) increases more significantly than the capital-labor ratio. In Ricardian terms, this suggests that a decrease in real wages supports capital accumulation. This perspective seems to reconnect us to Ricardo’s economic development theory, but from a Keynesian perspective.
Now, considering Mrs. Robinson's idea of a 'Golden Age,' which represents a state where labor is fully employed and capital is utilized to its fullest. This equilibrium is feasible if we accept that (K/N) = θ = constant under conditions of complete employment and maximum capital use; the increase in fully employed labor is expressed as ∆N = ∆K/θ (K/N = θ).
From this equation, we can determine the growth rate of fully employed labor:
The relationship demonstrates that the growth of fully employed labor occurs at a pace matching the growth of capital. This suggests that if the capital-labor ratio (θ) remains stable, capital must expand to keep up with the labor force. In simpler terms, it indicates that the change rate of the labor force (∆N/N) equals the change rate of capital (∆K/K). Therefore, with a sufficient supply of labor in terms of output, this equation points to a balanced state where both labor and capital are fully employed.
Figure 44.4 illustrates this, where Y represents net national income, N denotes the amount of labor in use, K signifies the employed capital resources, p stands for the average output price and capital equipment cost, w indicates the wage rate, and n describes the profit rate (including interest) necessary for the proper use of the current real capital. To derive the distribution equation in real terms, we divide both sides of equation (i) by p (the average price):
Y = W/P N + πK...(viii)
Our focus is on determining the profit rate depicted as n in this equation to achieve an equilibrium state from the economy's demand perspective.
Let's reshape this into a clearer format while keeping the meaning intact:
We can reformulate this according to Robinson's assumptions as follows:
In the first quadrant of the graph, the horizontal axis represents the capital-labor ratio (K/N) while the vertical axis indicates the labor income ratio or productivity (Y/N). The line OW denotes the minimum wage rate. Moving to quadrant II, ON indicates the growth rate of the workforce. The path of expansion is shown by OY, with a tangent touching point C. The formula for the growth rate of capital is expressed as ∆I/I = Output - Input/Input = Surplus/Input = HC/OW x OK = HC/WH x 1/OW (since tan β remains unchanged). Therefore, HC/OK = HC/WH, leading to WH equating to ON and OW equating to HC. Hence, HC/WH 1/OW = OW/ON x 1/OW = 1/ON, which represents the workforce growth rate. Essentially, the growth of surplus, measured as HC, needs to correspond with the growth rate of the labour force, represented by ON. This scenario introduces the concept of the ‘Golden Age’ as described by Joan Robinson.
Understanding the Golden Age:
After examining how capital accumulation influences economic growth, Mrs. Robinson shifts her focus to the effects of population growth on development. An increase in both population and the labor supply, without a sufficient rise in the capital stock, will lead to a decrease in productivity. If real wages do not increase, this results in lower profit rates, ultimately hindering capital accumulation.
This situation generally leads to higher unemployment levels, particularly in underdeveloped nations. Achieving full employment is only feasible when the population growth rate aligns with the capital stock growth rate.
When these growth rates are equal, the economy reaches a state of full employment equilibrium. This scenario is what Joan Robinson defines as the ‘Golden Age’. She argues that if technical progress remains neutral and consistent, production patterns stay steady, competition functions properly, population grows at a stable rate, and capital accumulation keeps pace with the labor supply, the profit rate will stabilize, and real wages will rise alongside output per worker.
In this balanced system, internal conflicts are absent; as long as political factors do not disrupt the situation and entrepreneurs believe in future growth, there are no barriers to maintaining their investment rates.
Consequently, the total annual output and capital stock (measured in commodities) will grow at a consistent proportional rate that factors in both the labor force growth and the productivity increase. These conditions can be termed a ‘golden age,’ reflecting an idealized scenario that is unlikely to be realized in practice.
This period can be described as a time of happiness, where consumption is growing at the highest possible technical rate. According to Harrod, during this Golden Age, the natural, warranted, and actual rates of national income growth are identical. Regardless of the current growth rate, further progress is always achievable.
The long-term limits on wealth growth are not governed by technical capabilities, but rather by the stagnation that arises when competition weakens and wage ratios rise. The balance of a 'golden age', featuring full employment and complete capital utilization, can only occur if the growth rate of the labor force (∆N/N) matches that of the capital stock (∆K/K). This means that when there is equilibrium with full employment, it holds that ∆N/N is equal to ∆K/K. If ∆N/N exceeds ∆K/K, the economy will face unemployment, and the reverse is also true.
We therefore understand that this concept is valuable for precise theoretical exploration. Unlike the ideal of full employment, which can be targeted through policies, it serves mainly as a means of explanation. Each growth rate correlates with a specific golden age, and the challenge lies in identifying the optimal growth rate fitting the conditions of the economy. Mrs. Robinson's golden age represents a time of abundance, in contrast to stagnation.
The crucial focus is on the relationship between profits and wages. This relationship is vital in determining an economy's ability to reach Golden Age equilibrium. According to her theory, capital accumulation within the ‘capitalist framework’ cannot grow unless the cost of labor (real wage rate) is lowered compared to the price of capital (essentially the profit rate) and labor productivity.
In a golden age scenario, wage and profit shares remain constant, as all components in the economy grow proportionately, indicating neutral technological progress aligned with optimal capital accumulation. Furthermore, in such an economic context, a stable profit rate from the past will likely persist in the future. Individuals who save their money will be eager to lend it, meaning that interest rates will not significantly fall below profit rates. A steady capital-output ratio is anticipated in this ‘Golden Age’, ensuring that wage and profit shares continue to remain stable.
When the ‘potential growth ratio’ is realized, Mrs. Robinson suggests that the economy enters a golden age. This phase is characterized by the highest sustainable rate of capital formation that can consistently maintain profits. For a golden age to exist, this growth ratio must remain stable, as frequent fluctuations can disrupt its harmony. However, even stability might not guarantee tranquility. An increase in total capital stock may reduce the motivation for accumulation, leading to stagnation and a drift away from the golden age path.
Evaluation:
In assessing Mrs. Robinson’s model, it closely resembles Keynes’ aggregative framework since both are macroeconomic models. Nevertheless, Keynesian theory lacks true dynamism. To transform Keynes’ General Theory into a long-term dynamic model, one must incorporate the 'growth' element, which could lead to a complete generalization of the theory.
We have examined the theories of Harrod and Robinson regarding growth. Harrod-Domar connects capital formation to the savings ratio, impacting aggregate community income rather than focusing only on profits and capital productivity. In contrast, Mrs. Joan Robinson ties capital accumulation to the relationship between wages and profits, along with labor productivity, aligning her views more closely with a real market economy.
Importantly, Joan Robinson emphasizes labor's role in capital accumulation, while Harrod-Domar focus on capital itself. This distinction leads to the understanding that despite Robinson’s model reaching similar conclusions as those of Harrod and Domar, they differ in their approaches: one considers a single factor while the other includes two.
Joan Robinson significantly contributes to post-Keynesian growth economies by merging classical value and distribution theories with modern Keynesian saving-investment theories into a unified system. However, this synthesis may also present challenges for policy implementation. Unlike Harrod-Domar models, Robinson's approach does not easily adapt to incorporate fiscal and monetary policy variables unless labor productivity, wage rates, profit rates, and the capital-labor ratio are treated as practical policy targets, akin to a fully planned economy.
Nevertheless, J. Robinson’s theory enhances our comprehension of capital accumulation's fundamental nature within the confines of capitalist principles. Finally, it should be noted that while her growth model can achieve a stable equilibrium solution, it remains as susceptible to instability as the Harrod-Domar models within a laissez-faire economic system.
Golden Age and Emerging Economies:
The behavior of the wage-profit relationship can vary, influenced by market conditions. If technology remains constant, an oversupply of labor will eventually lower wages, resulting in reduced real wages if prices stay the same. This decrease in wages would increase profits, thus accelerating the growth of capital until it compensates for the rising population, restoring the balance where ∆K/K = ∆N/N.
On the contrary, if real wages do not decline for any reason, the surplus labor would fail to create a balancing effect. Consequently, it becomes crucial to increase the capital stock of an underdeveloped nation through development planning. A similar situation occurs when capital accumulation outpaces labor growth, as seen in many advanced countries. However, advanced economies face a higher likelihood of returning to a ‘golden age’ stable path than developing economies do.
Restoration of equilibrium is more likely to occur through advancements in technology, which would shift the entire production function and enable the economy to adjust to a higher capital-to-labor ratio. In developed economies, even if real wages are inflexible, changes in labor productivity (ρ) or the capital ratio (θ) could still positively influence profit rates and thereby stimulate capital growth as required to stay on the golden age trajectory. This is where Mrs. Robinson’s analysis evolves, taking on a more Schumpeterian perspective than a strictly Ricardian one.
Moreover, her model emphasizes that critical issues such as economic growth should not simply rely on capitalist dynamics, especially in developing regions. It convincingly illustrates the risks associated with depending on private profit motives to achieve consistent economic growth that aligns with the demands of an increasing population and evolving technology.
Mrs. Robinson subtly suggests that impoverished economies should not strictly adhere to capitalist principles for achieving growth but instead embrace a Keynesian framework featuring mixed economies, with fiscal and monetary strategies aimed at fostering independent investment.
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Joan Robinson’s Model of Economic Growth | Economics
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