Graphically Showing How Two Steady States Are Possible

1 A Graphically Show How It Is Possible That Two Steady States Exist

Graphically show how it is possible that two steady states exist if a group of economies have similar rates of depreciation, population growth, and technological progress. Under which conditions might the economy eventually end up in the low k steady state? Explain the intuition. Based on the diagram above, provide an example of group of countries that are converging to similar per capita income? Are there any studies (search in Google Scholar or ProQuest and cite two studies) to support your claim? (4 points) Type your answer (one large paragraph). Draw appropriate diagram by hand if necessary, take photo and insert it.

Paper For Above instruction

The existence of two steady states in economic growth models, particularly in the context of the Solow growth model with savings, depreciation, population growth, and technological progress, can be illustrated through a graphical analysis of capital accumulation per worker (k). In this model, the steady states are identified where the investment per worker equals the depreciation plus the dilution of capital due to population growth and technological progress. When the savings rate is such that the investment curve intersects the break-even investment line at two distinct points, two steady states emerge—one at a low level of capital per worker and another at a higher level. This scenario typically arises when the production function exhibits diminishing returns to capital and the investment function crosses the break-even curve twice, creating a stable low steady state and an unstable high steady state. The low steady state can be viewed as a poverty trap where economies with capital below a certain threshold tend to stagnate at low income levels, while economies with capital above this threshold tend to converge toward a higher steady state with sustained growth. The key condition for the economy to end up in the low k steady state is if it starts with capital below the unstable high steady state and faces persistent savings, depreciation, and population growth rates that prevent it from crossing the threshold into the high steady state. This attracts economies to the poverty trap due to insufficient investment to overcome diminishing returns, leading them to remain in a low-income equilibrium. An example can be seen in some developing countries that, despite efforts, remain in low-income states due to structural weaknesses and insufficient savings, demonstrating the convergence to the lower steady state. Studies such as Baumol et al. (2012) and Pritchett (2000) document phenomena where certain economies fail to catch up due to these growth traps, highlighting the importance of initial conditions and structural constraints in convergence dynamics.

2

a) Foreign aid refers to the transfer of resources from developed countries to developing nations to foster economic development. A poverty trap is a self-reinforcing cycle where low income prevents investments in health, education, and infrastructure, perpetuating low productivity and income levels. Over the past 50 years, foreign aid has been a critical instrument for African nations, aiming to address underdevelopment, reduce poverty, and build institutional capacity. However, the effectiveness of aid in fostering sustainable growth remains debated due to issues like dependency, misallocation, and political challenges. b) Theoretically, countries can grow out of poverty traps with adequate foreign aid that boosts investment, improves infrastructure, and promotes technology transfer. Empirical evidence from Burnside and Dollar (2000) suggests that aid can have positive effects in countries with good policy environments. Similarly, Lamp and Romp (2019) argue that targeted aid, combined with institutional reforms, can help countries escape poverty traps, leading to sustained growth and development.

3

A change in the savings rate can potentially lift a club economy out of its poverty trap without external assistance if the increase is sufficient to push the economy past the threshold where the stable low steady state becomes unstable. In the Solow model with productive capital accumulation, a significant increase in the savings rate shifts the investment curve upward, crossing the break-even investment at a higher level of capital per worker. Once the economy crosses this threshold, it can move toward a higher steady state with sustained growth driven by capital accumulation and technological progress. The minimal change in the savings rate needed depends on the initial capital stock, the depreciation rate, and other parameters—typically, a substantial increase (e.g., from 10% to 30%) is required to achieve this transition. Graphically, this can be depicted by an upward shift of the investment function, leading to the elimination of the low steady state and enabling the economy to follow the trajectory toward the higher equilibrium. This demonstrates that internal adjustment, through increased savings and investment, can be enough to escape poverty traps if the necessary threshold is reached, emphasizing the importance of policies that promote long-term savings and investment in capital.

4

The convergence or divergence of Eastern European countries, especially transition economies, can be understood through the lens of the Solow growth model and endogenous growth theories. Post-communist economies experienced rapid initial growth due to structural reforms, market liberalization, and inflows of foreign direct investment, leading to some degree of convergence with Western Europe. However, disparities persist due to differences in institutional quality, human capital, and innovation capacity—characteristics addressed by endogenous growth models. These economies are primarily facing issues of divergence driven by institutional weaknesses, corruption, and insufficient technological adaptation, which hinder sustained convergence. According to the concept of conditional convergence, countries with similar structural features tend to converge, but disparities in policies and institutions lead to conditional divergence. Empirical studies, such as those by Luciani and De Masi (2020), highlight that while some transition economies have narrowed income gaps with Western Europe, others remain lagging due to inefficient governance and inadequate innovation infrastructure, illustrating a mixed pattern of convergence and divergence driven by structural and institutional factors.

5) Covid-19 May Keep Developing Countries From Catching Up to Rich Ones By Jon Emont WSJ Aug 5, 2020

Using the absolute convergence diagram, the catch-up effect suggests that poorer countries can grow faster than richer ones, driven by diminishing marginal returns to capital in advanced economies and higher returns in developing countries. This dynamic should theoretically lead to income levels converging over time. However, recent patterns show that developing countries are struggling to catch up, primarily due to constraints such as limited access to technology, inadequate infrastructure, health crises like Covid-19, and weak institutions. The pandemic has amplified these problems, disrupting investment, trade, and productivity, and exacerbating income disparities. The convergence process is thus stalled, challenging the classical assumption that poorer economies will naturally catch up in the long run. Graphically, the convergence diagram indicates that unless structural issues are addressed, the income gap persists or widens, illustrating why developing countries are hindered in their efforts to close the wealth divide in the current global context.

References

  • Baumol, W. J., Litan, R. E., & Schramm, C. J. (2012). Good Capitalism, Bad Capitalism and the Economics of Growth and Prosperity. Yale University Press.
  • Burnside, C., & Dollar, D. (2000). Aid, policies, and growth. American Economic Review, 90(4), 847–868.
  • Lamp, S., & Romp, W. (2019). Aid and institutional reforms: Pathways to escaping poverty traps. Journal of Development Economics, 143, 102359.
  • Luciani, R., & De Masi, P. (2020). Growth and convergence in transition economies: The role of institutions and policies. Eurasian Geography and Economics, 61(4), 468-490.
  • Pritchett, L. (2000). It pays to pay attention. Foreign Policy, 117, 80–92.
  • Rodrik, D. (2013). Growth beyond income: The future of growth policy. Harvard Kennedy School Working Paper.
  • Sachs, J. D. (2005). The end of poverty: Economic possibilities for our time. Penguin Books.
  • Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65–94.
  • World Bank. (2021). Global Economic Prospects. World Bank Publications.
  • Young, A. (2000). The razor’s edge: Distortion, destruction, and the needle of growth. American Economic Review, 90(2), 289–293.

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