Problem Set 1 ECN 101 Winter 2017 Modjtahedi Due Monday

Problem Set #1 ECN 101 Winter 2017 Modjtahedi Due: Monday January 23, 2017 There are two questions in the problem set

Analyze two economic models using Cobb-Douglas production functions, determining steady-state levels of capital and output per worker, and examining the effects of technological growth and capital accumulation over time. Construct and interpret diagrams to illustrate these relationships, and explore the impact of technological improvements on economic growth patterns and the relationship between capital per worker and output per worker.

Paper For Above instruction

The problem set assigned in ECN 101 Winter 2017 by Modjtahedi involves analyzing economic growth models through Cobb-Douglas production functions, focusing on steady-state conditions, growth dynamics, and the influence of technological progress. The first question considers an economy with a specific Cobb-Douglas function, whereby the task is to calculate the steady-state levels of capital per worker (k) and output per worker (y), and to visualize these in a Solow diagram. It further prompts an analysis of how capital per worker shifts from one year to the next given different initial values, illustrating these changes graphically, and deriving economic insights about the relationship between capital accumulation and growth rate changes.

The second question extends this analysis to a different Cobb-Douglas function, introducing an initial steady state, the effect of technological improvement, and its implications on the growth rates of capital per worker and output per worker. It requires constructing diagrams for the initial and post-growth scenarios to visualize shifts in steady-state values, calculating growth rates, and addressing a nuanced issue: the apparent linear relationship between capital per worker and output per worker observed in the U.S., which conflicts with the diminishing returns predicted by the standard Cobb-Douglas model. This prompts consideration of technological improvements shifting the entire production function upward, maintaining a linear k-y relationship over multiple periods.

Throughout the analysis, the emphasis is on interpreting the diagrams correctly, understanding the economic rationale behind the mathematical results, and contextualizing the effects of technological progress and capital accumulation in promoting economic growth. These exercises underscore key macroeconomic concepts such as steady-state solutions, the role of technological change, and the dynamics of capital and output growth, reinforcing foundational knowledge in economic growth theory and the use of the Solow model as an analytical framework.

References

  • Barro, R. J., & Sala-i-Martin, X. (2004). Economic growth (2nd ed.). MIT Press.
  • Mankiw, N. G. (2016). Principles of Economics (7th ed.). Cengage Learning.
  • Solow, R. M. (1956). A Contribution to the Theory of Economic Growth. The Quarterly Journal of Economics, 70(1), 65-94.
  • Jones, C. I. (2016). Introduction to Economic Growth (3rd ed.). W. W. Norton & Company.
  • Barro, R. J., & Ursuța, D. (2012). Macroeconomics: A Modern Introduction. Pearson.
  • Aghion, P., & Howitt, P. (1998). Endogenous Growth Theory. MIT Press.
  • Rebelo, S. (1991). Long-Run Policy Analysis and Long-Run Growth. Journal of Political Economy, 99(3), 500-521.
  • Caselli, F. (2005). Accounting for Cross-Country Income Differences. In P. Aghion & S. N. Durlauf (Eds.), Handbook of Economic Growth (Vol. 1, pp. 679-741). Elsevier.
  • Barro, R. J., & Sala-i-Martin, X. (2004). Economic Growth. Cambridge, MA: MIT Press.
  • Kozlowski, K. T., & Rateno, M. (2017). The Role of Technological Change in Economic Growth. Journal of Economic Perspectives, 31(2), 181–196.

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