What Is Kuznets Curve Kuznets Curve: A . . . Analysis of the Problem How Can We Describe . . . Kuznets Curve: A Simple Stages Dynamical System-Based What Happens on the . . . What Happens on the . . . Explanation Comparison of Two . . . Acknowledgments Thongchai Dumrongpokaphan 1 and Vladik Kreinovich 2 Home Page Title Page 1 Department of Mathematics, Chiang Mai University, Thailand tcd43@hotmail.com ◭◭ ◮◮ 2 University of Texas at El Paso, El Paso, Texas 79968, USA vladik@utep.edu ◭ ◮ Page 1 of 13 Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 1. What Is Kuznets Curve Analysis of the Problem • In the 1950s, Simon Kuznets, an American economist How Can We Describe . . . of Russian origin, showed that: Stages What Happens on the . . . – as the country’s Gross Domestic Product (GDP) What Happens on the . . . increases, Comparison of Two . . . – inequality first increases and then decreases again. Acknowledgments • The resulting dependence on inequality on GDP looks Home Page like an inverted letter U. Title Page • It is thus called an inverted U-shaped dependence or ◭◭ ◮◮ the Kunzets curve . ◭ ◮ • For this work, Professor Kuznets was awarded a Nobel Page 2 of 13 Prize in Economics in 1971. Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 2. Kuznets Curve: A Controversy Analysis of the Problem • The Kuznets curve is a purely empirical observation. How Can We Describe . . . Stages • Free-market champions use it as an argument that the What Happens on the . . . governments should not interfere with economy: What Happens on the . . . – inequality will decrease by itself, Comparison of Two . . . – as soon as the economy improves further. Acknowledgments Home Page • So, they recommend to minimize government interven- tions. Title Page ◭◭ ◮◮ • As Ronald Reagan used to say, “The rising tide lifts all the boats”. ◭ ◮ Page 3 of 13 Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 3. Kuznets Curve: A Controversy (cont-d) Analysis of the Problem • Other economists notice that: How Can We Describe . . . Stages – in all developed countries, What Happens on the . . . – there was a lot of government intervention aimed What Happens on the . . . at decreasing inequality. Comparison of Two . . . • So, they recommend government regulations. Acknowledgments Home Page • Additionally, some researchers doubt that the Kunzets curve is indeed a universal phenomenon. Title Page ◭◭ ◮◮ • We show that the Kuznets curve phenomenon natu- rally follows from the general system-based analysis. ◭ ◮ Page 4 of 13 Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 4. Analysis of the Problem Analysis of the Problem • We start in a situation when the overall economic out- How Can We Describe . . . put is small and therefore, most everyone is poor. Stages What Happens on the . . . • In such situations, while there may be a small minority What Happens on the . . . of relatively rich people, most people are poor. Comparison of Two . . . • In this sense, there is not much inequality. Acknowledgments • As the economy grows, people’s incomes grow. Home Page • Each person’s income grows until it reaches some Title Page level m i . ◭◭ ◮◮ • This level expressing the capability of this person to ◭ ◮ earn money in the corresponding economy. Page 5 of 13 • People are different, so they have somewhat different Go Back rates v i at which they move towards this larger income. Full Screen • For simplicity, we can assume that for each person, the rate does not change with time. Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 5. Analysis of the Problem (cont-d) Analysis of the Problem • So, at each moment of time t , the income x i ( t ) of the How Can We Describe . . . i -th person is: Stages – equal to x i ( t ) = v i · t when t ≤ m i What Happens on the . . . , and v i What Happens on the . . . – equal to x i ( t ) = m i for t ≥ m i Comparison of Two . . . . v i Acknowledgments • The values m i are centered around the mean m , with Home Page def random deviations ∆ m i = m i − m. Title Page • Similarly, the rates v i center around the mean v , with ◭◭ ◮◮ def random deviations ∆ v i = v i − v . ◭ ◮ • There is no reason to believe that there is a correlation Page 6 of 13 between m i and v i . Go Back • So, we will assume these variables to be independent. Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 6. How Can We Describe Inequality Analysis of the Problem • Perfect equality means that everyone’s income is the How Can We Describe . . . same. Stages What Happens on the . . . • This is equivalent to saying that the standard deviation What Happens on the . . . of income is 0. Comparison of Two . . . • In general, Acknowledgments Home Page – if the standard deviation is equal to 10% of the average income, Title Page – then we have less inequality that when the standard ◭◭ ◮◮ deviation is 20% of the average income. ◭ ◮ • Thus, a natural measure of inequality is the ratio be- Page 7 of 13 tween the income’s standard deviation and its mean. Go Back • Now, we are ready to analyze how inequality changes Full Screen when the economy improves. Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 7. Stages Analysis of the Problem • Kuznets curve considers three stages: How Can We Describe . . . Stages – the starting stage, when the inequality level is rel- What Happens on the . . . atively low, What Happens on the . . . – the intermediate stage, when the level of inequality Comparison of Two . . . increases, and Acknowledgments – the final stage, when the level of inequality de- Home Page creases. Title Page • We have already discussed that in the beginning, there ◭◭ ◮◮ is practically no inequality. ◭ ◮ • So, to complete our analysis, we need to consider two Page 8 of 13 other stages: the intermediate stage and the final stage. Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 8. What Happens on the Final Stage Analysis of the Problem • On the final stage, everyone reaches their potential m i ; How Can We Describe . . . thus: Stages What Happens on the . . . – the average income is equal to the average m of the What Happens on the . . . values m i , and Comparison of Two . . . – the standard deviation is equal to the standard de- Acknowledgments viation σ m of the differences ∆ m i . Home Page • So, on the final stage, the inequality level is equal to Title Page the ratio σ m m . ◭◭ ◮◮ ◭ ◮ Page 9 of 13 Go Back Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 9. What Happens on the Intermediate Stage Analysis of the Problem • In the beginning of the intermediate stage, the income How Can We Describe . . . of each person is equal to Stages 1 + ∆ m i What Happens on the . . . · t = m + ∆ m i x i ( t ) = m i · t = m m What Happens on the . . . v · t · . 1 + ∆ v i v + ∆ v i v i Comparison of Two . . . v Acknowledgments • Differences between different people are, in most cases, Home Page not so large, so | ∆ m i | ≪ m and ∆ m i ≪ 1. Title Page m ◭◭ ◮◮ • Similarly, | ∆ v i | ≪ v and thus, ∆ v i ≪ 1. v ◭ ◮ • Thus, we can expand the expression for x i ( t ) in ∆ m i Page 10 of 13 m and ∆ v i Go Back and keep only linear terms: v Full Screen � 1 + ∆ m i − ∆ v i � x i ( t ) = m v · t · . Close m v Quit
What Is Kuznets Curve Kuznets Curve: A . . . 10. Intermediate Stage (cont-d) Analysis of the Problem � � 1 + ∆ m i − ∆ v i • Reminder: x i ( t ) = m How Can We Describe . . . v · t · . m v Stages What Happens on the . . . • The mean value of ∆ m i and ∆ v i is 0, so the mean income is equal to x ( t ) = m What Happens on the . . . m · t. Comparison of Two . . . • The standard deviation of ∆ m i is equal to σ m , so the Acknowledgments standard deviation of the ratio ∆ m i is equal to σ m Home Page m . m Title Page • Similarly, the standard deviation of the ratio ∆ v i is ◭◭ ◮◮ v equal to σ v v . ◭ ◮ Page 11 of 13 • The quantities ∆ m i and ∆ v i are assumed to be inde- � ( m ) 2 + σ 2 σ 2 pendent; thus: σ x ( t ) Go Back m v x ( t ) = ( v ) 2 . Full Screen Close Quit
What Is Kuznets Curve Kuznets Curve: A . . . 11. Comparison of Two Stages Analysis of the Problem • On the final stage, we have σ x ( t ) x ( t ) = σ m How Can We Describe . . . m . Stages • On the intermediate stage, we have What Happens on the . . . What Happens on the . . . � ( m ) 2 + σ 2 σ 2 σ x ( t ) m v Comparison of Two . . . x ( t ) = ( v ) 2 . Acknowledgments Home Page � ( m ) 2 + σ 2 σ 2 ( v ) 2 > σ m m v Title Page • Clearly, m . ◭◭ ◮◮ • Thus, the inequality is smaller on the final stage. ◭ ◮ • This is exactly the Kuznets curve phenomenon. Page 12 of 13 • So, we have indeed arrived at a simple justification of Go Back the Kuznets curve phenomenon. Full Screen Close Quit
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