Lecture 9. Income disparity among countries Endogenous growth: a model of human capital accumulation

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1 Lecture 9 Income disparity among countries Endogenous growth: a model of human capital accumulation

2 We ve said that the Solow growth model was a good model to explain growth as it was able to replicate the regularities we see in real-world data

5 In the end, we said that increases in savings were not sufficient to justify the continuous growth over time. We concluded that total factor productivity (technological progress) was the one that allowed us to grow over time! Growth accounting allowed us to do this.

6 Now let s talk about convergence. Is there a tendency for poor countries to catch up with the rich? The Solow growth model says yes! As always, we need some assumptions: 1. We have two identical countries (same TFP, labor force growth rate, and savings rate). 2. The rich country initially has a higher level of capital per worker relative to the poor country. (Consequently, it also has a higher output per worker.)

7 Rich and Poor Countries and the Steady State Two otherwise identical countries have initial capital per worker of kp and kr. Both countries converge in the long run to the steady state k* Copyright 2008 Pearson Addison-Wesley. All rights reserved. 7-7

8 Convergence in Income per Worker Across Countries in the Solow Growth Model Two otherwise identical countries, one with lower income per worker than the other, both converge in the long run to the steady state y* Copyright 2008 Pearson Addison-Wesley. All rights reserved. 7-9

9 Convergence in Aggregate Output Across Countries in the Solow Growth Model The initially rich country and the initially poor country converge in the long run to the same long-run growth path, where aggregate output grows at a constant rate. Copyright 2008 Pearson Addison-Wesley. All rights reserved. 7-10

14 Figure 7.4 Differences in Total Factor Productivity Can Explain Disparity in Income per Worker Across Countries Differences in TFP can explain disparity in income per worker across countries Copyright 2008 Pearson Addison-Wesley. All rights reserved. 7-15

15 So, are poor countries doomed? Well, the answer is not exactly. There are some things that could be done, but it depends on the government to get things right. The government could 1. Promote greater competition among firms: Firms must innovate to remain competitive 2. Promote free trade. 3. Do selective privatization: Eliminate government ownership when there is no clear benefit of having a public enterprise vs. a private one. (But be really selective!)

16 The Solow Growth Model is an exogenous growth model Long run growth can be accounted for in the Solow Growth Model through the growth of TFP. But where is this TFP growth coming from? It is exogenous. Perhaps models of endogenous growth can explain

17 Endogenous Growth: A Model of Human Capital Accumulation In this model, the growth rate of per capita income is determined by the efficiency with which human capital is accumulated, and the fraction of available time devoted to human capital accumulation.

18 Let s first look at the representative consumer

19 Consumer s Budget Constraint Consumption is equal to total wage income. C = S wh u u: units of time used working H: human capital

20 Technology for accumulating human capital Future human capital depends on current human capital and time devoted to training and education. u: units of time used working b: parameter that captures efficiency of human capital accumulating technology (quality of education)

21 Now let s consider the representative firm

22 Production Function Firms use labor efficiency units (uh) to produce output: Y: current output z: marginal product of efficiency units of labor

23 Firm s Profits If z<w, firm hires no labor If z>w, firms desires to hire infinite amount of labor Can you guess what the equilibrium wage is going to be?

24 Determination of the Equilibrium Real Wage

25 Now let s characterize the competitive equilibrium

26 Equilibrium Characterization Consumption is given by: Human capital evolves in equilibrium according to:

27 Human Capital Accumulation The colored line shows future human capital as a function of current human capital. H >H for any H, so human capital increases forever

28 Growth rate of Human Capital Equilibrium growth rate of human capital: Note: A decrease in u, i.e. less time working, implies lower initial consumption, but higher human capital growth and thus higher consumption growth

29 Growth rate of Consumption Equilibrium growth rate of consumption: C C ' zuh ' 1= 1= zuh Human capital, consumption, and output all grow at the same rate in equilibrium

30 Growth rate of Consumption Equilibrium growth rate of consumption: C C ' zuh ' 1= 1= zuh Discussion: So what happens when u decreases because of, for example, education subsidies?

31 Effect of a Decrease in u on the Consumption Path

32 Discussion: what is the implication of this model for convergence? Two otherwise identical countries that differ only in additional incomes

33 No Convergence in the Endogenous Growth Model Two otherwise identical countries that differ only according to their initial incomes never converge

34 How about increasing b? This would also lead to higher growth rates

4.2 A Model of Production. 4.1 Introduction. A Model of Production. Setting Up the Model. Chapter 4

4.2 A Model of Production. 4.1 Introduction. A Model of Production. Setting Up the Model. Chapter 4 Chapter 4 A Model of Production By Charles I. Jones Media Slides Created By Dave Brown Penn State University 4.2 A Model of Production Vast oversimplifications of the real world in a model can still allow