Persistent Inequality By- Dilip Mookherjee and Debraj Ray.

Slides:



Advertisements
Similar presentations
An Efficient Dynamic Auction for Heterogeneous Commodities (Lawrence M.Ausubel - september 2000) Authors: Oren Rigbi Damian Goren.
Advertisements

Lecture 3: Taxes, Tariffs and Quota (Chapter 5) Relation to work horses Government and taxation Taxes and quotas in general equilibrium Welfare implications.
Introduction to Portfolio Selection and Capital Market Theory: Static Analysis
XII. Monopoly pricing and limited needs
Chapter 14 : Economic Growth
ECO 402 Fall 2013 Prof. Erdinç Economic Growth The Solow Model.
The securities market economy -- theory Abstracting again to the two- period analysis - - but to different states of payoff.
1 Chapter 14 The Debt Crisis of the 1980s © Pierre-Richard Agénor and Peter J. Montiel.
Diploma Macro Paper 2 Monetary Macroeconomics Lecture 6 Mark Hayes
An Analytical Framework of Government Role in Technological Promotion as a Cause of Inequality.
2. Free Trade and Protection. Summary 1.Theory of Comparative Advantage: Why trade is good. 2.Where comparative advantage comes from: Heckscher-Ohlin.
Ch.7 The Capital Asset Pricing Model: Another View About Risk
Contemporary Models of Development and Underdevelopment
6.896: Topics in Algorithmic Game Theory Lecture 15 Constantinos Daskalakis.
P.V. VISWANATH FOR A FIRST COURSE IN INVESTMENTS.
Market size and tax competition Gianmarco I.P. Ottaviano, Tanguy van Ypersele.
Behavioral Finance and Asset Pricing What effect does psychological bias (irrationality) have on asset demands and asset prices?
ELM Part 2- Economic models Manuela Samek
L11: Risk Sharing and Asset Pricing 1 Lecture 11: Risk Sharing and Asset Pricing The following topics will be covered: Pareto Efficient Risk Allocation.
Announcements Presidents’ Day: No Class (Feb. 19 th ) Next Monday: Prof. Occhino will lecture Homework: Due Next Thursday (Feb. 15)
Who Wants to be an Economist? Part II Disclaimer: questions in the exam will not have this kind of multiple choice format. The type of exercises in the.
Endogenous Technological Change Slide 1 Endogenous Technological Change Schumpeterian Growth Theory By Paul Romer.
The basic neoclassical model: Labour demand (1)
Labor Market Overview (Part 2). The Labor Market Labor markets determine –Terms of employment Earnings versus total compensation Working conditions –Levels.
© The McGraw-Hill Companies, 2005 CAPITAL ACCUMULATION AND GROWTH: THE BASIC SOLOW MODEL Chapter 3 – first lecture Introducing Advanced Macroeconomics:
Oligopoly (Game Theory). Oligopoly: Assumptions u Many buyers u Very small number of major sellers (actions and reactions are important) u Homogeneous.
1 Chapter 9 Stabilization and the Labor Market © Pierre-Richard Agénor and Peter J. Montiel.
Robinson Crusoe model 1 consumer & 1 producer & 2 goods & 1 factor: –two price-taking economic agents –two goods: the labor (or leisure x 1 ) of the consumer.
L2: Market Efficiency 1 Efficient Capital Market (L2) Defining efficient capital market Defining the value of information Example Value of information.
Lecture 3: Arrow-Debreu Economy
EC 936 ECONOMIC POLICY MODELLING
Chapter 16 Unemployment: Search and Efficiency Wages.
Economic Models Real economy is too complicated to understand
Neoclassical production function
Lecture #7. Lecture Outline Review Go over Exam #1 Continue production economic theory.
Assumptions for discussion on this topic In our class on National Income we saw that output Y = C + I + G + NX We shall ignore NX. This means we are assuming.
Chapter 3 Productivity, Output, and Employment Copyright © 2012 Pearson Education Inc.
Consumption, Production, Welfare B: Competitive markets (partial eq) Univ. Prof. dr. Maarten Janssen University of Vienna Winter semester 2013.
Chapter 37 Asymmetric Information. Information in Competitive Markets In purely competitive markets all agents are fully informed about traded commodities.
Lecture # 2 Review Go over Homework Sets #1 & #2 Consumer Behavior APPLIED ECONOMICS FOR BUSINESS MANAGEMENT.
Chapter 16 Income Taxation
Chapter 3 Discrete Time and State Models. Discount Functions.
On the implementability of the Lindahl correspondence by means of an anonymous mechanism Sébastien Rouillon GREThA, Bordeaux 4 Journées LAGV, 2008.
Monetary Macroeconomic Modeling Setting the stage.
Of 261 Chapter 26 Long-Run Economic Growth. of 262 Copyright © 2005 Pearson Education Canada Inc. Learning Objectives 3. List the main elements of Neoclassical.
Perfect Competition A perfectly competitive industry is one that obeys the following assumptions:  there are a large number of firms, each producing the.
ECONOMIC FOUNDATIONS OF FINANCE BASIC ELEMENTS OF THE THEORY OF CAPITAL.
Post-Katrina New Orleans: Inequality and Schooling S. Barbieri – J. Edwards Tulane University New Orleans Political Economy Workshop Tulane University.
Welfare effects of housing price appreciation in an economy with binding credit constraints Welfare effects of housing price appreciation in an economy.
Gießen, Differentiated products Vertical differentiation: different qualities Horizontal differentiation: equal qualities, but consumers.
Microeconomics Corso E John Hey. Chapter 26 The LABOUR MARKET The supply of labour. The demand for labour. Equilibrium. Minimum wage legislation?
Ecological Economics Lectures 04 and 05 22nd and 26th April 2010 Tiago Domingos Assistant Professor Environment and Energy Section Department of Mechanical.
6 © 2004 Prentice Hall Business PublishingPrinciples of Economics, 7/eKarl Case, Ray Fair The Production Process: The Behavior of Profit-Maximizing Firms.
Lecture 7 and 8 The efficient and optimal use of natural resources.
Chapter 4.  “Second Generation” growth models  The role of human capital in economic growth  Determinants of technological progress  Externalities.
Faculty of Economics Optimization Lecture 3 Marco Haan February 28, 2005.
Intermediate Micro Theory Firm Supply. We assume firms make decisions to maximize profits π(q) = pq – c(q) Therefore, how much should a profit maximizing.
1 MODERN PORTFOLIO THEORY AND MARKET EFFICIENCY BY PROF. SANJAY SEHGAL DEPARTMENT OF FINANCIAL STUDIES UNIVERSITY OF DELHI SOUTH CAMPUS NEW DELHI
The Capital Asset Pricing Model Lecture XII. .Literature u Most of today’s materials comes from Eugene F. Fama and Merton H. Miller The Theory of Finance.
Critique of Hotelling Hotelling’s “Principle of Minimum Differentiation” was flawed No pure strategy exists if firms are close together. With quadratic.
Part IIB. Paper 2 Michaelmas Term 2009 Economic Growth Lecture 2: Neo-Classical Growth Model Dr. Tiago Cavalcanti.
Economies of Scale Introduction and appropriation issues.
Capital Deepening and Nonbalanced Economic Growth Presenter: Dai, Qian.
L6: Risk Sharing and Asset Pricing1 Lecture 6: Risk Sharing and Asset Pricing The following topics will be covered: Pareto Efficient Risk Allocation –Defining.
Security Markets V Miloslav S Vošvrda Theory of Capital Markets.
Theory of Capital Markets
Status-seeking behavior, the evolution of income inequality, and growth Presented by Miyoung Oh 602Macro_ Spring2009.
Fiscal policies in the nonstohastic growth models
Tutorial 4: Asymmetric Information
AS-AD curves: how natural is the natural rate of unemployment?
Presentation transcript:

Persistent Inequality By- Dilip Mookherjee and Debraj Ray

The Model There is a continuum of agents indexed by i on [0,1] Each agent lives for one period, and has one child who inherits the same index. Assume preferences are fully altruistic. Each individual enjoy consumption of a single good c, with one period utility u. It is assumed that u is increasing, smooth and strictly concave. Given altruistic preferences, the payoff to generation t is given by the “tail sum” :

Professions There is some set of professions which individuals in each generation select from. It is assumed to be a compact set of the Euclidean space. A population distribution of professions is simply a measure The technology combines a production sector with an educational/training sector. The technology is represented by means of a set which contains various combinations of the form where there is at least one profession that requires no training.

Prices and Behavior The price of the consumption good is normalized to unity. There are two sets of prices relevant at each stage : is the wage function summarizing the returns to the profession, and is the cost function that gives the costs incurred by the parents to train their offspring for different professions

Equilibrium

Defining a Steady State

Characterizing Steady States

Two Profession Scenario Let there be only two professions – Skilled and Unskilled. For the Unskilled labour take the training cost to be zero. For Skilled labour assume that there is an exogenous training cost x, which is the units of the consumption good used in the training process. Let denote the fraction of population at any date that is skilled. Let f be a well-behaved production function satisfying INADA conditions. Then, where the subscripts denote appropriate partial derivatives

A fraction o of skilled people is said to be compatible with a steady state if and only if The LHS of the above equation represents the utility sacrifice of a skilled parent in educating its child. Denote it as The RHS of the above equation represents the utility sacrifice of an unskilled parent in educating its child. Denote it as The term in the middle is the present value benefit of all successive descendants being skilled rather than unskilled. Denote it as

Persistent Inequality (continued) Dilip Mookherjee Debraj Ray

Review H – Compact set of professions. Individuals indexed on [0, 1] as dynasties with fully altruistic preferences on descendants. Population The technology combines a production sector with an educational/training sector. Wage function of returns to profession -

Review Cost incurred by parent to train child in profession h – Technology is given by set T with elements of the form Firms and households solve for professions’ and consumption goods’ demands and supplies by maximizing profit and discounted utilities. Equilibrium is a collection which is obtained from this exercise along with market clearing conditions.

Review Steady State – Proposition 1 – There is no mobility across professions in steady states. Proposition 2 – occupying distinct professions in steady state (ie professions with different training costs) implies having different consumpitions and utilities.

Review Characterize steady states through two necessary and sufficient conditions. i)Profit maximisation – ii)No ‘one-shot deviation’ –

A Case of Two Professions Assume training cost to be exogenous. Two professions – skilled and unskilled. Training cost of skilled is x, 0 for unskilled. Proportion of skilled population is λ. Assume a well-behaved production function for consumption good.

A Case of Two Professions Compatibility with steady state iff – Utility sacrifice of skilled parent educating child - Utility sacrifice of unskilled parent educating child - Benefit if successors are skilled -

A Case of Two Professions

First part follows from continuity of the curves and concavity of utility function. Continuum of steady states, but may be disconnected. For second part, consider maximising –

A Continuum of Professions H = [0,1] We impose the restriction of a well-defined unit cost function for each profession. This requires assumption T.1: Well defined production function for profession h : Production function for consumption good :

A Continuum of Professions Thus, T is generated by production functions such thatand subject to T.1 implies the existence of a well defined unit cost function for training an ‘h’ professional: In competitive equilibrium, this unit cost will equal x(h).

A Continuum of Professions T.2 assumes :

A Continuum of Professions Claim: Range of x is [0,X]. There is function W, where w(h) = W(x(h)). Full support implies W is continuous.

A Continuum of Professions For an interior x: Hence, Claim proved.

A Continuum of Professions We need to prove that this is the unique steady state wage function.

A Continuum of Professions We need to prove that this is the unique steady state wage function.

A Continuum of Professions We need to prove that this is the unique steady state wage function.

A Continuum of Professions We need to prove that this is the unique steady state wage function.

A Continuum of Professions Examples for the previous result: A ‘Fixed-coefficient recursive technology: A Cobb-Douglas Technology

A Continuum of Professions Examples for the previous result: A Cobb-Douglas Technology

A Continuum of Professions

Summary and Research Directions Long-run inequality is inevitable in any steady state with occupational diversity. If indivisibilities in investment options are removed, we get a unique steady state, with population distributions, unlike when indivisibilities are present. Non-steady state dynamics, financial bequests, where countries are agents etc. are potential research areas.