Unit 3: Theories of Economic Development II: Migration, Surplus Labour, and Development Models

1. Migration and Economic Development

Conceptual Overview

Migration in developing economies refers to the physical movement of labor from rural agrarian areas to urban industrial centers. In classical and modern development economics, migration is viewed not merely as a spatial relocation of individuals, but as an essential component of structural transformation—the process by which an agrarian economy transitions into an industrial and service-oriented economy.

Role in Economic Growth

During early stages of development, agricultural productivity is relatively low, while industrial capital offers higher marginal productivity. Labor reallocation serves key economic functions:

• Resource Reallocation: Transfers underutilized rural labor to productive urban manufacturing sectors.
• Capital Accumulation: Provides cheap labor to urban firms, generating profits that are reinvested into capital goods.
• Remittance Flows: Urban workers send income back to rural families, enhancing consumption, health, and rural enterprise capital.
• Knowledge and Skill Transfer: Returning migrants bring technical skills and modern work habits back to rural areas.

Economic Consequences of Rural-Urban Migration

2. Surplus Labour and Disguised Unemployment

Definitions and Fundamental Concepts

Surplus Labour: A situation in underdeveloped agrarian economies where the quantity of labor available exceeds the labor required for maximum agricultural production, given existing technology and institutional arrangements.

Disguised Unemployment: A specific form of surplus labor where workers appear to be fully employed on family farms or smallholdings, but their withdrawal from the workforce produces zero change in total output.

Mathematical Formulation

Let aggregate agricultural output be represented by the production function:

Y_A = f(L_A, K, T)

Where Y_A is agricultural output, L_A is agricultural labor force, K is capital, and T is land availability. Disguised unemployment occurs when:

MPL_A = ∂Y_A / ∂L_A = 0

In this state, the Marginal Productivity of Labour (MPL_A) is zero or approaches zero. While total agricultural output (TP_A) is at its maximum, average agricultural product (APL_A) remains positive:

APL_A = Y_A / L_A > 0

Distinction Between Concepts

Causes of Disguised Unemployment

• High Population Growth: Rapid population expansion without a matching increase in cultivated land area.
• Lack of Non-Farm Opportunities: Insufficient industrial and service sector jobs to absorb rural workforce growth.
• Institutional Family Farm Structure: Work and income are shared among family members regardless of individual productivity.
• Static Agricultural Technology: Reliance on traditional labor-intensive techniques without modern capital equipment.

Exam Notes and Common Pitfalls

Important Note: Disguised unemployment does not mean that workers do not work; rather, it means that work is spread out over more workers than necessary. If surplus labor is withdrawn, the remaining workers increase their work effort per person, maintaining total output constant.

Common Mistake: Confusing zero marginal product of labor (MPL = 0) with zero average product (APL = 0). Family farm members receive a wage equivalent to the average product (subsistence wage), even though their marginal product is zero.

3. Lewis Theory of Unlimited Supply of Labour

Background and Core Premise

Formulated by Nobel Laureate W. Arthur Lewis in 1954, the Dual-Sector Model explains the process of economic growth in developing countries with dual economic structures. Lewis posited that many underdeveloped nations possess an unlimited supply of labour available at a fixed subsistence wage.

Structural Division of the Economy

Key Assumptions

• The economy has two distinct sectors: a rural subsistence sector and an urban capitalist sector.
• Surplus labor exists in the subsistence sector where MPL_A = 0.
• Supply of labor to the urban capitalist sector is infinitely elastic at a constant wage rate.
• Capitalist sector wage (w_m) is set above the subsistence wage (w_s), typically by a 30% to 50% margin (urban wage premium) to induce voluntary migration.
• Capitalists re-invest 100% of their profits into capital expansion.
• Technical progress in the industrial sector is constant or labor-augmenting.

Mechanism of Economic Growth

1. Initial Labor Transfer: Capitalist firms hire rural surplus labor at the institutional wage rate w_m.
2. Profit Generation: Since industrial marginal productivity (MPL_M) exceeds the institutional wage (w_m), capitalists generate a profit surplus.
3. Reinvestment and Capital Accumulation: Capitalists reinvest their surplus into expanding industrial capital stock (K₁ → K₂ → K₃).
4. Demand Shift: Capital expansion increases the marginal productivity curve of labor (MPL₁ → MPL₂ → MPL₃), shifting the demand curve for labor outward.
5. Continued Expansion: More surplus labor is absorbed from the agricultural sector at the constant wage w_m without increasing labor costs.
6. Lewis Turning Point: The process continues until all surplus rural labor is absorbed. Beyond this point, the labor supply curve becomes upward-sloping, and real wages begin to rise.

Mathematical Representation

In the capitalist sector, employment is determined where marginal product equals real wage:

MPL_M = ∂Y_M / ∂L_M = w_m

Total Capitalist Surplus (Profit) = Total Industrial Output - Total Wage Bill:

Profit = Y_M - (w_m × L_M)

Investment of this surplus increases the capital stock:

ΔK = Profit

This leads to higher marginal productivity of labor in subsequent periods.

Limitations and Criticisms

• Reinvestment Fallacy: Capitalists may invest in labor-saving automated technology rather than labor-intensive machinery, reducing labor absorption capacity.
• Capital Flight: Profits may be transferred abroad rather than reinvested locally.
• Rising Urban Wages: Industrial wages may rise prior to the exhaustion of surplus labor due to labor union pressure or minimum wage legislation.
• Agricultural Neglect: The model assumes zero output loss in agriculture when labor leaves, ignoring potential food supply shortfalls.

4. Ranis-Fei Model of Economic Growth

Overview

Developed by Gustav Ranis and John Fei in 1961, the Ranis-Fei Model formalizes and extends Arthur Lewis’s theory. It integrates agricultural development explicitly, emphasizing that balanced growth between agriculture and industry is necessary to sustain economic expansion.

The Three Stages of Agricultural Labour Absorption

1. Stage 1: Redundant Labour Phase (Redundant Labour Sector)
   • Condition: MPL_A = 0.
   • Description: True disguised unemployment exists. Labor can be transferred to industry without reducing agricultural output.
   • Food Supply: Total agricultural output (TP_A) remains unchanged. Food supply per remaining worker increases, generating agricultural surplus.
   • Industrial Supply Curve: Perfectly elastic labor supply.
2. Stage 2: Disguised Unemployment / Shortage Phase
   • Condition: 0 < MPL_A < Institutional Wage (w_s).
   • Description: Labor is productive, but its marginal contribution is less than the institutional subsistence wage it consumes.
   • Economic Impact: Withdrawing labor reduces total agricultural output (TP_A decreases). An agricultural shortage emerges, causing food prices to rise relative to industrial goods.
   • Terms of Trade Effect: Industrial real wages must rise in terms of manufactured goods to cover increased food costs. The labor supply curve slopes upward.
   • Shortage Point: The transition mark between Stage 1 and Stage 2.
3. Stage 3: Commercialization Phase (Commercialized Agriculture)
   • Condition: MPL_A ≥ Institutional Wage (w_s).
   • Description: Agricultural sector operates on purely market-driven capitalistic principles. Dualism disappears.
   • Commercialization Point: Reached at the end of Stage 2. Labor is paid its marginal product in both sectors (MPL_A = MPL_M).
   • Industrial Supply Curve: Inelastic labor supply; classical growth dynamics take over.

Key Equations and Turning Points

Policy Implications of Ranis-Fei Model

• Balanced Growth Requirement: Agricultural productivity growth must accompany industrial expansion to prevent terms of trade from shifting against industry.
• Agricultural Investment: Innovation, fertilizers, and rural infrastructure are essential to raise MPL_A during structural transition.
• Avoiding Development Bottlenecks: Without rural technological progress, early food shortages in Stage 2 can stall industrial growth before full development is achieved.

5. Harris-Todaro Theory of Rural-Urban Migration

Background and Central Paradox

Formulated by John Harris and Michael Todaro in 1970, this model explains a persistent economic paradox observed in developing countries: high rates of rural-urban migration in the presence of massive urban unemployment.

Classical models (like Lewis) predicted migration would stop if urban unemployment increased. The Harris-Todaro model explains why migration rational choices persist under these conditions.

Key Assumptions

• Migration is an economically rational decision made on the basis of expected rather than actual current income differentials.
• The urban modern sector wage (W_u) is fixed above market-clearing levels by institutions (minimum wage laws, collective bargaining, government regulations).
• The rural agricultural sector wage (W_r) is flexible and equals the rural marginal product of labor (MPL_A).
• Urban job selection follows a probabilistic mechanism based on the ratio of urban jobs to job seekers.

Mathematical Formulation

The expected urban income E(W_u) is defined as:

E(W_u) = P_e × W_u

Where:

• W_u: Urban modern sector wage rate.
• P_e: Probability of securing an urban job.

The probability of employment (P_e) is calculated as the proportion of modern sector jobs available relative to the urban labor force:

P_e = L_u / E_u

Where L_u is total urban employment (jobs available) and E_u is the total urban labor force (employed + unemployed seekers).

Migration Equilibrium

Rural-to-urban migration continues until expected urban income equals actual rural wage:

W_r = E(W_u) = (L_u / E_u) × W_u

Rearranging the equation yields the equilibrium urban labor ratio:

L_u / E_u = W_r / W_u

Because W_u > W_r, the probability P_e must be less than 1 (L_u < E_u). Consequently, equilibrium requires the existence of urban unemployment (E_u - L_u > 0).

Numerical Example

Consider an economy with the following parameters:

• Rural Wage (W_r) = $100 / month
• Urban Wage (W_u) = $250 / month
• Urban employment jobs (L_u) = 1,000

At equilibrium:

W_r = (L_u / E_u) × W_u
100 = (1000 / E_u) × 250
100 × E_u = 250,000
E_u = 2,500

Out of 2,500 urban job seekers, 1,000 are employed while 1,500 remain unemployed. The equilibrium unemployment rate in the urban sector is:

Unemployment Rate = [(2500 - 1000) / 2500] × 100 = 60%

The Todaro Paradox

Todaro Paradox: Policies designed to reduce urban unemployment by creating modern urban jobs can paradoxically increase total urban unemployment.

Explanation: Creating ΔL_u new urban jobs increases the job probability P_e. This increases expected urban income E(W_u), inducing a larger number of rural migrants (ΔE_u > ΔL_u) to move to cities, thereby expanding the absolute pool of unemployed workers.

Policy Implications of Harris-Todaro Model

• Dismantling Urban Bias: Reduce artificial wage distortion policies that push urban wages far above productivity levels.
• Rural Development Strategy: Increase rural income levels (W_r) directly via agricultural investments to reduce expected income gaps.
• Integrated Employment Creation: Urban job creation alone will fail unless accompanied by rural development programs.
• Wage Subsidies: Provide subsidies to urban industrial employers rather than artificially fixing minimum wages.

6. Comparative Analysis of Development Models