Harris-Todaro model

The Harris-Todaro model is a model from the field of economics , which was published in 1970 by John R. Harris and Michael P. Todaro in the article: 'Migration, Unemployment and Development: A Two Sector Analysis'. The model presented tries to justify migration between two sectors, but the authors deliberately refrain from assuming full employment and flexible wages. The article also discusses the import of so-called shadow prices and the restrictive treatment of migration.

Structure of the model

The model differentiates between a permanent urban and a rural sector, with industrial goods in the former and agricultural products in the latter. Furthermore, in the rural sector it is assumed that the workforce is either fully employed in the production of agricultural products or that migrates to the urban sector. It is the individual of this workforce that makes the decision as to whether migration to the city is worthwhile on the basis of an increased income. This assumes that once the expected wages of the urban and rural sectors are balanced (equilibrium condition), no further migration will take place. Migration is seen as a kind of " arbitrage movement" that only takes place until an equilibrium of expected wages has been achieved. The decisive factor here is the expected income, i.e. the income taking into account a certain probability of unemployment in the city. In this way, the model can explain why people in cities migrate from the countryside to the city even when there is high unemployment in the city. The model assumes that the urban workers do not leave the city to work in the countryside. Furthermore, a minimum wage is assumed, which results from the proportion of employees to the workforce in the city, multiplied by the goods produced. In the course of the original text, the minimum wage is also defined in terms of agricultural goods, which does not change anything in terms of the emergence of unemployment in equilibrium.

formalism

${\displaystyle f'}$= Marginal product of industrial work (production function ) ${\displaystyle X_{\mathrm {M} }=f(N_{\mathrm {M} },K_{\mathrm {M} }),{\text{wobei}}\ K_{\mathrm {M} }={\text{fix}}}$

${\displaystyle K_{\mathrm {A} }}$ = Capital (fixed) in the agricultural sector

${\displaystyle K_{\mathrm {M} }}$ = Capital (fixed) in the industrial sector

${\displaystyle L}$ = Country (fix)

${\displaystyle N_{\mathrm {A} }}$ = Size of the workforce in rural areas (no unemployment)

${\displaystyle N_{\mathrm {M} }}$ = Number of employees in the industrial sector

${\displaystyle N_{\mathrm {U} }}$ = Size of the workforce in the city

${\displaystyle P}$ = Price of an agricultural product (expressed as the share of the output of the agricultural products in the output of the industrial goods)

${\displaystyle q'}$= Marginal product of the agricultural work (production function ) ${\displaystyle X_{\mathrm {A} }=f(N_{\mathrm {A} },L,K_{\mathrm {M} }),{\text{wobei}}\ L,K_{\mathrm {M} }={\text{fix}}}$

${\displaystyle W_{\mathrm {A} }}$ = Real wage in the agricultural sector (country)

${\displaystyle W_{\mathrm {M} }}$ = Real wage in the industrial sector (city)

${\displaystyle W_{\mathrm {U} }^{\mathrm {e} }}$ = expected real wage in the urban sector

Mathematical background (abbreviated)

For a complete and accurate representation of the Harris and Todaro model, the reader is advised to consult the original article.

Real wages in the agricultural sector (country): ${\displaystyle W_{\mathrm {A} }=P\cdot q'}$

Real wages of the industrial sector (city): ${\displaystyle W_{\mathrm {M} }=f'}$

(For reasons of profit maximization, the real wage is equated with the marginal product of industrial work)

Expected wage of the urban sector: ${\displaystyle W_{\mathrm {U} }^{\mathrm {e} }={\frac {W_{\mathrm {M} }\cdot N_{\mathrm {M} }}{N_{\mathrm {U} }}}}$

(Here describes the minimum wage, the number of employees, the totality of the urban workforce) ${\displaystyle W_{\mathrm {M} }={\text{fix!}}}$ ${\displaystyle N_{\mathrm {M} }}$ ${\displaystyle N_{\mathrm {U} }}$

The equilibrium is described as follows:, it follows by substitutions: ${\displaystyle W_{\mathrm {A} }=W_{\mathrm {U} }^{e}}$ ${\displaystyle N_{\mathrm {U} }=\psi \left({\frac {W_{\mathrm {M} }N_{\mathrm {M} }}{N_{\mathrm {U} }}}-P\cdot q'\right)}$

On the right-hand side within the brackets in this formula is the expected real wage in the urban sector, minus the real wage in the rural sector (or the marginal product of labor in the agricultural sector). The entire urban workforce is thus described as a derivative over time to a certain fraction of this wage difference. ${\displaystyle \psi }$

Results of the model

A key message of the model is that migration will continue as long as the expected wage in the urban sector exceeds the wage in the rural sector. More precisely, when wages in the urban sector, corrected for unemployment , exceed the marginal product of labor in the agricultural sector, expressed in terms of manufactured goods, migration takes place. Another statement of this model relates to the implicitly assumed minimum wage and concludes that a fixed minimum wage above the level that the free market would reach leads to an equilibrium with unemployment.

literature

• J. Harris and M. Todaro (1970). Migration, Unemployment & Development: A Two-Sector Analysis. American Economic Review, March 1970; 60 (1): 126-42.