Harris–Todaro model

The Harris - Todaro model is a model in the field of economics, which in 1970 by John R. Harris and Michael P. Todaro in the article was published: ' A Two Sector Analysis, Unemployment and Development Migration '. The proposed model attempts to explain migration between two sectors, while the authors do not intentionally it assumed full employment and flexible wages. In the above article the importation of so-called Shadow Prices and the restrictive treatment of migration will be discussed also.

Composition of the model

The model distinguishes a permanent urban and rural sector one, which are produced in the former industrial goods, agricultural products in the latter. Furthermore, it is assumed in the rural sector of a workforce that is either used completely for the production of agricultural products, or migrated to the urban sector. The single individual of these workers thus makes the decision whether the migration is worthwhile in the city, due to increased income. Thus, it is assumed that once the reward of the urban sector and the rural sector are balanced ( equilibrium condition ), will take place no more migration. Migration is therefore seen as a kind of " arbitrage " movement, which takes place only as long as until an equilibrium was reached in wages. The model assumes that the workers of the city of the same does not leave to work on the land. Furthermore, it is assumed a minimum wage, which is derived from the proportion of workers to workers in the city, multiplied by the manufactured goods. In the course of the original text, the minimum wage is also defined on agricultural goods, which does not change the result in terms of the emergence of unemployment in equilibrium.

Formalism

= Marginal product of industrial work ( production function: )

= Capital (fixed) in the agricultural sector

= Capital (fixed) in the industrial sector

= Country (fixed)

= Size of the labor force in the country ( no unemployment )

= Number of employees in the industrial sector

= Size of the labor force in the city

= Price of an agricultural product ( expressed as a proportion of the output of agricultural products at the output of industrial goods )

= Marginal product of agricultural labor ( production function: )

= Real wage in the agricultural sector (country )

= Real wage in the industrial sector (City)

= Expected real wage in the urban sector

Mathematical Background ( abridged)

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

Real wages in the agricultural sector (agriculture ):

Real wages in the industrial sector (City):

( For the sake of profit maximization is the real wage equal to the marginal product of industrial work )

Expected wage of the urban sector:

( This describes the minimum wage, the number of employees, the totality of the urban workforce )

The equilibrium is described as follows:, it follows by substitution:

On the right side inside the brackets can be found in this formula, 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 workers is thus described as a derivative of the time to a certain fraction over this wage difference.

Results of the model

A main message of the model is that migration will continue to take place as long as the expected wage in the urban sector, the wage in the rural sector exceeds. More precisely: If the wage in the urban sector, adjusted for unemployment, the marginal product of labor in the agricultural sector, in terms of industrial goods exceeds, migration takes place. Another statement of this model refers to the implicitly assumed minimum wage and concludes that a fixed minimum wage above the level that would achieve the free market, leads to an equilibrium with unemployment.