The Harris Todaro model is a model from the range of the political economy, which in the year 1970 of John R. Harris and Michael P. Todaro in the article: "“Migration, Unemployment and development: A Two second gate analysis was published"”. The presented model tries to justify migration between two sectors, the authors do intentionally without it from full employment and flexible wages to proceed. In the article mentioned besides the import of so-called Shadow Prices and the restrictive treatment are discussed of migration.

Structure of the model

The model differentiates between a permanent urban and a rural sector, whereby in first industrial goods are manufactured, in latter agricultural product. Further in the rural sector from workers proceeds, which either completely for the production of the agricultural products one uses, or into the urban sector migrates. The individual individual of this workers makes thus the decision whether the migration is worthwhile itself into the city, due to a increased income. Thus it is accepted that as soon as the wages of the urban sector and the rural sector are balanced (balance condition), no further migration will take place. Migration is seen thereby as a kind "“arbitrage movement"”, which takes place only until an equilibrium of the wages was reached. The model assumes that that the workers of the city do not leave the same, in order to work on the country. The moreover a minimum wage is accepted, which results from the portion of the persons employed to the workers in the city, multiplied by the manufactured goods. In the process of the original text the minimum wage is defined also over the agrarian goods, what does not change anything in the result regarding developing unemployment in the equilibrium.

Formalism

f' = marginal product of the industrialism (production function: X_M = f (N_M, K_M), whereby K_M = fixed)

K_M = capital (fixed) in the agrarian sector

K_M = capital (fixed) in the industrial sector

L = country (fixed)

N_A = size of the workers on the country (no unemployment)

N_M = number of persons employed in the industrial sector

N_U = size of the workers in the city

P = price of an agricultural product (expressed as portion of the output of the agricultural products of the output of the industrial goods)

q' = marginal product of the agrarian work (production function: X_A = f (N_A, L, K_M), whereby L, K_M = fixed)

W_A = real wages in agrarian sector (country)

W_M = real wages in the industrial sector (city)

W_ {U} ^ {e} = expected real wages in the urban sector

Mathematical background (shortened)

To consult recommended for a complete and correct representation of the model of Harris and Todaro the reader the original article.

Real wages in the agar sector (country): W_A = P * q'

Real wages of the industrial sector (city): W_M = f'

(For reasons of the profit maximization real wages the marginal product are equated by industrialism)

Expected wages of the urban sector: W_ {U} ^ {e} = \ frac {(W_M * N_M)}{N_U}

(Here W_M = fixed describes! the minimum wage, N_M the number of persons employed, N_U the whole of the urban workers)

The equilibrium is described as follows: W_A = W_ {U} ^ {e}, from this follows by replacements: N_U = \ psi (\ frac {W_M N_M} {N_U} - P*q')

On the right side within that clammy one is in this formula expected real wages in the urban sector, less real wages in the rural sector (and/or [[marginal product of the work in the agrarian sector). All urban workers are thus described as derivative over the time to certain fraction \ a psi over this wage difference.

Results of the model

A main statement of the model is the fact that migration will further take place as long as expects wages in the urban sector, the wages in the rural sector exceeds. More exactly: If the wages in the urban sector correct, for unemployment, which exceeds marginal product expressed by work in the agrarian sector, in industrial goods, migration takes place. A further statement of this model refers to the implicitly accepted minimum wage and concludes that a fixed minimum wage leads over-half the level, which the free market would reach to an equilibrium with unemployment.

Literature

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

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