Abstract
Keeping the characteristics of dualistic agriculture in view, a model is developed by deriving the decision rules that the family and capitalist farms will adopt about the use of inputs and allocation of wealth on the basis of certain well-defined maximising objectives.
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Notes
- 1.
Alternatively, one can assume that the labour force is a certain fixed proportion 0 < α < 1 of \( {\overline{L}}_1(t). \)
- 2.
We have already mentioned it before (cf. p. 4n), and we repeat it here, that for our analysis and final conclusions it is not essential that saving of the family farm be zero and the amount of its consumption loan positive. What we need is a situation where, because of the existing distribution of income, the family farm cannot save enough and it has to take some loan from the capitalist farm, be it consumption loan or renting of capital (in other words, the credit market should be allowed to remain in the picture). Given such an upperbound on saving on the part of the family farm properly defined, it can be shown just by using the property of imperfection of the credit market and the stated objectives of the farms that, under very plausible conditions, the system will evolve over time in such a way that after a certain period of time the saving of the family farm will in fact drop to a negligible amount and that it will also have to take consumption loan. And, the present analysis applies from then on. Therefore, the assumptions of zero saving and positive consumption loan on the part of the family farm are not analytically essential.
- 3.
The second-order Legendre condition is satisfied by the concavity of utility function.
- 4.
For a discussion of the Euler conditions in the discrete-time case, see P.A. Samuelson, “A Turnpike Refutation of the golden Rule in a Welfare-Maximising Many-Year Plan” in (R.C. Metron ed.) The Collected Scientific Papers of Paul A. Samuelson, Vol. 3, pp. 108–110.
- 5.
For similar reason \( e{}_{\psi, {y}_1}{} \) will also dominate eψ, w since wage is supposed to be received at the end of the period.
- 6.
See, Bhagwati , J. and Chakravarty , S. “Contributions to Indian Economic Analysis: A Survey,” American Economy Review, 59, No. 2 Suppl. (September 1969); Sen , Amartya K.: “Peasants and Dualism with or without Surplus Labour,” Journal of Political Economy, October 1966.
- 7.
See, Bardhan , P.K., Loc. cit. pp. 1379–1381. For empirical evidence in the Indian context, see Visaria, P., “The Farmers’ Preference for Work on Family Farms,” in Report of the Committee of Experts on Unemployment Estimates, New Delhi, Govt. of India, 1970.
- 8.
There is an alternative explanation of the wage gap, due to Lewis (cf. his “Economic Development with Unlimited Supplies of Labour”. Manchester School of Economics and Social Studies, May 1954), which suggests that the peasant leaving his family to work outside loses his income from the farm, equal to the average product per person, and the wage rate outside must compensate for this. This explanation can also be accommodated in our analytical framework. Note that for this argument to be valid, it is necessary to assume that the outgoing peasant cannot rent out or sell his share in the land held by the joint family, that the family refuses to subsidise him with remittances, and that he does not remit back his wages. What all this means is that when the peasant goes out in this way, he, in effect, ceases to be a member of the family. To capture this situation, therefore, the wage term in the expression of net income of the family should be dropped, and then the wage rate of the outgoing peasant indeed becomes equal to the average net income of the family farm. It should be emphasised, however, that this explanation of the wage gap, based as it is on a particular kind of relationship between the outgoing peasant and the family, is more appropriate for the rural-urban migration than for the allocation of family labour between its own farm and the capitalist farm within agriculture. In this context see also Stiglitz , Joseph: “Rural-Urban Migration, Surplus Labour and the Relationship between Urban and Rural Wages,” East African Economic Review, December 1969, and “Wage Determination and Unemployment in L.D.C.’s,” The Quarterly Journal of Economics, May 1974.
- 9.
The second-order conditions are again taken care of by the concavity of U.
- 10.
Equation (3.25) can be regarded as the analogue of the Ramsey rule for the problem of the capitalist farm.
- 11.
This special situation is likely to arise particularly in the event of some unpredictable needs in consumption or production, and then the family farm can indeed find itself placed in a vulnerable position.
- 12.
The process cannot go beyond this point, because it is to the obvious interest of the capitalist farm to keep the family farmer alive in order to get the supply of labour.
- 13.
See Gelfand, I.M. and Fomin, S.V., Calculus of Variations, Prentice-Hall (1963), pp. 18–19.
- 14.
As pointed out at the end of Chapter 2, most of the decision rules of the family and the capitalist farms as well as the signs of the time derivations of the parameters could have been derived from a simpler specification of the objective, where both the farms are trying to maximise their respective net income (i.e., profit) in any period with an additional intertemporal requirement that this net income of any period should not fall below that of the last period. In the case of the family farm, for example, the maximisation of y1 subject to (3.5) with a given value of c1 yields the decision rules with respect to the use of L1 and K1 which are the same as (3.8) and (3.9). Similarly, for the capitalist farm, the maximisation of y2 subject to (3.7) with a given value of A2 gives the decision rules with respect to the use of L2 and the allocation of A2 between M and \( {\overline{P}}_k{K}_2 \) which are again the same as (3.20) and (3.23). The only problem about this kind of specification of the objective function, however, is connected with the derivation of the demand function for \( P{C}_1^l \) Consumption loan and A2. The question of the demand function for \( P{C}_1^l \) can still be settled at least in our case, by specifying the level of per head consumption, c1, to some predetermined minimum level, although that is not always the best way of explaining the consumption decision. But the problem is more serious with respect to the determination of the capitalist farm’s decision on A2. Furthermore it needs to be written that, with an open-ended specification of the intertemporal objective, such as dy2/dt ≥ 0 the decision on A also gets characterised by inequality and thus remains somewhat ill defined. And, to dodge the issue by saying that A2 is a certain fixed proportion of, say, y2 is not really explaining an important dimension of the choice problem of the capitalist farm with respect to A2. This choice problem can be analysed only in terms of the type of specification of the objective function such as we have been working with.
References
Bhagwati, J., & Chakravarty, S. (1969). Contribution to Indian Economic Analysis. American Economic Review, 59, 1–73.
Gelfand, I. M., & Fomin, S. V. (1963). Calculus of Variations (pp. 18–19). New Jersey: Prentice-Hall.
Lewis, A. (1954). Economic Development with Unlimited Supplies of Labour. Manchester School of Economics and Social Studies, 22, 139–191.
Ramsey, F. (1928). A Mathematical Theory of Saving. Economic Journal, 38(152), 543–559.
Samuelson, P. A. A Turnpike Refutation of the Golden Rule of Welfare-Maximising Many-Year Plan. In R. C. Metron (Ed.), The Collected Scientific Papers of Paul A. Samuelson (Vol. 3, pp. 108–110). Cambridge, MA: MIT Press.
Sen, A. K. (1966). Peasants and Dualism with or Without Surplus Labour. Journal of Political Economy, 74, 425–450.
Stiglitz, J. E. (1969). Rural-Urban Migration, Surplus Labour and Relationship Between Urban and Rural Wages. East African Economic Review, 12, 58–67.
Stiglitz, J. E. (1974). Wage Determination and Unemployment in L.D.C.s. Quarterly Journal of Economics, 88, 194–227.
Visaria, P. (1970). The Farmers, Preference for Work on Family Farms. Report of the Committee of Experts on Unemployment Estimates, Government of India.
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Dasgupta, A.K. (2018). The Model. In: Income Distribution, Market Imperfections and Capital Accumulation in a Developing Economy. Palgrave Pivot, Singapore. https://doi.org/10.1007/978-981-13-1633-3_3
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