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Feldman–Mahalanobis Model of Development Planning

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Abstract

This chapter develops the theory of Feldman and Mahalanobis how to allocate resources in the optimal ways to maximize the growth rate with a stable planned economy. While Feldman provides numerical methods, Mahalanobis provides a closed-form algebraic method to arrive at the same solution of the optimal allocation of investible funds.

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Fig. 5.1
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Fig. 5.5
Fig. 5.6

References

  • Araujo, R., and J. Teixeira. 2004. Structural Economic Dynamics: An Alternative Approach to North-South Models. Cambridge Journal of Economics 28 (5): 705–717.

    CrossRef  Google Scholar 

  • Basu, D.R., and A. Lazaridis. 1983. Stochastic Optimal Control by Pasedo Inverse. Review of Economics and Statistics LXV (2): 347–352.

    CrossRef  Google Scholar 

  • Basu, D., and V. Miroshnik. 2015. Dynamic Systems Modelling and Optimal Control. Basingstoke: Palgrave Macmillan.

    Google Scholar 

  • Bose, S. 1968. Optimum Growth and Investment Allocation. Review of Economic Studies 35 (4): 465–480.

    CrossRef  Google Scholar 

  • Bose, S. 1970. Optimal Growth in a Non-shiftable Capital Model. Econometrica 38 (1): 128–152.

    CrossRef  Google Scholar 

  • Dasgupta, P. 1969. On the Concept of Optimum Population. Review of Economic Studies 36 (3): 295–318.

    CrossRef  Google Scholar 

  • Domar, E. 1957. Essays in the Theory of Economic Growth. New York: Oxford University Press.

    Google Scholar 

  • Feldman, G.A. 1928. On the Theory of Growth Rates of National Income. Planovoe khozyaistvo.

    Google Scholar 

  • Feldman, G.A. 1929. An Analytical Method for Constructive Perspective Plans. Planovoe khozyaistvo.

    Google Scholar 

  • Karmakar, A. 2012. Development Panning and Policies Under Mahalanobis Stragy. International Journal of Business and Social Research 2 (2): 122–129.

    Google Scholar 

  • Kaushal, G. 1979. Economic History of India 1757–1966. New Delhi: Kalyani Publishers.

    Google Scholar 

  • Lazaridis, A. 2015. Dynamic Systems in Management Science: Design, Estimation and Control. Basingstoke: Palgrave Macmillan.

    CrossRef  Google Scholar 

  • Mahalanobis, P.C. 1952. Some Observations on the Process of Growth of National Income I. Sankhya XII: 307–312.

    Google Scholar 

  • Mahalanobis, P.C. 1953. Some Observations on the Process of Growth of National Income II. Sankhya XIV: 3–62.

    Google Scholar 

  • Mahalanobis, P.C. 1955. The Approach of Operations Research to Planning. Sankhya XVI: 63–89.

    Google Scholar 

  • Mahalanobis, P.C. 1956. Draft Plan-Frame for the Second Five-Year Plan. Sankhya 16: 3–62.

    Google Scholar 

  • McIntosh, J. 1975. Growth and Dualism in Less Developed Countries. Review of Economic Studies 42 (3): 421–433.

    CrossRef  Google Scholar 

  • Mellor, J.W. 1976. The New Economics of Growth: A Strategy for India and the Developing World. Ithaca: Cornell University Press.

    Google Scholar 

  • Rudra, A. 1975. Indian Plan Models. Bombay: Allied Publisher.

    Google Scholar 

  • Rudra, A. 1992. Political Economy of Indian Agriculture. Calcutta: KP Bagchi.

    Google Scholar 

  • Spulber, N. 1964. Foundations of Soviet Strategy for Economic Growth. Bloomington: Indiana University Press.

    Google Scholar 

  • Taylor, L. 1979. Macro Models for Developing Countries. New York: McGraw-Hill.

    Google Scholar 

  • Weitzman, M. 1971. Shiftable Versus Non-shiftable Capital: A Synthesis. Econometrica 39 (3): 856–863.

    CrossRef  Google Scholar 

  • Zarembka, P. 1970. Marketable Surplus and Growth in the Dual Economy. Journal of Economic Theory 2 (2): 107–121.

    CrossRef  Google Scholar 

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Appendices

Appendix A

Linearization

Suppose the production function is

$$X_{i} = \exp (at) \, K_{t}^{a} L_{t}^{b} \quad \left( {a + b \ge 1} \right)$$

We can write the above equation as

$$\dot{X}_{t} /X_{t} = a\left( {\dot{K}_{t} /K_{t} } \right) + b\left( {\dot{L}_{t} /L_{t} } \right)$$

where

$$\dot{X}_{t} = (\text{d}X/\text{d}T)$$

Linearizing using Taylor series expansion we get

$$\dot{X}_{t} = \lambda_{0} + \lambda_{1} X_{t} + \lambda_{2} \dot{K}_{t} + \lambda_{3} K_{t} + \lambda_{4} \dot{L}_{t} + \lambda_{5} L_{t}$$

Or in discrete time formulation

$$X_{t} = \frac{1}{{1 - \lambda_{1} }}\left[ {X_{t - 1} + \left( {\lambda_{2} + \lambda_{3} } \right)K_{t} - \lambda_{2} K_{t - 1} + \left( {\lambda_{4} + \lambda_{5} } \right)L_{t} - \lambda_{4} L_{t - 1} + \lambda_{0} } \right]$$

where

$$\lambda_{1} = \frac{{\partial \dot{X}}}{\partial X},\lambda_{2} = \frac{{\partial \dot{X}}}{\partial K},\lambda_{3} = \frac{{\partial \dot{X}}}{\partial K},\lambda_{4} = \frac{{\partial \dot{X}}}{\partial L},\lambda_{5} = \frac{{\partial \dot{X}}}{\partial L},$$
$$\lambda_{0} = \left[ {a \, \left( {\dot{K}/K)X + b \, (\dot{L}/L)X)} \right)} \right]_{t - 1}$$

For the purpose of linearization, we evaluate the production function term by term (i.e. to determine the parameters X) at the points t and \(t - 1\). In the optimal control set-up every time we linearize the system, we have to change A, B and D matrices in the system equation.

Appendix B

Stochastic Simulation or the VAR Creation

The addition of the stochastically simulated disturbance term does not change the system equations significantly, but it would change the time path of the state and control variables and the value of the cost functional. The €(t,j) vector comes from the estimation of the model within the same period. The generated errors should also be such as to satisfy a Gaussian process of zero mean and with a given positive semi-definite covariance matrix.

Appendix C

Experiment with Lower Level of Desired Paths

In this experiment, we have followed all the assumptions for Experiment 1 but have lowered the desired rate of growth for \(aY\) and \(mY\) from 6% to 3–5% to see the effect of that on the optimum rate of investment for the two sectors. The result is given in Table 5.2.

Table 5.2 Actual and optimum (stochastic) path for \(mI/I\) (in percentage)

We can see that the ratio of industrial investment to the total investment is not very different from the actual ratio. This suggests that lowering of the desired goal for the economy would not affect the intersectoral allocation patterns given all other variables. In almost all the cases, we have seen the optimum allocation asks us to put more emphasis on the industrial sector (as the ratio given above implies).

Appendix D

Notations Used

  • mY = industrial sector output

  • aY = agricultural sector output

  • aI = investment in the agricultural sector

  • mI = investment in the industrial sector

  • aK = gross capital stock in the agricultural sector

  • mK = gross capital stock in the industrial sector

  • aL = labour force in the agricultural sector

  • mL = labour force in the industrial sector

  • AS = annual acreage sown in the agricultural sector

  • IMF = import of foodgrains from abroad

  • MS = marketable surplus of foodgrains

  • MD = demand for the marketable surplus of foodgrains

  • P = intersectoral terms of trade (price of agricultural goods in terms of industrial goods)

  • W = annual wage rate in the industrial sector

  • A = annual acreage sown in the agricultural sector labour force in the agricultural sector

  • t = time-trend

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Basu, D., Miroshnik, V. (2020). Feldman–Mahalanobis Model of Development Planning. In: Imperialism and Capitalism, Volume II. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-54891-9_5

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  • DOI: https://doi.org/10.1007/978-3-030-54891-9_5

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