Regional Allocation of Investment as a Hierarchical Optimization Problem

The problem of investment allocation between regions has been studied in the sixties using the techniques of modern control theory [e.g., Rahman (1963), Intriligator (1964), Takayama (1974)]. All these studies used constant capital-output ratio for the production function and a finite horizon optimization problem. Pitchford (1977) discussed extension to general production function and infinite planning horizon. The solutions discussed in Takayama (1974) under various criteria functionals were 'bang-bang' in character, with the possibility of one switch. This strategy is somewhat academic, r-articularly in the context of planning in an underdeveloped country where d',lal economy prevails. If the purpose of the central planning board is to maximize the percapita consumption over the whole planning period, it may quite well be optimal to invest all the savings in the advanced sector of the economy. The recent debate on development planning convincingly shows the fallacy of such a policy. The work of Todaro (1969) is particularly illustrative in this context. Myrdal (1968) and Singer (1975) advocated different type of criteria which would reflect some kind of transfer of actual consumption from the advanced to the traditional sector of the economy. The transfer of too much of the development fund to the traditional sector is, however, not politically possible when one realizes that most of this capital comes out of the savings incurred in the advanced sector of the economy. To introduce this aspect to the problem, we do not consider the savings rate of the advanced sector fixed, as assumed in Takayama (1974). We reforrr.,ulate the problem where the advanced region has the flexibility to choose its savings strategy once it knows the allocation decision