Dynamic Programming in a Multi-Product Model of Economic Development

Abstract

CONSIDER AN underdeveloped economy with a public sector directed by a planning commission and a private sector operating through the market mechanism. The public sector produces (a) n consumer goods labeled 1, -.., n with the help of n different types of imported machines labeled 1, ..., n-type i machine being used in type i consumer good industry, (b) m types of domestic machines labeled n + 1, ... , n + m with the help of m types of imported machines labeled n + 1, ... , n + m -type i imported machine being used in type i domestic machine industry and (c) m consumer goods labeled n + 1, ..., n + m with the help of the domestic machines -type i domestic machine being used in type i consumer good industry. The public sector imports I consumer goods, labeled n ? m + 1, ***, n + m + I and exports a portion of the output of each domestic consumer good. Domestic machines are not exported. It will be understood that domestic machines and domestic consumer goods refer to the goods produced in the public sector. We assume perfect competition in international trade so that the public sector can buy or sell any amount of the relevant goods at market prices, which are assumed to be known throughout the planning horizon. We assume away joint production. The production of any commodity is constrained only by the available stock of the appropriate machine; all other inputs, labor and raw materials, are supplied by the private sector and are too abundant, relative to capital, to put any effective constraint on production. The picture depicted above will resemble an underdeveloped economy which has gone through several initial stages of development. We will define a linear social welfare function for a planning horizon of T periods and compute optimal production, consumption, inventory, export and import policies. If the planning horizon is indefinitely large, then a special case of the model will exhibit the switching policy of capital accumulation described in Rahman [4] and Dorfman [2]. The model can also be interpreted as a theory of a multi-product firm. From this point of view, we will show how monetary and fiscal