Mr. Rahman is concerned with planning investment in an underdeveloped country so as to maintain a reasonable balance among the rates of progress in different regions of the country. The importance of this problem does not require discussion. But, as Rahman notes, it is strongly analogous to another, more pervasive problem, the allocation of investment among different industrial sectors of an underdeveloped country so as to attain a maximum over-all rate of growth in a specified planning period. In this version of the problem the rates of progress of the different sectors need not be kept in balance if doing so interferes with the basic goal, namely attaining maximal wealth at the end of the planning period. It is therefore somewhat simpler than the regional allocation problem and since it has some interesting implications of its own, it will be discussed in this note. Let the length of the planning period be T. Let Kit be the capital stock, measured in appropriate physical units (for example, number of looms, nameplate capacity of generators, and so on), in sector i at date t (t = 0, 1,..., T). Let ca be the value assigned by the planning commission to a unit of capital in sector i at the terminal date, T. These valuation numbers, ci, are entirely arbitrary. They might approximate the income-producing potential of capital in various sectors; they might, if industrial employment is an important national goal, approximate the employment opportunities per unit of capital; they might be simply unity for sectors deemed desirable and zero for others. Whatever they are, we take it that the objective of the plan is to maximize the value of capital at the terminal date, namely W = UCXKIT. Investment in each year is to be financed out of saving or reinvestible surplus, computed as follows. Each unit of capital in sector i contributes vi per year to the total value added in the economy. This contribution can be divided (for example) into three parts: wages equal to nmwj, where nm is employment per unit of capital and wj is the wage rate in sector i; rentier and interest payments equal to ri per unit of capital; and profits equal to vi niwi ri. Differing proportions of these three streams of income are reinvestible, so the total reinvestible surplus per unit of capital in the ith sector is