Let us incorporate the natural resources, or land, in the system of prices and outputs. For the sake of simplicity we will suppose the absence of joint products, fixed capital and human capital.
IT WILLl as a rule is assumed that the 'marginal land', i.e. the least productive land, can always be identified independently of the rents and/or the other unknowns of the system. But, in view of the fact that the gradation of land changes with its occupations, a land which is deemed marginal in the production of one commodity need not be so when used in the production of another. The identification of the marginal land must therefore be made only with reference to the occupations, i.e. the commodities in the system.
This, however, necessitates some criterion for identifying the marginal land. The required criterion is as follows; that land (when equal quantities of lands are being compared) on which a greater quantity of at least one of the inputs is required, but no less of any other, per unit of the commodity produced than on the other grades of land is the marginal land with reference to that commodity. Being the least productive land it would earn no rent if used in the production of that commodity. As for the other grades of land, their order of productiveness will be determined only after their rents have been determined.In what follows, therefore, we will assume that corresponding to every commodity in the system there exists a marginal land.
The process that produces a commodity on the marginal land will be called the marginal process for the commodity. It follows that there will be as many marginal processes as there are commodities in the system.Suppose that there is one type of land of differing grades. For each commodity in whose production land is used there will be as many processes as the relevant grades of land. Thus, if there are v grades of the land there will be NV price equations in the system, The rent earned by land of grade k when used in the production of commodity I, N ?k is the quantity of land and Lt the quantity of labour required to produce x k units of commodity I.
Next, there are the m demand equations for the capital goods, and n ? m consumption demand equations. We also assume that for simplicity that the wage and rent incomes are entirely spent on consumption goods. Finally, there are the restrictions that the products of the rents earned on the lands of all grades are equal to zero for each commodity in whose production land is used. These restrictions arise from the fact that the marginal land in each commodity will earn no rent.There are in all 2n+NV equations above to which can be added the conservation-of-labour equations. These will solve for 2n+NV+1 unknown, viz. n ? 1 relative prices, n outputs, nv rents, the rate of profit and the wage. As is immediately obvious, a situation where v grades of land earn NV different rents can only be one of disequilibrium.
Thus, some method will have to be employed to ensure that every grade of land earns a uniform rent irrespective of the commodity in whose production it is used. This method will be made clear below.To solve the system we proceed as follows. Consider, firstly, the price equations of the marginal (i.e. no-rent) processes of the n commodities. Suppose, for a moment, that the Vth grade of land is the marginal land for all commodities with the result that the vth is the marginal process for all commodities. To obtain an initial solution for the unknowns set up the equations of a standard equilibrium system, where is the aggregate quantity of commodity j produced by the marginal processes and used in the consumption goods industries? Equations (5) solve for the rate of growth and m scale multipliers. Using these in the price equations of the marginal processes and the demand equations for intermediate goods, we obtain an initial solution for the wage, the rate of profit and the relative prices.