In this short section -- the final section of Chapter I -- Hicks dispenses with the simplifying assumption that the consumer is choosing between only two possible consumption goods. Although two-dimensional indifference diagrams are no longer useful for higher dimensions, the mathematical principles illustrated by them still hold.
The marginal rate of substitution can be defined as before, with the added proviso that the quantities consumed of all other commodities (Z...) must remain unchanged. The consumer is only in full equilibrium if the marginal rate of substitution between any two goods equals their price-ratio.
The principle of diminishing marginal rate of substitution must be generalized slightly. In addition to diminishing marginal rate of substitution between each pair of goods,
more complicated substitutions (of some X for some Y and some Z) must be ruled out in the same way. We may express this by saying that the marginal rate of substitution must diminish in every direction.
And this concludes Chapter I! Thank you for reading along this far.
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