LATEX

LATEX

Tuesday, April 14, 2015

CHAPTER I -- Section 9

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.

Thursday, April 9, 2015

CHAPTER I -- Section 8

In this section Hicks examines the foundation for the principle of Diminishing Marginal Rate of Substitution.  He reviews the fact that his goal is to deduce laws that deal with the reaction of a consumer to market conditions.  In particular, when conditions change, we expect the consumer to move from one position of equilibrium to another.  The principle of Diminishing Marginal Rate of Substitution must hold at the new position, or else it would not constitute an equilibrium.  Moreover, as Hicks argues, if there were some intermediate point between the two positions of equilibrium where the principle did not hold (and hence there were a "kink" in the indifference curve), then "there will be some systems of prices at which the consumer will be unable to choose between two different ways of spending his income."  The principle of Diminishing Marginal Rate of Substitution is a simple assumption that rules out these kinds of difficulties, and it is consistent with our experience as well.

After some discussion, Hicks argues that "other principles can be discovered whose foundation is exactly similar."  He describes how some of these principles will be worked out in later chapters, and he concludes this section with the statement that, "We are in sight of a unifying principle for the whole of economics."