CHAPTER I UTILITY AND PREFERENCE

Chapter I has nine sections, the first of which I'll discuss in this post.  Section 1 summarizes the main assumptions and conclusions of Alfred Marshall's theory of demand.  The point of that theory is to express mathematically how a consumer chooses to divide his expenditures among several consumption goods, assuming the prices of these goods are already determined.  For mathematical convenience the theory assumes the goods can be purchased in very small units.  A footnote explains:

This convenient assumption of continuity does, of course, falsify the situation a little (or sometimes more than a little) as far as the individual consumer is concerned.  But if our study of the individual consumer is only a step towards the study of a group of consumers on the market, these falsifications can be trusted to disappear when the individual demands are aggregated.

The theory makes several assumptions: that the individual spends his income so as to maximize his satisfaction (or as Marshall, Hicks and other writers have come to call it, "utility");  that utility depends on the quantities of goods purchased;  and that as one increases consumption of some good, each additional unit brings less satisfaction than the previous one -- this is called "the principle of diminishing marginal utility."

With these fairly reasonable (even obvious) assumptions, the conclusion is that "utility will be maximized when the marginal unit of expenditure in each direction brings in the same increment of utility."  In other words, the consumer will choose quantities of the various goods in a way that causes the last (tiny) unit of each good to bring the same additional amount of utility.

This conclusion seems reasonable if one considers a situation where the condition doesn't hold -- that is, in some planned set of purchases, one good has a strictly greater marginal utility than another good.  This clearly can't be the set of purchases that maximizes utility, since the consumer could increase his utility by purchasing (at least a tiny bit) less of the good that has lower marginal utility and using the extra money to buy more of  the good with the higher marginal utility.  With the ability to purchase small units, we have the additional conclusion that the marginal utilities of the various goods are proportional to their prices.  Again, thinking about this conclusion by assuming that the condition doesn't hold, we can see that shifting the planned purchases slightly in the direction of a good with higher marginal utility per unit of price would increase total utility.

In section 2, Hicks will begin to ask some probing questions about the nature of "this 'utility' which the consumer maximizes."