Editing Marginalism (section)

=== Marginal rate of substitution ===
{{Main|Marginal rate of substitution}}
The ''rate of substitution'' is the ''least favorable'' rate at which an agent is willing to exchange units of one good or service for units of another. The ''marginal'' rate of substitution (MRS) is the rate of substitution at the margin; in other words, given some constraint.

When goods and services are [[Discrete mathematics|discrete]], the least favorable rate at which an agent would trade A for B will usually be different from that at which she would trade B for A:
:<math>MRS_{AB} \neq \frac1{MRS_{BA}}</math>

When the goods and services are continuously divisible in the [[limiting case (mathematics)|limiting case]]
:<math>MRS_{AB} = \frac1{MRS_{BA}}</math>
and the marginal rate of substitution is the slope of the [[indifference curve]] (multiplied by <math>-1</math>).

If, for example, Lisa will not trade a goat for anything less than two sheep, then her
:<math>MRS_{SG} = \frac{2\text{ sheep}}\text{goat}</math>

If she will not trade a sheep for anything less than two goats, then her
:<math>MRS_{GS} = \frac{2\text{ goat}}\text{sheep} \neq \frac{1\text{ goat}}{2\text{ sheep}} = \frac1{\left(\frac{2\text{ sheep}}\text{goat}\right)} = \frac1{MRS_{SG}}</math>

However, if she would trade one gram of banana for one ounce of ice cream ''and vice versa'', then
:<math>MRS_{IB} = \frac{1\text{ oz ice cream}}{1\text{ g banana}} = \frac1{\left(\frac{1\text{ g banana}}{1\text{ oz ice cream}}\right)} = \frac1{MRS_{BI}}</math>

When indifference curves (which are essentially graphs of instantaneous rates of substitution) and the convexity of those curves are not taken as given, the "law" of diminishing marginal utility is invoked to explain diminishing marginal rates of substitution&nbsp;– a willingness to accept fewer units of good or service <math>A</math> in substitution for <math>B</math> as one's holdings of <math>A</math> grow relative to those of <math>B</math>.  If an individual has a stock or flow of a good or service whose marginal utility is less than would be that of some other good or service for which he or she could trade, then it is in his or her interest to effect that trade. As one thing is traded-away and another is acquired, the respective marginal gains or losses from further trades are now changed. On the assumption that the marginal utility of one is diminishing, and the other is not increasing, all else being equal, an individual will demand an increasing ratio of that which is acquired to that which is sacrificed. One important way in which all else might not be equal is when the use of the one good or service complements that of the other. In such cases, exchange ratios might be constant.<ref name="mc_culloch" /> If any trader can better his or her own marginal position by offering an exchange more favorable to other traders with desired goods or services, then he or she will do so.