ET's first law of consumer behavior is:
(The consumer optimum condition is)
MUa/Pa = MUb/Pb
Consumers must consume the products of interest (here 2) in such quantities that the extra utility for the last unit consumed, divided by its price, is the same for both items.
In English we mean that the additional satisfaction for the last unit of each item must be the same when it is expressed per dollar of expenditure.
Suppose the consumer has purchased some amount of A, such that the MU for the last unit is 40, and the price is $8. Also, the consumer has purchased an amount of B, such that the MU for the last unit is 25, and the price is $5. This is the ending point after all the budget is spent. This information is presented below:
Q amount of A, MU =40, P=$8
Q' amount of B, MU =25, P=$5
The question is, ignoring indivisibilities (lumpiness), is the consumer achieving maximum satisfaction? The answer is no. When we set it up we get:
40/$5 =? 25/$5 (8 vs. 5, we see they are not equal) the value of the left side is greater than the right, and if one dollar's worth of expenditure is shifted from B to A (more A, less B), a gain in total utility will result.
Therefore, the consumer would accept the opportunity to do his/her shopping over again. (Presumably, the consumer usually gets it right the first time, but we introduce the error in order to prove a point.) We can picture the result of shifting dollar after dollar from B consumption over to A consumption. Each time the consumption of A is increased and B is decreased, two things happen. For one thing, the total utility goes higher and higher. For another thing, the satisfaction for the additional unit (last unit) of A decreases, because of the principle of diminishing marginal utility -- the more you consume the less the additional satisfaction for the additional unit. Also, the marginal utility of B increases (as less is consumed). So we are saying the value on the left side falls and the value on the right side rises.
When would the consumer say: "Hold it! This is the best combination of A and B." When the values on both sides were the same -- when the marginal utility per one dollar was the same for A and B. We don't have enough information for a precise answer, but perhaps the final equation is: 33/$5 = 33/$5
This demonstrates the sense of ET's law. Finally, ET's law is the basis of a proof of the law of demand. The details of that will not be shown here, but the essence is we start with a consumer who is in equilibrium, the we allow for an increase or decrease in the price of one of the items. This change of course disturbs the equilibrium, and, restoring equilibrium implies behavior which supports the law of demand (for example, a higher price requires quantity demanded to be reduced).