Why doesnt Law of Diminishing Marginal Utility not affect price effect?

Question

Ok so in my textbook, it is given that the downward slope of the demand-price curve is justified by three factors:

1. Law of Diminishing Marginal Utility

2. Income Effect(Real income)

3. Substitution effect

Then after all this it goes on to state, that :

price effect=income effect+substitution effect

Doesn't Law of Diminishing Marginal Utility, affect price too? By keeping a low price on a slice of pizza, the marginal utility that is gained by people with each additional slice would be more likely to be equal or more than the price per slice, and hence demand will increase. So why isnt it included?

Answer 1

This may just be a semantic misunderstanding. The Law of Diminishing Marginal Utility (LDMU) does "affect" the price in the sense that it is responsible for the convexity of preferences, which in turn guarantees a well-defined price effect. The formulation "price effect = income effect + substitution effect" is just a short way of saying that the change in consumption following a change in the price of a good can be decomposed into two different (consumption changing) effects called income effect and substitution effect. The LDMU itself is not a change in consumption and therefore not part of this identity; it is more like a prerequisite to be able to establish this identity in a unique way.

(PS: The LDMU only makes sense for cardinal utility functions which have long ago been replaced by ordinal ones, at least in deterministic contexts. It should be replaced by the Law of Diminishing Marginal Rate of Substitution. What I said above holds analogously then.)