# what is monotonicity and strict monotonicity in preferences?

I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the

• When preferences are monotone / weak monotonic preference, the
consumer prefers more of both goods.
• When preferences are strictly monotone or having strong monotonic preference, the consumer prefers more of one good but no less of the other.

whereas when I read this other paper it says

• Monotonicity means that if c1 contains more of some or all commodities, but no less of any, than c2 (c1 ≥ c2) then c1 ≿ c2.
• Strict monotonicity means that if c1 contains more of each commodity than c2 (c1 > c2) then c1 strictly prefered c2

I am confused as both the answers are quite contradicting as the (first as per sequence I mentioned) says that in strict preferences the consumer more of at least one good but no less of the other.

whereas (second as per sequence I mentioned) says in strict monotonicity we prefer more of both the goods. Also, I am able to understand the graphical representation of the monotonicity. Please tell me where I am getting it wrong I am really stuck on this. Thank you.

• See the first para of wiki page on monotonic preferences. Does this answer your question? – Dayne Nov 2 '20 at 16:39

## 1 Answer

The word monotonic means "always moving in the same direction", in our case, always going up.

Monotonic preferences mean that the customer always prefers more of a good.

This comes in two flavors:

1. Strictly monotonic: More of one good is always preferred to less of that good.
2. Weakly monotonic: More of one good is always equivalent or better than less of that good.
• Thank you so much for answering. Just one more doubt: so we will represent Strict monotonicity as c1 ≻ c2 (where c1 has more of both the goods)Weakly monotonicity as c1 ≿ c2 (where c1 has more of at least one of two good but no less of the other good) – Anishka Mishra Nov 2 '20 at 17:13
• Minor edit: The content in parens should be the same for both: Strict monotonicity as c1 ≻ c2 (where c1 has more of at least one good but no less of any other good) Weakly monotonicity as c1 ≿ c2 (where c1 has more of at least one good but no less of any other good) – RegressForward Nov 2 '20 at 17:14
• okay, thanks a lot! :) – Anishka Mishra Nov 2 '20 at 17:16
• Sir, where can I find a graphical representation of strictly and weakly monotonic preferences? If you have any idea or suggestion for the references please let me know. Thank you. – Anishka Mishra Nov 2 '20 at 17:22
• The Cobb-Douglas function $U(L,K) = L^\alpha * K^{1-\alpha}$ is strictly monotonic in preferences. Plot it with U on the vertical and it will be a nice smooth arch increasing in L and K. – RegressForward Nov 2 '20 at 20:19