What are monotonic preferences?

In this post, I will be focusing on monotonic preferences. Notes that utilisation of graphs will be used here for better clarifications.

In order to better understand the shapes for these graphs. We need to first define the indifference curve (IC).

What are IC? IC are graphs showing different bundles of goods I.e different combinations of good X and good Y in which the consumer has the same preferences as long as it lies on the same curve. In the IC shown below for the different utility functions, any combinations of goods that is obtained by the green line creates the same level utility for the consumer. This means to say that the consumer will be indifferent between the different bundles of goods i.e i like Bundle A of goods as much as Bundle B as long as it is on the same IC.

In economics, we can understand monotonicity in simple terms which simply means  "the more the merrier". When an individual has monotonic preferences, it means that he prefers more of a quantity of goods as compared to less.

See graphical illustration below:

 

We often subdivide this monotonic preferences into 2 categories.

1. Monotone or weak monotonic preference
2. Strictly monotone or strong monotonic preference

Although written in different way, strictly monotone preferences for example, is exactly the same as strong monotonic preferences, same for point 1.

Let me better clarify the terms.
1. When preferences are monotone / weak monotonic preference , the consumer prefers:

More of both goods.

If bundle A = (2,3) and bundle B = (4,5), we can represent it mathematically as:

B>>A

This implies that: 4 is preferred to 2 (4>2) and 5 is preferred to 3 (5>3). Generically , it can be represented as if X = (X1, X2) and Y = (Y1, Y2), X>>Y => X1>Y1 and X2>Y2 => X>Y

 

For instance, let us look at the case of a perfect complement:

 

A perfect complement (PC) utility gives preferences that are monotone but not strict monotone. Why so?

 

We can show this through proof by contradiction: Assuming it is strictly monotone, then x(whether it is on the x or y axis), which is on the IC will be preferred to y. However, what we saw earlier was that consumers will be indifferent between any bundles on the same IC. From here, we can see that a PC utility function results in preferences that are monotone (they will prefer the point x that is not on the IC) but not strictly monotone.

 

In general, IC that gives will flat region either horizontal or vertically will be monotone but not strictly monotone.

 

Mathematically, it can be written as:

 

x≥y but x ≠ y => x > y

 

2. Strictly monotone or strong monotonic preferences
When preferences are strictly monotone or having strong monotonic preference , the consumer prefers:

 More of one good but no less of the other.

For instance, let us use the case of a perfect subsitutes (PS)

In the above graph illustrating the utility function that represents PS, if a imaginery L can be drawn from the original bundle of A that the consumer chooses, we can evidently see that the consumer will prefer bundle B eventhough the amount of Good Y in bundle B remains the same and only the amount of X has been increased. Therefore, we can see that it satisfies the criteria of being strictly monotone.

The same effect can be seen for cobb douglas utility functions.