# Indifference Curve Confusion and Possible Critique

I am confused about one of the assumptions made when doing indifference curves. The assumption I am talking about is the monotonicity assumption, which is generally described as the ‘more is better’ assumption. That is to say, suppose there are n commodities in both c1 and c2. Monotonicity means that if c1 contains more of some or all commodities, but no less of any, than c2 (c1 ≥ c2) then c1 ≥* c2 (where ≥* means weakly preferred). **But doesn’t this assumption fail when applied to the perfect complementary in difference curve model?

The basic concept is that X and Y are consumed at a fixed proportion. The only way to get utility are at points like A and B. The intersections of the indifference curves (ICs) are the only way one can get utility. Anything outside this intersection point gives an extra utility of zero. So at point C, the utility would only be that of A.   But doesn’t this contradict this ‘more is better’ assumption. As Shon says, from the University of Chicago, an increase of a commodity, even if the other commodity is fixed, would still be preferred, and this is shown by the increase of utility. Nevertheless, in this prefect complementary model, an increase of a commodity, such as X1 to X3, would result in a utility equal to A, thus it is not preferred if there was an increase of commodity X.

Am I just not understanding the implications of this assumption, or is it legitimate to conclude that this is a contradiction?

-Isaac Marmolejo

## 13 responses to “Indifference Curve Confusion and Possible Critique”

1. Hi, monotonicity of preferences, it is called, holds only up to a point, which is known as satiation point. So I guess the bundles (x1, y1) and (x2, y2) have already reached the satiation point, where further increment of one good or both goods will not lead to higher utility.

• Feng,
So ‘more is better’ is not a legit assumption to make then, right? Because, regardless on how one wants to define this assumption in words, the notation is still the same: If the two goods are c1 and c2 then if c1 ≥ c2. then c1 ≥* c2 (where ≥* means weakly preferred).

But this still does not hold up in theory. For example, a good perfect complementary good to compare is left and right shoes. You need one right shoe and one left shoe to give you utility. Having two right shoes and no left shoes gives you no utility. But the same goes if you had two right shoes and one left shoe (well you get the utility of the one left shoe to one right). But in reality, no one can say that you get no utility from the extra right shoe. To say such a thing is presuming what his preferences are.

2. Isaac, I get what you mean, I thought about the problem and here offer another possible explanation. The satiation argument is flawed, by the way, sorry.

I was thinking in the case of complementary goods, ((where two types of goods have to be consumed in some fixed proportion, in your example, one left shoe and one right shoe)), the assumption of monotonicity might not be applicable in the way you have described.

You ask why consuming one extra right shoe, in addition to a pair of shoes give you the same utility. But the implicit assumption is that you always have to consume a pair of shoes, not a single shoe. Essentially, (I’m guessing), the consumption of 2 right shoes and 1 left shoe is still treated as ONE unit of consumption, where one unit of consumption of shoes must have a fixed ratio of one to one.

• Feng,

“You ask why consuming one extra right shoe, in addition to a pair of shoes give you the same utility. But the implicit assumption is that you always have to consume a pair of shoes, not a single shoe. ”

Exactly right, this is an implicit assumption in the case of perfect complementary goods that they are consumed at a fixed proportion. Thanks for the conversation because now I have two problems with this. The assumption of consuming solely at a fixed proportion is flawed in reality because 2 right shoes and 1 left shoe might give you more utility than 1 left and 1 right.

But even if we take this assumption as given, then we are faced with contradiction because this clearly contradicts the monotonicity assumption. We are left with deciding what assumptions to make in certain situations. While monotonicity is supposed to be one of the key assumptions of ICs, it is clearly ignored when we model perfect complementary goods.

This raises another question then. If monotonicity can be ignored when dealing with perfect complementary ICs, then can it also be ignored when two ICs intersect?

• Isaac, I guess models are used to examine realities. We can’t really expect too much from them.

Further, I don’t think the fixed proportion assumption and monotonicity assumption contradict, because monotonicity (the more the merrier) in this case refers to the more pairs of shoes the merrier. In this case, two ICs will not intersect.

• Feng,

I beg to differ. I believe that the monotonicity assumption is supposed to be universal in all types of ICs. Thus the same context on what the assumption says must be applied consistently. And in notation terms: If the two goods are c1 and c2 then if c1 ≥ c2. then c1 ≥* c2 (where ≥* means weakly preferred). To add on to this assumption because it doesn’t fit well with the perfect complementary model is pretty odd. In other words, your claim, “…monotonicity (the more the merrier) in this case refers to the more pairs of shoes the merrier,” is not the same as the original monotonicity assumption stated in notation as,”If the two goods are c1 and c2 then if c1 ≥ c2. then c1 ≥* c2 (where ≥* means weakly preferred)”

• But it’s still the same thing, the greater the units of goods consumed, the higher the consumption. I would say, no doubt models are imperfect; yet we can’t expect them to incorporate every element in the real world, in that case there is no need for models.

• But it is not the same thing because perfect complementary models fix the consumption per IC, so ‘a greater unit of goods consumed= more utility’ is not the case, it is only the case if you consume in that fixed proportion, but to make that case, you must tweak the ‘more is better’ assumption.

3. This is the first time I’ve seen an indifference curve with a right angle. The preferred amount of consumption should be tangential to a budget constraint curve.

• Perfect complementary indifference curves are “L” shaped because of the fact that there is a fixed ratio of consumption and also because the MRS, which is the slope of the indifference curve, is always undefined in perfect complementary goods.

Update: And also a perfect complementary model is still tangent to the budget constraint, the apex of the perfect complementary model would be on the budget constraint curve.

• I guess the logic is that any increase of good X beyond X1 (on IC1) has zero marginal utility, since without its compliment the good is useless.

• Right but as I stated to the other commenter, to accept that is to assume away or tweak the initial “more is better” assumption just for that model. This then raises another concern though, if we are allowed to assume away or tweak the “more is better” assumption for this model, then why can’t we tweak it or assume it away in other types of ICs?

But also the initial assumption does not hold in reality because a person may find some marginal utility of an extra good. To think that one automatically gets no extra utility of an extra shoe, and doesn’t obey the fixed proportion, is to make preferences and uses of a good as a given.

• Silvano Fait says:

The assumption of perfect complementarity implies that consumption is possible only at fixed ratios (hence no utility even adding more goods). It is assumed that they behave like a single good even if they aren’t strictly equal from a physical point of view.