Hello, everyone. Finally, I’ve got a new iPad Air arrived, so much in love!!!❤️❤️ Also, the Parasite has got 4 oscars, 6 trophies!!! Oscars was so Korean yesterday, so proud. Hope this change leads to more diversity into the world.
I am one of the Bonghives 🍯 and so proud of myself for being his supporter for such a long time. (Those of you who has not seen Parasite, you have to check that out and also “Memories of Murder”. It is one of the best movies ever made in film industry, believe me.)
I need to calm down for a bit.
I. Introduction
In the last post we have looked at a very basic supply and demand analysis with the classic saying “Ceteris Paribus”. Similarly, we all have heard of “Scarce resources, rational behavior”. These 4 words explicitly convey how we see the economy or world, in general. There are limited resources in the earth and since we are all rational (assumed) we will allocate the resources to whom it is most appreciated. The level of appreciation will be shown as our barometer ‘price’.
This story is so familiar to both Econ majors and non-Econ majors. If we summarize all this story in to a mathematical format, we will get a negatively sloped demand curve. We recognize such downward sloped demand curve to be normal. (Since I do not want to repeat the words, from now on, I will just call the downward sloping demand curve to be normal or usual demand curve.)
So you might be surprised of what I am about to talk about. Humans don’t need to be rational. To put it into another way, it would be nice if humans were rational, however, only by assuming scarcity we are able to get a normal demand curve. Why is it so?
II. Scarcity and Rationality
Scarcity of resources is more general concept than rational behavior of humans. Scarcity principle arises economic problems in a society/market.
However, we do not always necessarily solve it according to rationality. Actually, we often behave irrationally. For instance, we often consume things just because others think that it is cool, even though you do not like it at all; bandwagon effect. I recently bought Lululemon leggings, although I know it is not worth 100 dollars.
So, even when households show irrational behaviors if scarcity principle is assumed, we can derive the usual demand function.
1. Opportunity Set
First, we will see opportunity set which presumably most of you have heard of. For simplicity of demonstration, we will simplify things a bit. Each household consumes goods X and Y. There are enough X and Y’s supplied in the economy although they are scarce relative to household’s resources, meaning there exist price.
Then we connect the possible combinations of X and Y that a household can consume with its available resources; Opportunity Set.
So in this diagram AB is the line that represents the maximum combinations available to a household. In other words, when household spends out all its income. We even consider saving or accumulation of cash as consumption on an additional good to simplify our analysis. So, we always think that households end up at the boundary or spend out all the income; ; Walas’ law.
A few things for a recap;
- Households can choose on the boundary or in the interior
- There can be kinks as in AB line. The boundary depends on the system and if, for instance, prices are chosen by rationing it will have some kinks.
- We simplify things a bit by assuming ‘single price’, prices are independent of the amount a household consumes, than we will have straight line like CD or C’D’.
- The slope of the boundary shows relative price of goods X and Y. In CD line, for example, you can get 2 units of Y if you give up 1 unit of X so the slope is 2. That is equivalent to price of X divided by price of Y.
- X is 10 dollars each and Y is 5 dollars each regardless of quantities(one price) you consume then, $10/$5 is 2=slope. So, if one price is assumed, we necessarily have a straight line.
2. Income Effect
We have seen the budget constraint and the opportunity set which are the numerical and graphical representation of scarcity. Then, what happens when I, the income, changes?
For example, due to a simultaneous increase in technology, everyone got richer without any changes in relative price. Common sensually, our opportunity set would look like C’D’ (paralleled shift).
In words, the total change in expenditures equal the change in income. With some differentiation and calculations we can derive so called income elasticity identity; weighted average of income elasticities will add up to one.
[proof] From the assumption of income=expenditure or the budget constraint, the income elasticity identity can be derived.
Income elasticity is famous parameter, right? Which good are you going to increase consumption if your income increases or decreases. Superior(>0), inferior(<0), luxury goods(>1), necessary goods (<1) are defined by the income elasticity (eta).
[Some implications]
- Not all or not more than a few goods can have negative income elasticities. (Everything must be balanced so no eta can be “very” negative nor too many goods can be negative or inferior goods.)
- Goods that take large share in the expenditure are unlikely to have extremely low or high income elasticity. Simply put, broader goods (that take larger share) or goods that are crucial to our daily lives tend to have non-extreme income elasticity.
3. Substitution Effects
Normally, when we look at income and substitution effects there are indifferent curves, however, here we will only look at opportunity curves. In other words, we will only consider scarcity without rationality.
What happens if relative price changes in opportunity set diagram. Here, we will consider a case where relative price of X rises or the slope increases; from ab to ab’. However, ab’ does not represent the pure change of relative prices.
By ‘PURE’, we mean that the real income is constant or “Income compensated”. Also, such price change is called compensated price change.
So, the demand derived from this approach is called ‘Hicksian demand’ and ‘Income-compensated demand’. [Spoil alert] Hicksian demand always follow the Law of Demand. Price increase — >decrease in quantity demanded.
While maintaining the slope of ab’, if we allow the household to hold the initial point consumption or make the opportunity set boundary to go through the initial point, we can represent the pure relative price change.
So, we have a*b*. Due to increase in price of X, what’s gone is the green area whereas what’s added to our set is the pink area, more Y and less X. There were no rationality or preferences assumed. Rather, what forces this shift from X to Y due to price increase in X is the change in opportunity set itself. From here, we can simply guess that the law of demand holds only with scarcity principle.
4. Random Choice Model
Let’s say people randomly choose a point on the boundary of opportunity set in the market. (We do not have utility nor indifference curves.) By random we mean every point of line is equally likely to be chosen, then in the market or as a whole, the mid-point is ‘expected’ to be chosen.
[Some points to make]
- Even with impulsive people(=irrational or people who randomly choose a consumption combination that is available to them), the law of demand holds. (The normal demand curve)
- There exist other behavior principles that are considered to be irrational but still show the usual demand curve.
III. Conclusion
So what we have seen is that without any rationality assumption, we can derive negatively inclined demand curves by scarcity, the very basic concept of economics. However, let’s not misunderstand the idea. Under certain behaviors assumed, we cannot imply the usual demand curve only with the scarcity.
The main purpose of this post was to give you some economic arguments to defend yourself from people saying that “people are irrational, so law of demand is a myth”.
Thank you for reading and I hope this helped you.
Have a pleasant week.
