Hello, how’s everyone? I’m focusing on moving my body at a gym despite the nCoV crisis. Also, I’ve got more spare time for yoga, so this week I’m focusing on my shoulders and upper body🧘🏻♀️. To get more strength, ironically, we have to let go of the tension in the body.
I. Introduction
We talked about the four magic words; “Scarce resources, rational behavior”. So, it is time to talk about the rationality part. We all are very familiar with the concept. But, are you sure? There are a lot of misconceptions regarding rationality of human beings in Economics.
- Rationality v.s. Selfishness
Have you read The Selfish Gene by Richard Dawkins? The book keeps talking about how creatures can be selfish for the sake of survival and successful reproduction the humans are no exception. In that perspective, the altruism, charity, and patriotism, etc are regarded as irrational and unnecessary or even self-destructing. However, in economics any actions or choices that can give you utility can be a rational action. The mentioned concepts can be proven to be rational in the perspective of Economics.
- Interdependency of rationality
When we talk about utility maximization of a household, it can easily be misunderstood that we make choices independent of others’. On the contrary, rationality does not necessarily imply that. Rather, households are affected by the cultural background and they are linked to one another more than we could imagine. If one household decreases its consumption on X, other households are more likely to react to that change in a certain way (increase or decrease their consumption on X). This is very intuitive and our rationality definition must not exclude such cases.
II. Rationality in Econ
Then, how economists define rationality?
A. Each consumer has an ordered set of preferences. When it comes to ordering of preferences, we have heard of these 3 words; completeness, reflexivity and transitivity. Some T or F questions from the intermediate microeconomic courses regarding these concepts are often irritating and bothersome. (it was for me :) ) However, come to think of it, preferences should be well ordered based on a common sense. Easy as it could be!
B. And he chooses the most preferred set available to him, in other words, maximize his utility as much as his budget constraint permits.
III. Indifference System and optimal choice
I assume that most of you have heard of indifference curves and optimal choices; the tangency condition between the indifference curve and the budget lines, algebraically, MRS=relative price.
We are very familiar with the following graph. However, a lot of intuitions are not provided in the micro courses. Or even though they are covered in the lectures, they are not asked in the exams so that we ironically forget at advanced levels.
A. First, we will find the utility maximizing condition in general case. Also, the idea of ‘commodities’ might be new, however, at this point it can be regarded as ‘goods’.
- What does lambda imply here? Marginal utility of Income/Money.
Lambda here is marginal utility divided by its price, in other words, the marginal utility that a dollar provides to you. The point we have to make from a is that a household allocates $ SO THAT every marginal utility of money is equalized. Intuitively, utility maximizing choice is made so that every dollar is worth the same.
Lambda here is formally called ‘Lagrangian multiplier’, which connects the object function (utility function) and the constraint (the budget constraint).
Cf. If you are not familiar with the first order condition process or Lagrangian method, it is your chance to look up 📚.
B. In 2 goods case.
Now back to the simple example. Why the tangency condition?
Let’s interpret what MRS=relative price imply in the graph.
- MRS or the slope of indifference curve that is derived by -MUx/MUy is the marginal value of good X in terms of good Y.
- And the relative price part is the cost of good X in terms of good Y.
- Orange point: value of X >cost of X so we should buy more of X.
- Green point: value of X < cost of X so we should buy less of X.
- At the optimum: value = cost.
IV. Details of Indifference curves
- Indifference curves do not cross each other
As the u0, u1, u2 in the previous figure, they do not cross each other. That is mainly because more of both goods are preferred to less.
This concept might seem very straigtforward, however, why is it? If less of any good is preferred to more and the price is non-negative, a consumer can increase his utility by reducing his consumption for that good down to zero. So, this is the basic reason that more is preferred to less for the goods that are actually consumed.
In this graph, since utility level of any points on an indifference curve are the same, u(e)=u(f) — on u0 and u(e)=u(g) — on u0’. Since f has more of both goods than g, f is more preferred to g — u(f)>u(g). There is contradiction!
2. Indifference curves are negatively sloped.
Here again, since more is preferred to less, any point on V is more preferred to that on L and for this reason any indifference curve cannot be positively sloped.
3. Indifference curves are mostly convex.
As shown in section III, the slope of the indifference curve, or the marginal value of X in terms of Y should decrease if we assume diminishing marginal utility. (This part is actually a famous misconception! This assumption is unnecessary.)
Then, why is the convexity generally assumed?
First, what happens if the indifference curves were concave?
In this figure, f is the tangent point, however, e is more preferred option or optimal choice. e is the point which does not consume X. So, if we restrict our cases for the goods that are ‘actually consumed’, concave indifference curves are ruled out.
Moreover, can indifference curves be convex and concave at the same time?
Since is b is strongly preferred to a, NO rational choice would be made on the concave segments.
So, back to the diminishing marginal utility part! Although D.M.U can be your safe house, it is unnecessary. For the goods that are actually consumed, without any assumptions, you can safely say that your indifference curve is convex.
Tips) Since the indifference curves are not directly observed, when we measure utility change from e to e’, it can be substituted by the change in real income. Green is easier than the orange. 🍊
V. Slutsky Equation
Remember that we are basically covering how DEMAND CURVES are derived.
First, I want to clarify some concepts regarding Hicksian and Marshallian demand curves. Hope you are not confused in between some fancy words.
What happens if relative price changes? The famous SLUTSKY appears here!
- The Hicksian or compensated relative price change is restricted to the pure substitution part; the change from A to B. We know this! ❤️
However, relative price can change as opportunity changes. We cannot restrict our scope to the cases where real income remains still.
With the subsidy to almond milk industry, the relative price of the almond milk will decrease. Moreover, if the subsidy was financed by a tax from cigarette consumers, their real income must have been decreased. Anyway the simultaneous change must be covered although life would have been easier without it.
So, now our real income changes.
This process can be viewed from different perspective, and for me it is more intuitive.
Decrease in a price of X changes our opportunity set from ab to ac, while the choice changes from A to C. Then we can divide the change into 2 parts.
- As relative price changes, you will consume more of X. (LOD holds in compensated demand curve case) That is pure substitution effect. ab to df AND A to B.
- Also, when price decreases it can also be viewed as an increase in your income itself; it has broadened his opportunity set(ab to ac). This part is captured by the change from df to ac or B to C that is pure income effect.
VI. Combined demand curves
So, in most cases, pure substitution effect and pure income effect reinforce each other to follow LOD.
However, if C situates at the left side of B, in words, when income increases from M’ to M the quantity demanded of X decreases, X is the inferior good.
Then, what if X is very much inferior? In words, with the income increase, quantity demanded of X decreases tremendously so that C situates on the leftside of A. The consequence would be even with the price decrease, the quantity demanded decreases LOD does not hold. Formally these goods are called Giffen goods.
Some True and False questions might help us.
- Giffen goods are always inferior. True
- Inferior goods still follow law of demand. Not always
- Giffen goods do not follow LOD. True
- Normal goods always follow LOD. True.
Until now we have seen a single household case. At this point, market’s demand curve is no more than horizontal aggregation of each household’s demand curve that is derived from the indifference curve and budget constraint analysis.
If there were only 2 households i and j in the market the market demand curve will be derived as the following.
Note that there is a kink in the market demand curve since at Pi household i enters and before that the market demand curve follows that of household j. In general cases, there are no kinks in market demand curve because there are (nearly) infinitely a lot of households in the market.
VII. Conclusion
We have seen indifference curves and demand curve analysis in the perspective of rationality. There was a delay for some personal reasons however, I will try to keep up with the schedule, I apologize 🙏.
What is missing at this point is the Slutsky equation with mathematics, I am not sure if it fits our aimed level. I might spare another posting for it.
Next time I will back with Uncertainty in Economics!
Mirabell garden from the movie Sound of music. 🎵
See you soon!
