How’s everyone? This is such a frustrating time in South Korea. Everyone seems to be calm but worried at the same time. The worst part is the boredom around. I hope we could get over this 🙏.
I. Introduction.
This will the last posting on the demand part in Microeconomics. So, this time we will wrap up the things a bit.
- Slutsky Equation
We have seen Slutsky theory with the graphs, in advanced levels they do cover Slutsky with numbers. (elasticities, to be precise)
- Household Production
Do you remember me mentioning “Commodities” rather than “Goods”? Literally, the “goods” is the antonym for the “bads”. Basically, goods are something beneficial to you, however, it does not mean that it could give you the utility directly. It’s OK if you cannot get it at this point, I will manage to help you out! 😉
- Uncertainty
Similar to “Scarce resources and Rational humans”, the concept of “UNCERTAINTY” is seems to be logical and straightforward. Has anything happening around you been certain? However, incorporating such a simple idea into Economics with numbers and equations is certainly not a simple job to do.
II. Cost Minimization and Hicksian Demand.
Before moving on to Slutsky Equation part, we have to look through how the Hicksian demand is derived in equations. Do you remember the utility maximization from the previous post? Now with Hicksian Demand we’ll see “cost minimization”. We always have to keep in mind that Hicksian deals with scarcity problem, in other words, budget constraint.
In detail, the problem would be what would be our consumption choices, i.e., Xi’s that minimizes expenditure or the income, M such that you can get certain level of utility. With some mathematical symbols, the sentence can be summarized into a few words.
[Here what does M imply?]
First, Lagrangian multiplier, of course. Also, M is the marginal cost of utility, to see that we can bring back the lambda from the utility maximization.
However, the duality is satisfied under certain constraints, so this cannot be generalized.
[Cost Function]
The key in Hicksian demand part is the cost function. Among some features that the cost function has, we have to cover the Shepard’s Lemma to solve the Slutsky equation.
III. Slutsky Equation
Now, we will be using equations to explain the same situation. You might be scared of equations and some calculus, however, once you get used to it, equations could contain more ideas than the graphs. As we go through the steps, you will be annoyed with drawing graphs all the time. 😖
Some Clarifications on notations
1) There are k number of goods and we will denote the quantity demanded for each goods as X1 to Xk.
2)Price of one good will change, say good j and Pj is the corresponding price of good j.
The most important point here is that at first (before any changes) Hicksian and Marshallian demand are the same, however, the approaches differ.
Now, it is time that PRICE of a good changes.
We will first take a derivative with respect to (w.r.t) pj, in other words, we will see how the Qd of good i reacts to the change of the other good j.
From *, there are a few point that can be simplified.
However, our main goal is to see how the Qd reacts to its own price change.
We need to take a deeper look at the implications of ***.
This is exactly same as the idea we have discussed with the graph analysis. Anyway, we revisit the normal good, inferior good, and Giffen good analysis.
As I’ve mentioned in the elasticity posting, the derivatives are unit sensitive. So, we will change these equations in the elasticities format.
As in step c, this can be rewritten in own price elasticity notion.
[How to become a Giffen good]
As we have discussed being a Giffen good is not an easy thing. (We haven’t see a lot of persuasive villains in the movies 🎥! I still cannot understand Thanos’ intention…)
The point in 2 is ironic, since for it to be very big, the share should be large. This means that the good is a broader good, however, in most cases broader goods are normal goods.
IV. Conclusion
I kind of failed with the length of the posting. In the continued posting, I will start with household production and uncertainty part. There will be no introduction in that post.
Thank you for reading and wish you a pleasant week!
+ It was international women’s day, congratulations, girls.
(You know, whether or not which gender the god is does not matter much. I believe the God’s got more things to tell us.)
See you,all.
