EPTAnyways:
The idea of economics is not what you may hear about in the news all the time. Many economists may work on Wall Street and the like, but the idea of economics, at its core, is a simple question: why do people do the things that they do? There are many branches of discipline that deal with this: psychology attempts to explain why people do certain actions, often having to deal with either a troubled past, an overflow of a certain hormone, or sexual relations with your mother. Similarly, political scientists attempt to figure out why certain governments are stable and why others are quickly dispatched by revolution. Historians attempt to figure out why things happened in the past, and hopefully to apply those lessons to the present. But economists? They purport that people’s actions are all due to responses to incentives.
The most obvious incentive is of course money and prices. If the price of something that I buy goes down, something will probably change in my consumption. I may buy more of it, or I may use the savings to buy other stuff. Of course, this begs the question, how are we supposed to tell what I will do?
The Utility Maximization Problem, or UMP, as it is called, is at the core of this question, the side of economics known as consumer theory. It claims that people derive “utility” from having certain amounts of goods. What exact kind of utility there is, we do not know-it could range from decoration to investment to self-penetration. But I digress. The fact is, we do not know how much utility someone will exactly derive from something-all that we can purport to know is that somebody will like a certain group of stuff more than others.
There are a few rules that are set into the idea of utility before we proceed: firstly, we argue that nobody has intratransitive preferences or irrational preferences. For instance, If I like apples more than pears, and pears more than oranges, I cannot like oranges more than apples. There are of course numerous loopholes in this assumption, as in the rest of them, but we’re ignoring them because otherwise we’d have to do even more calculus than I would like.
The second thing we argue is that preferences are usually convex. By this we mean that people tend to prefer averages of things to extremes, generally speaking (there are many notable exceptions). For instance, I would rather have 1 burger and one order of fries rather than two orders of fries or 2 burgers.
The third major assumption (other than stupid ones that aren’t important really) is that preferences are monotonic. This means that the more of something I have, it gives me more “utility.” Now, some of you may argue that there are clear flaws with this one, such as for instance women (two women are good, but five women will get out of hand) but for most goods, we will assume this as being true.
Now, you’ll notice I used the word “good” there. It’s not meaning just stuff, i.e. goods and services. It means that whatever we’re getting benefits us, i.e. it’s a good. There are also things which are called “neutrals” and “bads,” which you can probably conclude what they mean.
So now, how exactly do we show how this works? The first thing to do is to bring out one of the indecipherable graphs that you may see in class.
![[image loading]](http://www.bized.co.uk/virtual/vla/images/ind_map.gif)
Great, it’s a bunch of fucking lines. In actuality, those curves are what we call indifference curves. They mean that the person is indifferent as to what group of stuff he has along that line. For instance, if three apples and two oranges and three oranges and two apples are on the same indifference curve, it means that if I had to choose between the two groups, I would have a pretty hard time making a decision as I value them the same.
The higher value the utility is, then that means that I prefer anything on that indifference bundle to ones with less utility. For instance, the one labeled “5” is preferred to the one labeled “4” or “3” and so forth.
Now you may be asking, what the fuck does this do? All we know is that people like having more stuff. Cool. But that doesn’t help me with the calculus.
I’m getting to that. First we need to understand the other part of the UMP-the Budget Constraint.
The Budget Constraint is as follows: it is given by the equation M = p1x1 + p2x2, where x1 and x2 are two different goods.
This can be literally translated as follows: The amount of money that I can spend can give me the most utility through a certain combination of the two goods. Each good is at a certain price, and that price effects how much of each item I can buy.
Similarly, the idea of a Utility function is that it can be related to this. There are many different models of utility, so we’ll keep it in the general form U(x1, x2), meaning that this could be any utility function so long as it is related to only x1 and x2.
So the UMP is all about the following idea: we want to get the most use out of a group of items while spending no more than our budget. This should be pretty common sensey.
-To be continued with Part II: The Lagrangian and First Order Conditions.
![[image loading]](http://imgur.com/i1HkH.png)
