Sunday, November 26, 2006

Econ 101: Demand Part 1

Recall our assumption of rationality? Yes, by rationality we mean people’s preference relations are complete and transitive. In order to talk about demand, we now need two more (sorry, guys) assumptions, namely desirability and convexity.

Desirability simply means you prefer more to less. It is represented by the property of monotonicity that means if I ask you to choose between 3.1 apples and 3 apples given the same constraints, you opt for the former. Wait a minute, you say. What if it is not an apple, but something bad, like trash? Well, simply modify the offer statement: 3.1-unit reduction of trash and 3-unit reduction of trash.1

Convexity (of preference relation) means your willingness to give up a unit of a particular good in order to get another unit of different good in exchange given your constraints is increasing the more you have the former and the less the latter. (Note: our definition of convexity in the consumption and budget set still hold). This is called diminishing marginal rate of substitution.

So far we have been talking about preference. How do we really analyze it? We usually use a tool called utility function. This is simply a means to express how you would respond when facing a set of goods given the prices and your income. In order for us to represent preference relation with a utility function, we need (oh, shoot!) to assume continuity. It says, if you prefer 1 apple to 1 orange, 2 apples to 2 oranges, you can’t suddenly, out of blue, prefer 3 apples to 3 oranges.2

How do we put the utility function into use, then? By solving a maximization problem. That is, we suppose an individual is trying to maximize his satisfaction (i.e. utility) given his choice set and budget set. By maximizing we mean, he will use up all his income to consume the goods of interest (saving can be a form of a good; I see your eyebrows rising). We would continue on this.

Stay tuned.

---

1 But hold on, you say. You’re craving for ice cream. I give you one cone, you ask two. I give you two and offer a third. You start to look less eager, but you still take it. I offer a fourth; you give me a no-thanks-I’m-fine. This is called diminishing marginal utility. It is not contradictory to the monotonicity assumption of the preference relation. You can still prefer more to less, but the additional satisfaction the ‘more’ gives you is becoming less and less as the quantity grows. Four cones of ice cream are too much already for you; you prefer three. Remember that we have constraints that limit preference? Yes, one of the physical constraints is quantity that might be bound to taste (or well, your stomach capacity). In this case we can say that your set of ice cream is limited to three. But don’t take this anecdote very seriously; rather, we usually go around such problem with a weaker restriction called local non-satiation – you’re never satisfied, 'locally'. Meaning, you can still prefer 2.999999999999999-unit of apples to 3 apples and at the same time, prefer 3.000000000000001-unit of apples to 3 apples. But let’s not dwell into this technical necessity. We’re safe for now.

2 Again, do not take the numbers too seriously. It is the order that matters.

18 comments:

  1. hmmm... if i want 3 apples whilst i have only 2, i'm gonna sell 1 (my mom's) orange to get 1 more apple. my mom saved the orange for me. does this explain my demand of apples? or, say that it's my own orange, i'm still gonna find someone who wants orange and trade with me.

    ReplyDelete
  2. Anymatters, in the first case, that orange is part of your wealth, ex ante. Think of it as your 'income' that you can use to 'buy' something (in this case apple).

    In the other case, if you are considering to spend on (more) apples and (less) oranges, you're practically constrained by by your income (or wealth for that matter). The fact that you're substituting apple for orange already shows your preference. Here, your decision has nothing to do with whether or not there is somebody willing to trade with you.

    Either case, the answer to your question is yes.

    ReplyDelete
  3. on a tangential note, what about changing preference overtime? say i think i like orange now, or in fact i do like orange now, but due to various reasons, i will not like orange tomorrow, and tomorrow i will like apple or grape. people learn throughout their life, and therefore often change their preference. now how does economics deal with this?

    further, if it does so simply by observing my demand function/behaviour (surely tomorrow i will stop buying orange and start buying apple), how can economics predict people's changing preference? (this question is somehow related to the previous discussion about the origin of preference, but i think it can be addressed separately).

    ReplyDelete
  4. on a tangential note, what about changing preference overtime? say i think i like orange now, or in fact i do like orange now, but due to various reasons, i will not like orange tomorrow, and tomorrow i will like apple or grape. people learn throughout their life, and therefore often change their preference. now how does economics deal with this?

    further, if it does so simply by observing my demand function/behaviour (surely tomorrow i will stop buying orange and start buying apple), how can economics predict people's changing preference? (this question is somehow related to the previous discussion about the origin of preference, but i think it can be addressed separately).

    ReplyDelete
  5. tirta - i don't know the answer but i know there are economists who are working on dynamic preference, one of them is alan kirman.

    ReplyDelete
  6. tirta,
    that is why the demand curve of orange may shift from time to time. because people stop buying orange and start buying apple.

    ReplyDelete
  7. tirta,

    generally economists leave preference formation to you psychologists. it becomes rather disconcerting when you guys come over to us asking these questions :):)

    but here is what econ tells us (excuse if i repeat):

    if you imagine that ppl size up things on several scales. if i buy a PC for example i could size each option up according to speed and HD capacity. if i buy a laptop i could also factor in weight and battery life.

    so preferences could come from how much speed i require for my day-to-day computing, or how critical it is for my laptop to be light - do i travel lots, or rarely? they can change according to my circumstances too.

    (also perceptions are obviously important here -- but that brings us to advertising - which can also account for pref changes)

    there is another type of preference - horizontal preferences. some prefer v. spicy food, others (aka indonesians) love V.V. spicy food. but no one could say the spicier the food the better (/everyone/ has an upper limit).

    the only theory that i know that can explain such preferences, is by stigler and becker, if i can remember rightly the propose that such preferences are /acquired/ through consumption. other than that (AFAIK) economics stops and psychology begins.

    (interestingly human's pref for sweeter things is genetic - as sugar was v scarce and important for early humans.)

    /finally/ you orange one day apple the next, could be a result of intertemporal convex preferences - ppl generally like to mix things up and not be boring :).

    actually one more point, there is also a theory of randomised preferences, which means that ppl often choose whimsically (because of experimentation, or perhaps also to do with convex prefs).

    ReplyDelete
  8. weakties,
    thanks for the link.

    anonymous,
    sure, but i'm wondering if economics has any method to predict the change upfront, rather than doing post-hoc observations of demand curves.

    johnorford,
    perhaps i wasn't making myself clear before, so here's what i think. economics has the statistical tools to predict macro-behaviours, without having to deal with the micro-motives. thus i'm wondering if there's a way to predict the collective preference of any society, perhaps based on the (predictable) dynamics of the aggregate demand/supply curves overtime.

    a simplified example would be this: if i like orange now and apple tomorrow, but an economist happens to observe that the aggregate demand curves for orange and apple stay constant, i take it that someone else has to prefer apple now and orange tomorrow, so our individual changes of preference cancel each other out.

    so i guess i'm basically wondering if economics can predict the dynamics of macro-behaviour (which reflects collective preference), and if so, to what extent. i think psychology can learn a lot from this.

    ReplyDelete
  9. Tirta,
    If you think the abnormal people who like to change their preferences frequently are many and significant, I think we could do that by clustering the samples first into normal group and abnormal group. Then, we can get 2 demand functions for orange. Multivariate analysis and econometric can do that for a simultaneos relationship to get one demand function. However, if the abnormal people are not so many, there's no point to do that.

    OOT, 1 of 10 Indonesians are (maybe) affected by mental illness, how do they survive? It depends on us to understand them when they change their mood so often.

    ReplyDelete
  10. Tirta, one way to deal with the case you raised is to treat orange today and orange tomorrow as two different goods (that is, time becomes an explicit characteristic).

    On microfoundations for macroeconomics, I recommend Stokey and Lucas with Prescott.

    Weakties, John, Anymatters, and an anonymous, thanks!

    ReplyDelete
  11. tirta: "economics has the statistical tools to predict macro-behaviours, without having to deal with the micro-motives"

    i think economics deals with micro motive by the rationality assumption; which is fine.

    what is missing, i think, is the mezo level mechanisms that connect micro to macro.

    anymatters: changing preferences is abnormal? that's so obscene.

    ReplyDelete
  12. AnonymousSecond12/01/2006 02:20:00 AM

    hmm..changing preference, is that has something to do with some additive separability thing? do not know for sure, kindly, please explains that to me?

    thanks a lot..

    ReplyDelete
  13. tirta,

    "so i guess i'm basically wondering if economics can predict the dynamics of macro-behaviour (which reflects collective preference), and if so, to what extent. i think psychology can learn a lot from this."

    You can use factor analysis (invented/discovered by a psychologist in fact).

    Factor analysis surveys a sample, and finds the dimensions which the population (or a segment thereof) appraises a certain class of products.

    (e.g. for mobile computing, processor power is important, but weight will be v important, reliability is ultra important, and other factors are peripheral).

    also if you survey how much people would pay for laptops, you can create a budget constraint and learn about demand elasticities.

    once you have preferences, budgets and other products in the market you should be able to predict the demand of a hypothetical laptop. note the preferences aren't for the products themselves, but what the buyer perceives to gain from consuming / owning the product, these preferences are stable ceteris parabis.

    of course other factors can come into play -- perhaps public transportation takes off in jkt (/mobile/ computing is v important for commuters that travel 4 hours a day). or remote desktops take off, now everyone can access their data thru the net, therefore ppl will have little need for a laptop (remote desktops weigh nothing).

    (this is kinda condensed, feel free to email me and i'll try to elaborate...)

    ReplyDelete
  14. weakties,
    I'm very sorry for that. I just wanted to emphasise that people don't change their minds so often, even in a liberal society.

    However, we need to prove it if frequently changing preference is not common in a harmonious society.

    johnorford,
    I think the factor analysis would do in choosing an orange to buy. We need to put one more variable, say "inconsistency".

    ReplyDelete
  15. 'We need to put one more variable, say "inconsistency".'

    I don't think we need to. i can be completely consistent by choosing to eat an orange one day and an apple the next.

    how bizarre would it be, if you said you preferred apples to oranges, and /never/ ate an orange when there was an apple available... (point is, convex prefs)

    also ppl experiment - may seem like inconsistency - but the point is that they are researching what is good and not.

    ReplyDelete
  16. I just wanted to emphasise that people don't change their minds so often, even in a liberal society.

    wtf?!??!?

    just because you need the statistics to be streamlined and consistent doesn't mean that it's not there!
    what on earth are you talking about?

    it is indeed obscene.

    i think john is perfectly okay there that people can be consistent even as they shift preferences for one reason or another because the environment is also changing blah blah blah (read his for more).

    ReplyDelete
  17. If people appear to be inconsistent with what they like or want, it's fine.

    People may want to change to something different as the previous one was not worth to be kept longer as they may have received a new information in their mind. This still counts.

    But, I believe that people don't change their mind so often and so quickly. Even so, they may go back to the basic preference once the new information and reality no longer fits. There is still a preference consistency over time based on self control.

    I believe something (economic behaviour) would follow the fundamentals over time, however inconsistency still generates market noise and element of surprise in a smaller time horizon.

    In a liberal society (developed countries I mean), market might tend to follow fundamentals as the policy makers could manage to cope with the inconsistency issues and hold the rational choice assumption, whilst the society (consumers/producers) overall could managed to disregard noises of inconsistency. This might explain why the price of one product in such countries doesn't change so big and so often.

    Price of orange goes up and down every week 'cos many people change preference every grocery shopping, other things being equal. Is this true?

    ReplyDelete
  18. "But, I believe that people don't change their mind so often and so quickly"

    i can see where you are coming from:

    perhaps ppl don't want to take risks, you use Windows that works great but heard that Macs are better - chances are you stick with a Windows laptop cos it's "better the devil you know".

    In poor societies quite small losses mean more (maybe a family going without food?) so people are more conservative about even seemingly small decisions -- am sure others here have more knowledge about that...

    ReplyDelete