First of all, you have to keep in mind that indifference curves are not intended to represent real things that exist in the world. They are just models that simplify reality enough that we can make statements about the choice behavior of individuals (although you could argue that it has been simplified too much). The only thing you can know about an indifference curve that is further out from another indifference curve is that the individual will prefer any of the bundles on the outer curve to the ones on the inner curve. It isn’t meant to mean anything else. Thanks for your apology.
To get back to the original thread topic… No, calculus based mathematics are unnecessary to understand most of neoclassical theory. The optimization and equilibrium principles can be explained using verbal arguments. The advantage of mathematical economics is when you put your arguments into mathematical form all of your assumptions are made crystal clear for everyone to see, instead of having implicit premises that we may not even realize we are relying on. I agree with the Austrians that some of these assumptions are misleading when applied to the real world (that is why I am such a fan of Hayek). I don’t think abandoning mathematical economics is a good idea, but economists should spend more time criticizing the axioms of neoclassical theory and revising them than they do (and stop pretending that information is “given” when it clearly isn’t).
Wrong. The only thing we could say about a preference function that rated one thing as 1 util and another as 1.5 utils is that the second is more prefered than the first. If we introduced another bundle that was 1.3 utils, the only thing we could conclude is that {1 < 1.3 < 1.5}. If it is confusing just imagine that 1=A, 1.3=B, and 1.5=C. What we can conclude about the choice this individual will make is that when asked to choose between A and B they will choose B. If they are going to choose between B and C, they will choose C. If asked to choose between A and C, they will choose C. Of course this all assumes a well behaved preference function.
Also, its wrong to say that “the average person think” when talking about economic models. That sounds like the job of psychology or neuroscience. A model is not something that is “out there in reality”. It is something that is in our mind to help understand what is taking place and predict things. Think of a model as being like a map. Is a map saying that the ground is flat? No it gets rid of the information that isn’t needed for what we want to use it for. In fact, it gets rid of almost everything and is way smaller than the actual land it is trying to describe. In other words it is unrealistic. I think modern neoclassical theory is too simple and need expanding, but you can’t expect models to be something they are not. They aren’t meant to be the real thing we are studying. They are just supposed to be realistic enough to help us think about what we are interested in without becoming overly complex. There is a tradeoff between complexity and realism. If it is too complex it won’t help us understand the thing we are studying. If it is too simple it won’t correlate to the real world enough to be useful.
I found these questions very interesting. I have always thought of mathematics as universal logic. No matter where you are standing 2+2=4.
I am a Phd Student in Computer Science. Computer Science in terms of mathematics is the the application of mathematics with in boundaries. At least Theoretical Computation is in lay terms. I read political and economics books as a hobby. I was discussing economic policy with one of my committee members (i.e. gatekeeper), which led us to determine that the whole of economic transactions are uncountable, intractable, and not computable. Meaning a computer can not plan the economy. This is a very brief synapsis of the discussion and conclusion, that is anecdotal at best.
But I found it interesting none the less. Especially considering Greenspan blamed his computer algorithms. It seems that economists are defined by the grandeur of their mathematical models. Given that theoretical math could have a solution but a computer algorithm would not be able to give a solution, it seems that computational models should invalidate their economic hypothesis.
For any other CS or Math individual: We decided the economy was an amalgamation of different problems enumeration, optimization and decision problem. Or at least attempting to reduce it to a decision problem.
We started the discussion involving Walter Blocks lecture on Wage Gaps based on race and sex. I stopped my professor from trying to come up with a function for an economic market sector involving different types of discrimination. He was trying to come up with a discrimination constant.
We did not pursue this fully and was just a casual whim. I am interested in anyone else’s opinion. I glossed over a few topics but I hope I did the overall idea justice, whether it is good or bad.
This doesn’t answer my question at all. First, you make use of cardinal measures, which you yourself denounced. Secondly, wouldn’t it be more realistic to simply create a “value scale,” “preference table,” or something similar? e.g. I prefer C to B and B to A.
So, for example, you would say that Rothbard’s model of a value scale in his Man, Economy, and the State is completely unrealistic?
A man’s time is always scarce. He is not immortal; his time on earth is limited. Each day of his life has only 24 hours in which he can attain his ends. Furthermore, all actions must take place through time. Therefore time is a means that man must use to arrive at his ends. It is a means that is omnipresent in all human action.
Action takes place by choosing which ends shall be satisfied by the employment of means. Time is scarce for man only because whichever ends he chooses to satisfy, there are others that must remain unsatisfied. When we must use a means so that some ends remain unsatisfied, the necessity for a choice among ends arises. For example, Jones is engaged in watching a baseball game on television. He is faced with the choice of spending the next hour in: (a) continuing to watch the baseball game, (b) playing bridge, or (c) going for a drive. He would like to do all three of these things, but his means (time) is insufficient. As a result, he must choose; one end can be satisfied, but the others must go unfulfilled. Suppose that he decides on course A. This is a clear indication that he has ranked the satisfaction of end A higher than the satisfaction of ends B or C*.*
From this example of action, many implications can be deduced. In the first place, all means are scarce, i.e., limited with respect to the ends that they could possibly serve. If the means are in unlimited abundance, then they need not serve as the object of attention of any human action. For example, air in most situations is in unlimited abundance. It is therefore not a means and is not employed as a means to the fulfillment of ends. It need not be allocated, as time is, to the satisfaction of the more important ends, since it is sufficiently abundant for all human requirements. Air, then, though indispensable, is not a means, but a general condition of human action and human welfare.
Secondly, these scarce means must be allocated by the actor to serve certain ends and leave other ends unsatisfied. This act of choice may be called economizing the means to serve the most desired ends. Time, for example, must be economized by the actor to serve the most desired ends. The actor may be interpreted as ranking his alternative ends in accordance with their value to him. This scaling of ends may be described as assigning ranks of value to the ends by the actor, or as a process of valuation. Thus, suppose that Jones ranked his alternative ends for the use of an hour of time as follows:
(First) 1. Continuing to watch the baseball game
(Second) 2. Going for a drive
(Third) 3. Playing bridge
This was his scale of values or scale of preferences. The supply of means (time) available was sufficient for the attainment of only one of these ends, and the fact that he chose the baseball game shows that he ranked that highest (or first). Suppose now that he is allocating two hours of his time and can spend an hour on each pursuit. If he spends one hour on the game and then a second hour on the drive, this indicates that his ranking of preferences is as above. The lowest-ranking end—playing bridge—goes unfulfilled. Thus, the larger the supply of means available, the more ends can be satisfied and the lower the rank of the ends that must remain unsatisfied.
This model doesn’t seem very unrealistic to me. Now compare this to an indifference curve or even an opportunity cost curve, both of which would involve a healthy dose of mathematics just to prove something that can be shown through logical deduction.
Other models don’t necessarily have to be unrealistic. For example, it just might happen that demand will increase and supply will not, causing a price increase or a shortage. However, saying that the price will be in equilibrium for any extended period of time is unrealistic and illogical, since entrepreneurs do not know the entire demand curve, and hence cannot know the perfect price.