It works best in analysing simpler systems – such as making a selection from a fixed set of discrete choices (such as “Will I drive, or catch a bus?”). Of course the analysis gets pretty ugly pretty quickly unless you make some pretty heroic assumptions. Any non-simulation based solution requires very simple models, with identically distributed terms, no covariance, and simple normal-like distributions.

At least in my experience, there are still not too many models using the tools that I understand that computational physicists are using, such as Markov Chain Monte-Carlo models etc. But they are coming…

The concept of “rationality” in economics deals with decisions made given your beliefs about the world. It doesn’t, at this level, say what those beliefs should be.

Making costly (in the literal sense of cost > 0, not the figurative sense of cost = a lot) decisions on the basis of astrological advice when you don’t believe in astrology would be irrational. Not doing so when you do believe in astrology would also be irrational.

a) Economists are perfectly agreed that utility is non-linear. Indeed, the concept of marginal utility is of incredible importance in determining prices. Economists talk about the value of the marginal unit all the time, which doesn’t make sense if the marginal unit’s value is the same as the average value.

b) I think your statement (b) is too strong. Utility is a function of goods. It’s also a function of other things, but goods definitely come into it. Imagine, for example, that you have hiked with your loved ones into the wilderness, two days away from the nearest road or shop or cafe. You have a wonderful camp spot, a beautiful view of a sunset over a local gate, and any other immaterial good you care to add in (I don’t know if that means you’ve just finished two hours of yoga or whatever). I’m willing to bet that, all other things being equal, your utility will be higher if you also have some material objects, like some food.
There’s nothing in economics to stop one adding non-material utility in to a person’s utility function. For example, once my husband asked me what I meant when I said that I loved him, and I blinked in surprise and replied “That’s simple, I mean your utility is part of my utility function.” I would have gone on to add that my utility function increased with respect to his utility but he was laughing too hard for me to get a word in edgewise. I don’t know why.

Economists do use linear equations in modelling budget constraints. For example, a person cannot spend more money than they have (taking into account their ability to borrow). So we can write that someone is maximising their utility with respect to goods available on the market subject to a budget constraint, where the sum of all the goods they buy multiplied by the price must be less than or equal to a set amount of money. Perhaps you have been confused by these budget constraints?

c)I agree that the world “rational” can be confusing. But I also agree with Bad that the impulse to assume that people are rational unless proven otherwise has lead to some really fascinating discoveries.

d) I’m not sure how much value would be added by including non-deterministic models of utility. Economists don’t try to model every single behaviour someone does, we don’t know anyone’s actual utility functions so even with a deterministic model we don’t know what any one person would actually choose. What we use utility models for is things like explaining how prices are calculated (price = marginal utility), or saying that we don’t know if labour supply increases or decreases in response to an increase in the hourly wage. (This is something taught in Econ 101. Basically, imagine a self-employed worker called Carol who can increase or decrease her hours at will. And for a moment just think of Carol as only being interested in money and leisure. Her hourly rate goes up. Now Carol can earn more each hour she works, which creates an incentive to increase her hours, the substitution effect. But, since she’s richer, she can also increase her leisure while maintaining the same money income by decreasing hours – the income effect. The conclusion is that we don’t know if the subsitutition effect or the income effect will dominate in Carol’s case so we don’t know if she will work more or less hours in response to an increase in her hourly rate). Now, if we can’t tell what Carol, or you, would do, with a deterministic model, what’s the value of going to a non-deterministic model?

This may all be old news to philosophers who work on decision theory and related things, but I think it bears repeating.

There’s an interesting post up at Cosmic Variance by the physicist Sean Carroll wondering idly about some issues that come u…