Anton Rainer "Therefore, it is unrealistic, that a utility function for a relatively short period plays an important role for the choice." Why the adjustment would be supposed to happen in short period?

"not clear which measurable characteristics (size, number of rooms, situation?) of a flat"

Just, somehow, without knowing that either, rich people somehow avoid ending up living in slums.

"I have never heard of a case" Four day work week tried in some richest countries? Early retirement? Giving up side job?

"Therefore, these utility functions do not fit – also for other durable consumption goods." You buy coffee machine or orange juicer instead of second fridge.

"Therefore, I think that utility functions are useless, i.e. they have no utility (except as a mathematical riddle)." They work as approximate model of human behavior. There are some empirically calculated price elascities.

Utility functions in neoclassical models aim to represent consumer preferences under budget constraints, but they assume an unrealistic ability to precisely calculate optimal consumption. In reality, the difficulty of measuring product characteristics, the indivisibility of some goods, and the fixed nature of certain expenses such as housing limit their practical application. Therefore, these functions remain a useful theoretical tool in academic analysis but do not accurately reflect actual consumer behavior

@Hajer, a practical application of utility functions is not only limited, it is impossible. Why do you think that it is useful for academic theories? Do you have a (personal) utility function, and do you know it? I don't.

Marcin Piotr Walkowiak,

The utility function is a mathematical function, where the arguments are real numbers for quantities of consumption goods and services, which assigns real numbers (utility) to these quantities for a future period. This period could be an hour, a day, a week etc., but in most articles it, implicitly, seems to be a year or a quarter. One question is, is it relevant on a point of time at the beginning of the period for the spending decision for the whole period, e.g. one decides to consume 63.7 l beer in this period, and the utility function or the decision remains unchanged – independent of past consumption?

Now let us look at renting an apartment. To make it simple: utility is dependent only on square meters and the rent is a certain amount pr sqm. Most persons are already living in an apartment. Does that influence their utility function in this respect? I think, not. Nevertheless, they may be happy with their living situation, why should they decide to rent another apartment? Therefore, the utility function plays no role for their consumption expenditures.

What concerns working time: I know that there are different possibilities to reduce it. But do you know of case where an employee told his employer, that he would work e.g. 48 minutes less, because his wage was increased? It is likely that the optimal working time according to a Neoclassical utility function decreases when the wage increases. All usual functions also show reduced working time when tax credits are increased. Very strange results!

I brought the refrigerator as an example, where the utility is not increasing (dU/dCfr1). In this case, one cannot apply the usual optimum calculations. Coffee machines and orange juicers are not substitutes for refrigerators, they are in different positions in the utility function. Like fridges, they have falling utilities (after an optimal quantity) and are not divisible (one cannot buy 0.4 pieces). The purchase of durable consumption goods is, in general for several periods.

Price elasticities are not utility functions.

Anton Rainer "Price elasticities are not utility functions."

If you accept concept of price elasticity of demand -> consumer is adjusting his consumption to new price levels -> he is following his utility curve.

The difference is that price elasticity exist for particular point while utility curve is more generalized solution for more hypothetical price combination.

"Does that influence their utility function in this respect?" I'm not sure what's argument here. Yes, there is adjustment time / friction cost. So?

If you want higher level of precision at expense of higher complexity I remember studies on fuel price elasticity, where in short run it was demonstrated minuscule elasticity (pay any price just to be able to drive to work), while in the long run the elasticity was moderate (effectively replacing car). You can play the same with utility curve.

"I brought the refrigerator as an example, where the utility is not increasing" You have a share of population whose fridge get broken and has to be fixed or replaced for cheaper / more expensive model. Oh, and I personally know at least two households which due to convenience have 2 fridges. (So here you are effectively claiming that something that I've seen with my own eyes is impossible)

"The purchase of durable consumption goods is, in general for several periods."

So you calculate it as ~1/10 fridge per year. And when modeling purchases of wider population, it works as reasonable approximation.

Marcin Piotr Walkowiak For years, my job has been to forecast Austrian tax revenue. For taxes on goods and services, one needs assumptions on elasticities (especially when tax rates are changed). Some of them can, in principle be statistically estimated, if there are good data. But why choose a detour via a utility function, when, I think, there is nobody who has (or behaves according to) such a function. That is simply impossible. A principal disadvantage of the utility functions compared to elasticities is they do not take into account social aspects (people consume independent of other people), whereas elasticities do. What concerns price elasticities of fuels, I am with you, but why play the game with a complicated utility function – useless. Interesting, but strange idea to put 1/10 of a fridge into the utility function. I think, you are mixing-up utility and (effective) demand and depreciation. Let’s assume a simple Cobb-Douglas function where n fridges enter with n0.1. Then 1/10 of a fridge would have 80% of the utility of a complete fridge. If this contribution is high enough for an overall utility maximum, one would want to buy one (with credit). Otherwise, there would be no purchase. Next year, again 1/10 is included in the function, again 80% utility. But you have already a fridge. There will not be a purchase - no effect on consumption expenditure, even when fridge prices were reduced.

I also know people who have more than one fridge, but I think, that e.g. a fifth or sixth will be a disadvantage (i.e. decrease utility). The optimum = maximal utility will be far below infinity.

Anton Rainer "But why choose a detour via a utility function, when, I think, there is nobody who has (or behaves according to) such a function."

I think you could try to build point that you are able to collect data good enough to estimate price elasticity, but not good enough to reconstruct utility curve, thus claim that one is clearly useful while other not specially.

(though by this reasoning one could be dismissive of basic foundations of public health as COVID-19 infection / death data collected by my government had been too detached from reality to run Susceptible-Infected-Recovered-Dead models, so I had to skip more sophisticated models and hunt for more credible proxy indicators)

However, if you try to analyze how basket of goods changes over time, then you're observing odd shifts that make more sense as shifting utility curves than simple elasticity.

"A principal disadvantage of the utility functions compared to elasticities is they do not take into account social aspects (people consume independent of other people), whereas elasticities do."

The utility function is subjective, so can accommodate fads. The only challenge would be Veblen goods, though their elasticity would be already quite peculiar.

"I think, you are mixing-up utility and (effective) demand and depreciation." No, I'm pointing differences between micro and macro scale. In micro scale indeed buying 10% of fridge would be somewhat challenging, whenever I try to do so they call security. ;) In macro scale running model which predicts on average buying 10% of fridge per household and use that to estimate changes in aggregated demand on fridges would be much more reasonable, especially when used to calculate their price as people would have much leeway in picking different models.

EDIT: Isn't combination in which people desire extra square meters and extra fridges an example of utility function?

Marcin Piotr Walkowiak You are right that one would never have enough data to estimate somebody's utility function, if it existed. I am sure that I have no such function. But if you have a utility function (for the present period), then you need no data to know it and you could tell me, at least, what sort of function it is and formulate a part of it (e.g. for handful of goods like potatoes, bread, milk, butter, juices, beer etc.).

For the 10% fridge example, let's assume a simple Cobb-Douglas function in log-form:U=constant+a1*lnc1+a2*lnc2+......+af*lncf+.... with ai "utility weights for good/service ci and f the index for fridges. If you have a certain income (or budget to spend for consumption) and given (known) prices, you can, in principle, calculate the optimal consumption bundle. Maybe, that includes 0.78 fridges. If you have already one, you will not buy another, but if you have none or the "life time" of your old one is over, you may buy a new one. When the result of the optimum calculation is e.g. 1,32, the decisions get more complicated. By the way, with non-divisible goods, the calculation of the utility maximum becomes much more complicated (too complicated to do it within a realistic time even with the best computers). Nobody would calculate utility for 10% of a fridge, although it would be possible, to calculate the additional utility.

For most goods and services, the optimal quantity is far below that without budget restriction (e.g. dU/dCi

Anton Rainer "I am sure that I have no such function." How are you going to model shifting consumer preferences with changing income and relative price levels over long time where elasticity estimated at some particular point could no longer be simply extrapolated? (like in last ~30 years Polish consumer basket of goods changed from food being something like ~40% to ~20%)

"let's assume a simple Cobb-Douglas function" I really associate that function with economic output not consumer utility function. I'm assuming you mean utility function shaped like Cobb-Douglas function just taken into multi dimension, right?

I'd say that imposing that particular shape of utility function defeats mostly its purpose and indeed it form would be pointless. Let's go back to example of optimizing your flat surface and number of fridges.

To a tiny flat you'd want to cram fridge anyway, right? Maybe just a bit bigger fridge would be suitable for small and medium flat. However, if you have huge flat, you'd buy two and enjoy plentiful storage capacity, right?

OK, that would be points where the utility function of fridges and square meters of home meets budget line. Only some combinations would be preferred.

Marcin Piotr Walkowiak , Shifting consumer preferences means changing (non-existing) utility functions. But in most articles I have read to this subject, utility functions of the (representative) agents remained unchanged for their whole life ,which for many of them lasted for a very long time ("infinitely-lived agents or households"). The most-used functions were of Cobb-Douglas or CES type. I agree that these functions are "pointless", but do you know a feasible and tractable type.

Of, course, a second or even a third fridge could be an advantage (= higher utility), but the utility of the fourth, fifth etc. is likely to become negative - even if your flat is huge and you earn enough money to buy 50 or more. That can be seen as a "proof" against Cobb-Douglas and CES, because a function with fridges (or other durables) as arguments cannot be continuous and strictly increasing (until infinity). But these are the Neoclassical assumptions (which I think are made to get a solution (calculate an optimum).