<p>I am looking for experiments for estimating the form a utility function of a consumer on two or more commodities. In particular, I would like to know e.g. if the utility function of a consumer is of the form <span class="math-container">$u(x,y) = ax+by$</span> (linear), or <span class="math-container">$u(x,y) = \min(x/a,y/b)$</span> (Leontief), or <span class="math-container">$u(x,y) = x^a y^b$</span> (Cobb-Douglas), or some other form.</p>
<p>I found many papers on experiments that estimate the utility function of a consumer on <em>a single</em> commodity (e.g. whether the utility is a concave / linear / convex function with respect to money), for example <a href="https://psycnet.apa.org/record/2011-03782-002" rel="nofollow noreferrer">this one</a>. These experiments usually ask subjects to compare lotteries, which is somewhat problematic since the utility might be confounded with the attitude to risk and uncertainty.</p>
<p>There are also some papers on estimating utility functions in the context of a market, via the demand function. In my use-case, there is no market, and I need to assess the utility function of consumers as individuals (not as a group).</p>
<p>What are some papers describing experiments for measuring the utility of an individual consumer, on two or more commodities, in a deterministic way?</p>

CC BY-SA 4.0
2023-10-31T10:25:31.473Z
At best, you can try to estimate preferences. Specific functional forms have no economic meaning.
Michael Greinecker
CC BY-SA 4.0
2023-10-31T11:35:50.347Z
@MichaelGreinecker that's fine. I am not looking for an exact functional form - I just want to distinguish between classes of preferences, e.g. to know if an agent's preferences are linear, Leontief or Cobb-Douglas.
Erel Segal-Halevi
CC BY-SA 4.0
2023-10-31T13:52:18.547Z
That is not a Leontief utility function.
Giskard
CC BY-SA 4.0
2023-10-31T13:58:03.227Z
Can you please clarify what you mean by "*I would like to know e.g. if the utility function of a consumer is of the form*"? Do you assume that the behavior of the real life subject will be such that it is perfectly described by one of the famous utility function classes? Or do you want to approximate their behavior, find a 'best fit' in some sense? What exactly is your goal?
Giskard
CC BY-SA 4.0
2023-10-31T15:53:51.360Z
@Giskard: fixed the typo in Leontief, thanks. For your second question: I want to find a best-fit. My ultimate goal is to develop an algorithm for fair allocation, that optimizes some function of the agents' utilities. But to do this, I first need to know the form of the utilities.
Erel Segal-Halevi
CC BY-SA 4.0
2023-10-31T18:07:42.190Z
Okay, so it seems like you need to define what you mean by best fit over functional forms? Most research picks a form and calibrates the parameters to something.
Giskard
CC BY-SA 4.0
2023-11-01T02:48:58.590Z
The health economics literature has a whole bunch of material on estimating utilities. Like standard gamble, Time tradeoff and even simple visual analogue scales.  I know this is very much a non-answer (and quite possibly not useful) but I would recommend looking at a text like this one https://books.google.ca/books?id=1oEa-BiARWUC&printsec=frontcover&dq=Multi+attribute+utility+theory+keeny&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjE-rrr5KGCAxWshIkEHR3IB80Q6AF6BAgMEAI#v=onepage&q=Multi%20attribute%20utility%20theory%20keeny&f=false
EconJohn
CC BY-SA 4.0
2023-11-02T10:01:08.080Z
You can experiment to discover indifference curves by offering people different combinations of the two commodities and see which they prefer.  You can then try to turn these into a utility function that fits the indifference curves, remembering that any strictly increasing function of a utility function is also a utility function.
Henry
CC BY-SA 4.0
2023-11-02T14:29:55.897Z
@Henry I understand the general idea, but probably there are fine details that have to be taken into account when doing such an experiment. Do you have a reference to a paper that does something similar, so that I can understand the details?
Erel Segal-Halevi
<reference-request><consumer-theory><experimental-economics><measuring-utility><empirical-methods>
Estimating the form of a utility function on two or more commodities
Erel Segal-Halevi
# Estimating the form of a utility function on two or more commodities

(Asked by: username_0 on 2023-10-31)

I am looking for experiments for estimating the form a utility function of a consumer on two or more commodities. In particular, I would like to know e.g. if the utility function of a consumer is of the form $u(x,y) = ax+by$ (linear), or $u(x,y) = \min(x/a,y/b)$ (Leontief), or $u(x,y) = x^a y^b$ (Cobb-Douglas), or some other form.

I found many papers on experiments that estimate the utility function of a consumer on *a single* commodity (e.g. whether the utility is a concave / linear / convex function with respect to money), for example [this one](https://psycnet.apa.org/record/2011-03782-002). These experiments usually ask subjects to compare lotteries, which is somewhat problematic since the utility might be confounded with the attitude to risk and uncertainty.

There are also some papers on estimating utility functions in the context of a market, via the demand function. In my use-case, there is no market, and I need to assess the utility function of consumers as individuals (not as a group).

What are some papers describing experiments for measuring the utility of an individual consumer, on two or more commodities, in a deterministic way?

**Tags:** reference-request, consumer-theory, experimental-economics, measuring-utility, empirical-methods

> **Comments:**
> **username_1**: At best, you can try to estimate preferences. Specific functional forms have no economic meaning.  
> **username_0**: @username_1 that's fine. I am not looking for an exact functional form - I just want to distinguish between classes of preferences, e.g. to know if an agent's preferences are linear, Leontief or Cobb-Douglas.  
> **username_2**: That is not a Leontief utility function.  
> **username_2**: Can you please clarify what you mean by "*I would like to know e.g. if the utility function of a consumer is of the form*"? Do you assume that the behavior of the real life subject will be such that it is perfectly described by one of the famous utility function classes? Or do you want to approximate their behavior, find a 'best fit' in some sense? What exactly is your goal?  
> **username_0**: @username_2: fixed the typo in Leontief, thanks. For your second question: I want to find a best-fit. My ultimate goal is to develop an algorithm for fair allocation, that optimizes some function of the agents' utilities. But to do this, I first need to know the form of the utilities.  
> **username_2**: Okay, so it seems like you need to define what you mean by best fit over functional forms? Most research picks a form and calibrates the parameters to something.  
> **username_3**: The health economics literature has a whole bunch of material on estimating utilities. Like standard gamble, Time tradeoff and even simple visual analogue scales.  I know this is very much a non-answer (and quite possibly not useful) but I would recommend looking at a text like this one https://books.google.ca/books?id=1oEa-BiARWUC&printsec=frontcover&dq=Multi+attribute+utility+theory+keeny&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjE-rrr5KGCAxWshIkEHR3IB80Q6AF6BAgMEAI#v=onepage&q=Multi%20attribute%20utility%20theory%20keeny&f=false  
> **username_4**: You can experiment to discover indifference curves by offering people different combinations of the two commodities and see which they prefer.  You can then try to turn these into a utility function that fits the indifference curves, remembering that any strictly increasing function of a utility function is also a utility function.  
> **username_0**: @username_4 I understand the general idea, but probably there are fine details that have to be taken into account when doing such an experiment. Do you have a reference to a paper that does something similar, so that I can understand the details?  

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