6 votes

Indifference curve - Does $dU = 0$ hold in higher dimensions? / Problem of integrability

Seems to me $dU = 0$ is true by definition unless $dU$ is not defined because the function $U$ is not differentiable in some variable. E.g. $$U(x,y) = |x| + y$$ because there are a countably ...
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  • 26.7k
6 votes

Is it accurate to state that an economist cannot assign a true numerical value for utility?

I think the Investopedia article does not use clear terminology which leads to confusion. In Economics, utility can be split across two categories as ordinal and cardinal utility. In the case of ...
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  • 43.6k
5 votes

What are the units of utility?

No, you can not really say that. Here is the reason: Utility is generally used to describe preferences. Let's say my happiness is described by this utility of chocolates: $Y(X) = X$. So, two ...
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  • 152
5 votes

How to determine if people behave optimally with a generic utility function?

There is a whole literature on revealed preference analysis that looks at the testable implications on choice (consumption) data without imposing any functional form on the utility function. Is this ...
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  • 8,642
4 votes

which type of goods maximum utility function represent?

$u = \max(x, y)$ represents the preferences over two substitute goods that cannot be consumed together. For example - tea and coffee. In the event that the consumer gets x quantity of tea and y ...
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  • 5,267
4 votes

Is addiction a case of increasing marginal utility?

To expand on @1muflon1's answer. The theory of rational addiction assumes that the utility of a consumer at time instance $t$ depends both on current consumption of the addicitve good, say $c_t$, and ...
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  • 8,642
4 votes

Is it considered acceptable or unacceptable to use currency as a measure of utility?

Utility functions as ordinarily used are not a measure of well-being comparable among people, but a representation of preferences. Moreover, preferences could principally be elicited from choice ...
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4 votes

Purpose of a monotonic transformations in utility functions

Certain calculations using utility require utility functions to have some particular properties. The point of bringing up the invariance of preferences represented by different utility functions that ...
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  • 121
4 votes
Accepted

Measuring "Intangible Utility" (reference request/methodological discussion)

This is just a follow-up on denesp's comment. In economics, the utility is a tool used to represent choices, and therefore the right way of measuring the individual's utility from listening to the ...
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  • 3,202
3 votes
Accepted

Equality of ordinal vs. cardinal utility under transformations - who made the distinction first?

It appears to be the Theory of Games and Economic Behavior (1944) by John von Neumann & Oskar Morgenstern. I have the 1953 edition which is counted as "3d", but by reading the included ...
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3 votes

What is the concept of ordinal utility?

Suppose Alex, Bryan, and Chris run in a race. Alex is the fastest and Chris is the slowest. So far I have only given you ordinal information about where they finished. I guess you'd be okay with me ...
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  • 16.6k
3 votes

Is addiction a case of increasing marginal utility?

It is possible for an addict to be rational. A famous work on this was done by Becker (1988) Theory of Rational addiction. In order for agent to have rational preferences the preferences have to ...
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  • 43.6k
3 votes
Accepted

which type of goods maximum utility function represent?

Your thinking is correct that, in some ways, $x_1, x_2$ are substitute goods. We define substitute goods which have the following property: $$\left.\frac{\partial x_i}{\partial p_j}\right|_{u=\bar u}&...
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  • 1,630
3 votes
Accepted

Computing expectation of logit error conditional on choice

Let $X_j = v_j + e_j$ with $e_j$'s being IID type I extreme. Define $$\hat X= \max \{ X_1,...,X_J\},$$ and let $\hat X_j$ be the variables $X_j$ conditional on being the max. Then the invariance ...
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  • 3,176
2 votes

Utility Function Challenge

The solution to question Your Solution is correct. To get the total differential use the following formula $$d{U} = d{f}= \frac{\partial{U}}{\partial{G_1}}d{G_1} + \frac{\partial{U}}{\partial{G_2}}...
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  • 342
2 votes

Measuring and assigning utility numbers

There are no simple methods for estimating cardinal utility (ordinal utility would be a different matter - you could just observe few of your choices). This is not because cardinal utility would ...
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  • 43.6k
2 votes

Is the expected utility the inverse of the utility function?

This is trivially not true. Consider simple example of utility: $$u(x) = x^{1/2}$$ Expected utility $E(u(x)) = E[x^{1/2}]$ Inverse utility is $u^{-1} \implies x = u^2 $ clearly generally $E(u) \neq u^{...
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  • 43.6k
2 votes

finding optimal values of quantities through utility function when MRS is 1 and price ratio is 1:2

Linear utility functions like the one you have ($U = 2X_1+2X_2$) commonly lead to corner solutions where you only buy one of the goods. You can tell that this will occur here because utility is ...
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  • 606
2 votes
Accepted

Why are there infinitely many indifference curves?

Utility is constant for all points $(q_B,q_A)$ on an indifference curve. So there is a number $u_1$ such that $$ \forall (q_B,q_A) \in IC_1: \ U(q_B,q_A) = u_1. $$ Similarly there is a number $u_2$, ...
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  • 26.7k
2 votes
Accepted

Purpose of a monotonic transformations in utility functions

Utility is subjective, and as you wrote, "it doesn't matter to us", but only to the person who orders her choices. We are not able to quantify a subjective concept like the utility of another person, ...
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  • 2,692
2 votes
Accepted

Fair value that a risk averse individual would pay to enter a gamble

Yes. In general not. Let's say the individual has initial wealth $W$ and the gamble $g$ has payouts $0$ and $G$, each with probability $1/2$. As you say, the certainty equivalent $C$ of the gamble is ...
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  • 4,589
1 vote

Is it considered acceptable or unacceptable to use currency as a measure of utility?

If you assume that agents' utility functions over pairs $(x,t)$ of consumption bundles $x$ and monetary transfers $t$ are quasilinear in money, $u_i(x,t)=v_i(x)+t$, then $v_i(x)$ measures $i$'s WTP ...
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  • 4,589
1 vote

Relationship between expected utility and independence axiom

If the preferences do not have an expected utility representation, then either the preferences are not continuous, or they do not satisfy the axiom of independence. For example in prospect theory, ...
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  • 4,158
1 vote

Anscombe and Auman Expected Utility

AA approach appears to follow two stages: first, "nature" provides which event obtains, which results in the given lottery; second, the lottery is resolved, therefore revealing the intrinsic ...
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  • 11
1 vote

Do we really need accurate utility functions?

To the extent you are constructing marginal decisions from preferences, the general answer is no. Any utility function that preserves preference orderings maps to the same partial or total order ...
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  • 1,986
1 vote

Selecting the best utility function for households

According to Wikipedia and this notes from HKU, the indirect utility function is part of consumer theory, and is defined as the maximum utility that can be attained given a consumers' money income, ...
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1 vote

Mythbusters - Determine optimal boarding strategy based on time and satisfaction score

I would start with your generic $$f(t,s) = t \times s$$ and, instead of add weights or factors to this, I would add other variables related to time and satisfaction like: boarding time as function of ...
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1 vote

How to model best combination of resources

It sounds like you could simply use the Cost Minimization Problem: $$\underset{z_1,...z_N}{min}\sum_{i=1}^N q_iz_i$$ $$s.t.\quad f(z_1,...,z_N)\geq \bar{y}$$ $$z_1,...z_n\geq0$$ Where $z_i$ and $q_i$ ...
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  • 1,548

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