Questions tagged [utility]

Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.

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4
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2answers
1k views

Do discontinuous preferences imply no continuous utility function?

I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function. I know that you can represent continuous ...
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1answer
421 views

Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth

I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), ...
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1answer
211 views

Preorder and multi-utility function

Let $\succeq$ be a preorder, i.e., it is reflexive and transitive on $X$. Prove that there exists an index set $N$ and a multi-utility function $u:X \rightarrow \mathbb{R}^N$ such that $x \succeq y$ ...
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1answer
115 views

Consumer utility optimization question

I am having diffculty with this question: Can we proceed using Lagrange here since the utility function is convex, or do we have to treat them as perfect substitutes? If latter or any other method, ...
2
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2answers
343 views

CRRA utility function with a scale parameter

I am wondering if it is possible to write down a following CRRA utility function ; $$u\left(c(t)\right)=a\frac{c\left(t\right)^{1-\sigma}}{1-\sigma}$$ where $a>0$ is a constant scale parameter. I ...
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1answer
3k views

Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
5
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1answer
152 views

Interpretation of utility function

I am reading Lucas (1980) and I am a bit confused about the way he formulates the utility function. So there is one non-storable good that comes in $n$ colours and one unit of labor produces $y$ ...
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1answer
472 views

Specification form for household utility function

What determines the choice of the functional form to be adopted for the household CRRA utility function, when utility depends on consumption and leisure? For examples, we have these three functional ...
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1answer
70 views

What is one dimensional, ordered type?

I am reading papers about moral hazard. What is one dimensional, ordered type $\theta\in\Theta$? What is one dimensional, not ordered type $\theta\in\Theta$? Could you please give an example? ...
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0answers
44 views

Terminology for separability in price and value

Take an agent with mean-variance utility over something that is uncertain: $$ U(x) = \mu_x^\theta - \sigma_x^\lambda $$ $A\in \{0,1\}$ happens if $U(x)>0$, and $x$ is a random variable $$ A = \...
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2answers
177 views

Equivalence of definitions of continuity [closed]

One of the definitions of continuity is that the Upper Contour Set and the Lower Contour Set are closed. I am trying to show that if preference is continuous and $x>y>z$, then there is some $\...
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4answers
172 views

Examples of behavioural breakdowns in game theory?

I'm trying to compile multiple scenarios of the breakdown of game theory. Specifically, I'm looking for scenarios where game theory predicts certain behaviours, but in real-world scenarios or ...
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1answer
39 views

Optimal taxing in case of negative externalities

Suppose an individual $i$ has the utility function $U= f(x(i)) - k$(sum of all $x$ with index not equal to $i$) Where $x(i)$ denotes the miles driven by $i$, and $k$ is a positive constant. The ...
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1answer
353 views

Different terminology for discrete vs. continuous “marginal” concepts?

e.g. Marginal Utility. If the good you're consuming is discrete, like "slices of pizza eaten", then authors (or at least the author of my textbook) talk about Marginal Utility at each quantity eaten ...
2
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1answer
93 views

Is comparative advantage only beneficial with convex utility functions?

I've been playing around with the numbers associated with the traditional comparative advantage problem provided by Ricardo. (https://en.wikipedia.org/wiki/Comparative_advantage) I looked at ...
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1answer
8k views

How to derive utility function from indirect utility in this exercise [closed]

Derive the consumer’s direct utility function if his indirect utility function has the form $$v(\boldsymbol{\mathbf{p}},y)=yp_1^\alpha p_2^\beta$$ where $\beta ,\alpha$ are negative.
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1answer
2k views

Link between elasticity and marginal utility

The above is taken from "Economics" 8th Edition by John Sloman, a textbook commonly used at the introductory undergraduate level. I would like assistance in understanding the bracketed portion - how ...
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1answer
184 views

Show result is the same with two utility functions [closed]

How do you show that the utility function $$U = (X + A)^p (Y + B)^q$$ gives the same result than $$ U= p \log (X+A) + q \log (Y+B) $$
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1answer
54 views

Confusions about calculations in Utility Theory Paper

Recently I was improving my knowledge of Utility Functions in finances. I stumped upon very nice (yet quite old) article: "An Introduction to Utility Theory" by John Norstad (1999). What drove my ...
2
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2answers
538 views

Preference for consumption smoothing and actual smoothing

The typical dynamic consumption-saving under certainty model can be written as: $$ \max V(c)=\sum_{t=1}^{T} \beta^{t-1}\; u(c_t) $$ Subject to the intertemporal budget constraint $$ \sum_{t=1}^{T}\...
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1answer
98 views

how to raise utility of an individual having min utility function

I was doing an exercise of utility and got confused with a min utility function. endowments can redistribute among individuals. How am i supposed to increase his utility. Can i simply reduce the ...
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1answer
37 views

Revealed preferance: elementary question

When the market prices are Rs 5 per apple and Rs 6 per orange a person buys 16 apples and 28 oranges. When the prices are Rs 4.4 per apple and Rs 6.4 per orange ,the person buys 20 apples and 25 ...
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1answer
309 views

Troubleshooting Utility Maximization with the Lagrange Method

I'm trying to solve a utility maximization problem through the Lagrange method. The utility function is something like $u(x,y)=x+B(y-a)$. However, I'm running into problems as x and y do not come up ...
3
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1answer
2k views

Positive Monotonic Transformations and Nested Functions

Suppose there is an economic agent with the utility function $u(x,y)$. A second agent has the utility function $h(g(f(u(x,y))))$. Am I correct in thinking that if $f'(x)>0$, $g'(x)>0$, and $h'(...
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1answer
2k views

Are lexicographic preferences strictly monotonic?

I'm a bit confused about lexicographic preferences and whether they abide by the strict monotonicity axiom. The definition we were given for strict monotonicity is: For any two bundles $x$ and $y$,...
2
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2answers
758 views

Lancaster's Characteristics Theory

In 1966 Kevin Lancaster proposed a new Economic Theory based on product characteristics instead of product utility. I would like to know the status of this theory nowadays among economists ...
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1answer
235 views

How to derive the demand function of $U(x_1,x_2)=x_1-x_2$

I'm trying to find the uncompensated demand function. How would you do that, when I have the following utility function $u(x_1,x_2)=x_1-x_2$, and the budget constraint $p_1\cdot x_1+p_2\cdot x_2=p_1\...
2
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1answer
1k views

General equilibrium regarding on U= max(ax,ay) + min(x,y) [closed]

Please kindly instruct me on solving the following in a general equilibrium framework with standard budget constraint, $$ u^{1}\left ( x \right )= max\left [ \frac{x_{1}}{10}, \frac{x_{2}}{10}\right ]...
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1answer
104 views

Additive multiattribute nonlinear utility functions

I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form: $u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \...
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3answers
129 views

Maximize utility given an arbitrary number of goods and the condition that exactly X number of items must be bought

How does one maximize the utility given some budget restriction, an arbitrary number of different goods (with varying utility and prices) and the added condition that exactly X number of items must be ...
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1answer
328 views

Setup and solve utility maximization

A consumer wants to maximize his utility function $U(X_1,X_2)=Min(X_1,X_2)$. The price of $X_1$ is 2 and the price of $X_2$ is 4 and his income is 40. Setup the utility maximization problem and solve ...
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0answers
257 views

Fisher Separation with negative interest rate

In class we discussed Fisher Separation which states that the investment decision is independent of the financing decision. The optimality conditions are that MRS = MRT = (1+i) (i = interest rate). ...
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1answer
799 views

Preference ordering relation

≳ is a preference ordering if it is reflexive , transitive and complete. In Mathematics relations are said to be in a equivalence relation if they are reflexive, symmetric and transitive. Can we ...
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2answers
628 views

Do contemporary Marxist economists still deny the utility/value theory which underpins classical economics?

Do contemporary Marxist economists still apply the labor theory of value when analysing economic phenomena? Or do they e.g. acknowledge that value (and utility) is subjective as is common knowledge in ...
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1answer
989 views

Finding a walrasian demand function

If I have a sum utility function like this $U(y) = \sum_{j=1}^J u(y_j)$ where $u$ is convex. Is there then a way to find walrasian demand for such a function without using calculus or do you need to ...
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1answer
302 views

Implication of first-order stochastic dominance

Use the utility index $U(x) = x$ to prove that if the distribution of $F$ first-order stochastically dominates distribution $G$, then the mean of $x$ under $G$ cannot exceed the mean of $x$ under $F$. ...
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0answers
120 views

Consumer's maximization problem

I am an undergrad trying to learn the basics of NK models (on my own) and I am having some difficulties understanding the derivation of certain equations. So we have the representative household ...
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1answer
46 views

Finding the minimum and maxium price given utility index [closed]

Say you have the expected utility index $U(Y ) = \sqrt{Y}$ and an initial wealth $Y = 10$. Consider the lottery with a payoff of $10$ with probability $\pi\in (0,1)$ and a payoff of $5$ with ...
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1answer
82 views

Research on the existence of utility functions?

I've been having difficulty finding some research on indifference curves/utility functions and methods in constructing them in an applied manner. Does anyone have any papers or pdf books to ...
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1answer
2k views

“Elasticity of marginal utility of consumption ( μ ) with respect to utility.” (Green Book quote)?

In the Green Book (page 97) it is stated "the elasticity of marginal utility of consumption (μ) with respect to utility". What is it? Is it an error ? I always heard of the elasticity of the marginal ...
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2answers
308 views

Budget constraint with leisure and consumption

I am given the following utility function: $u(x_{1}, x_{2})=x_{1}^2x_{2}$ where $x_{1}$ represents leisure and $x_{2}$ represents consumption. I am also given the budget constraint with the price of ...
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0answers
39 views

General equilibrium allocation with “altriustic” utilities

Has any work been done on market allocations where market participants have utility functions that depend on other players' allocations? For example, suppose I have a general equilibrium model with ...
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0answers
456 views

What is the difference between utility function and characteristic function

I read that normative theories such as social welfare and game theory have as tasks computing the peoples' (average) utility function in the first case, and the characteristic function in cooperative ...
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3answers
333 views

Consumer preferences

I want to know under what preferences relation will I not want to consume all of my budget. Because if my preferences are strictly monotonic, strictly convex or convex, even LNS or continuous. I would ...
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1answer
141 views

Does the utility function U(X, Y) = 12x^0.2 y^0.8 represent homothetic preferences? [closed]

Does the utility function U(X, Y) = 12x^0.2 y^0.8 represent homothetic preferences? I was given this question but I have no idea how to work it out. I understand what homothetic preferences are in ...
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1answer
4k views

Quasi-linear utility functions

I have the following quasi-linear utility function given: $u_0 = f(x_1) + x_2$ (with $f'>0$,$f''<0$). I know that the indifference curves are vertically parallel, which means that the slope is ...
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1answer
3k views

Using the Slutsky equation

Suppose we have utility: $$U(x,y)=x^{0.5}y^{0.5}$$ Then Marshallian Demand for good $x$ is: $$x(p_{x},p_{y},I)=\frac{0.5I}{p_{x}}$$ And Hicksian Demand for good $x$ is: $$x^{c}(p_{x},p_{y},U)=p_{...
9
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2answers
888 views

Thin indifference curves

If a consumer follows the rationality axiom of continuity (i.e. no jumps in his preferences), the indifference curves of a utility function are said to be thin. Why does continuity ($x \succeq y \...
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1answer
2k views

Proving existence of utility function

In Advanced Microeconomic theory by Jehle and Reny there is a proof of the theorem which states the existence of utility function. In order to prove the existence of a utility function $u(\mathbf{x})$...
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1answer
373 views

maximize untility AND minimize disutility

DISCLAIMER: This could very well be all bogus, I'm talking about my intuition as a beginner/intermediate economics student, you have been warned. I got the feeling agents do not just maximize utility ...

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