# Questions tagged [utility]

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

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### Given an MRS how to be better off

Let's assume we have 2 agent A and B. A has n good x and m good y and B has a good x and 2a good y. If we know their MRS's at their current bundles how can we offer them a trade that makes both of ...
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### How to calculate CRRA bounds from Holt and Laury (2002) type lottery?

Lottery is between: Option A: a certain choice of £5 Option B: £10 with probability 0.1 and £1 with probability 0.9 The probability of receiving £10 increases in each subsequent choice. How do I ...
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### How can I prove $U(x) = [𝛼_1𝑥_1^𝜌+𝛼_2𝑥_2^𝜌]^{(1/𝜌)}$ is equal to Cobb-douglas Utility function when $𝜌\rightarrow0$ [closed]

This is the question, I have problem with part b, I don't know what function should I use to reach the result thanks in forward
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### Does utility in economics also refer to producer's surplus ? How to balance the consumer surplus and producer surplus?

I am confused about the use of utility in economics and how it relates to allocative efficiency. At 4:35 and 5:07 in this video (https://www.youtube.com/watch?v=9a3wXj1o91k) he talks about how at the ...
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### Prove this indirect utility function is quasi-convex

The indirect utility function is as follows: $$v(m,p) = \frac{m}{p_{1}^{1/2} p_{2}^{1/4} p_{3}^{1/4}}$$ I need to prove that it is quasi-convex. I tried both definition of a quasiconvex function ...
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### Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour

While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
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### Why are interpersonal utility comparisons not possible

Why is it not possible to compare utility across individuals? Is this only impossible when we consider ordinal utility where we have no numerical unit?
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Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies: \begin{align} &1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\... 2answers 74 views ### Prove quasi-concavity of utility function [closed] How do you prove from definition (no Hessians) that U(x_1,x_2)=x_1^2 x_2 is quasi-concave? 1answer 35 views ### How can I prove ∇U(x).D_m x(p,m)= \text{shadow price}? Why inner multiplication of the gradient of utility function in derivative of demand function with respect to income is equal to shadow price? This is the equation which is given but I don't know ... 1answer 106 views ### Does quasi-concave utility function imply convex indifference curve? It is well-known that convex indifference curve (i.e. the function is convex)/ preference would imply quasi-concave utility function. But does quasi-concave utility function imply convex indifference ... 1answer 52 views ### How to prove the relationship between the expected value of a lottery and its certainty equivalent? Utility function u(x) is monotonic. I want to prove that u(x) exhibits risk aversion if and only if for all lottery F: E(x) \geq CE(F,u) (CE is certainty equivalent). (Definition of CE: the ... 2answers 99 views ### Are there any examples for u(x_1, x_2) = \max\{x_1, x_2\} in real word? I know how its graph looks like, and it's like when you want to choose between 2 inferior goods you choose the cheaper one so you can have more, but is there another examples? 1answer 62 views ### A question about the property of quasi-linear preference In case of quasi-linear preference, why would one unit more of the numeraire good (good 1) give the same additional utility as spending an additional amount of wealth equal to the cost of one unit of ... 2answers 49 views ### Why is the nature of graph of utility function different from indifference curve? I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that ... 1answer 89 views ### A question about MWG Exercise 3.D.4 I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...). It is about exercise 3.D.4, the full statement of the exercise ... 0answers 35 views ### Does quasilinear preference contain rationality, monotonicity or other assumptions? I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on (-\infty,\infty)\times R^{L-1}_+ is quasilinear with respect to the first ... 1answer 79 views ### Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation? Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer: Suppose we have a preference ordering \succeq, which is ... 1answer 38 views ### How to find change in the optimal choice with a utility function in general form? Suppose the utility function is represented as U(x_1,x_2;I), where I is the level of information the consumer possesses. How to find the change in the optimal choice of x_1 as price of x_1 ... 1answer 38 views ### Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences? According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ... 2answers 260 views ### Finding demand functions for an unusual utility function I have a utility function: U = x + \min\{x,y\} I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ... 1answer 55 views ### Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete? According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ... 0answers 45 views ### How to prove that the walrasian demand function x(p,w) is continuous in p and w? If the utility function u is continuous and satisfies local nonsatiation, and walrasian demand function x(p, w) is a function (i.e. always map to only single values), how to prove that x(p,w) is ... 1answer 40 views ### Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle? In the context of Walrasian demand: Suppose u is continuous, satisfies local nonsatiation, and is strictly quasi-concave, each w(p, x) contains a single consumption bundle. The proof I got from a ... 1answer 32 views ### Deriving demand function in case of multivariable utility functions with min and max structures Suppose I have utility function like this: u(x_1,x_2,x_3)=min\{x_1,a-x_1\}\times min\{x_2,b-x_2\}+x_3 where a and b are real numbers and x_1\in [0, a] and x_2\in [0,b]. What will be a procedure ... 2answers 113 views ### Algebraic approach towards convexity I have a function:  u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex. 1answer 41 views ### Why does quadratic utility function imply \mu-\sigma preference? Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply \mu-\sigma preference? 2answers 118 views ### Utility function_maximazation [closed] A consumer is deciding about her hours (h) and consumption (c), her preference over bundles of work and consumption are as follows: U(c,h)= c + \sqrt{24-h} The consumer would get an hourly wage ... 1answer 30 views ### Is there any evidence for consumer utility-maximising behaviour, at individual or market level? Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence. Is there any evidence that some consumers do ... 0answers 44 views ### derive value function from utility function We have the utility function.U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}}) And I am trying to find the value function. $U$ is utility function. $c_t$ is consumption at ...
I have utility function given by: $U(x_1, x_2) = \begin{cases} x_1+x_2 & \text{if$x_1+x_2<6$} \\ 6 & \text{if$6\...
In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?