Questions tagged [utility]

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

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consumption, income and utility

Question Description: Consider an economy populated by a large number of Farmers (F) and Computer Scientists (CS). Each person divides his 24-hour day into labour and leisure. If a Farmer decides to ...
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Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

If we have 2 consumers (a and b) and 2 goods (x and y) -- so we are in an exchange economy setup. From what I understand, due to 2FWT, we can choose any Pareto efficient outcome (x*), calculate the ...
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Derive indirect utility function - Problem with CES

Consider the following CES utility function for the $h$ household \begin{equation} U^h(x^h_1,\ldots,x^h_N) = \left[ \sum_{j=1}^{N} (x^h_j - \zeta^h_j)^{\frac{\sigma-1}{\sigma}} \right]^{\frac{\sigma}{\...
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Convex to origin - precise definition

This question asks about what "convex to origin" means. IMO even though there are half a dozen answers, they are all unsatisfactory. So in this question I ask for a precise definition of &...
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Finding Utility Function for Optimal Allocation in Consumer Choice Model

I'm working on a consumer choice model involving a consumer with one good and a numeraire. In this model, the price of the numeraire is assumed to be one. My objective is to identify the utility ...
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Clarifying question about utility theory and preferences

I am trying to solve this question about preferences and I got into an argument about it. I just want to make sure I am not overlooking something really simple. What can you tell about the risk ...
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What is a utility function rationalizes these preferences?

For a consumer deciding between goods A and B, with a budget of w: If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A. As the relative price of A ...
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Monotonicity of Concave Indifference Curves

I'm doing an intermediate micro course, and we've been given a problem asking to draw curves that correspond to the utility function with the expression of a circle centred at (3,4). I understand that ...
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Von Neumann-Morgenstern utility and taxes

"Consider a risk-averse individual with Von Neumann-Morgenstern utility and who invests in a risky asset. If the return on the risky asset is taxed, so the consumer has an incentive to invest ...
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How to derive the indirect utility function of $u(x_1,x_2) = x_2+ 2\sqrt{x_1}$?

I derived the utility $u(x_1,x_2) = x_2 + 2\sqrt{x_1}$ from the indirect utility $V(x_1,x_2) = \frac{y}{p_2} + \frac{p_2}{p_1}$ but cannot go the other direction without finding very complicated ...
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Proof that utility function is differentiable

after a little problem (I asked my question in the answer section, apologize, all my bad for this), I repost my question here with the same message : "I'm new on economics stackexchange, and I've ...
Economos's user avatar
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How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
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Varian Analysis Non satiation question

Consider preferences defined over the nonnegative orthant by (xl,x2)> (yl,y2) if X1 + X2 < y1+ y2. Do these preferences exhibit local nonsatiation? If these are the only two consumption goods ...
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Questions about demand curve as marginal benefit curve

I understand that the demand curve can be viewed as a marginal benefit curve in that, for a given quantity, the price needed for that quantity to be demanded will be equal to the marginal benefit of ...
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Utility functions that exhibit nonconstant elasticity of marginal utility

Consider there is a single good in the economy. The class of utility functions for which the elasticity of marginal utility $\eta$ is constant is given by $$U(C)=\frac{C^{1-\eta}}{1-\eta}$$ for $\eta&...
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Cobb-Douglas utility function

Why in Cobb-Douglas utility function, the exponents have to sum to one? Can they not be equal to 1 and why?
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Convex preference and convex utility

What are the differences between convex preferences and covex utility function? Why are convexity preferences usually represented by the quasi-concave function and not the convex function?
Huy Lê Thanh's user avatar
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Example of a utility function with cross-price effects in demand functions

I am looking for examples of utility functions where the demand function for a good does not depend solely on its own price, but on the price of the other good(s) as well. For instance, Cobb-Douglas ...
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Finding the competitive equilibrium in an exchange economy with two perfect complements

I am currently in a Microeconomics class and have come across the problem described below. I have tried to solve the problem algebraically but only get to the intercept (x1a,x2a)=(8,4). I know that ...
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Confusion on deriving Walrasian price changes using IFT

I am trying to derive price changes $$\frac{\partial x_1^*(p_1,p_2,w)}{\partial p_1}$$ for Cobb Douglas utility functions $$u(x_1,x_2)=x_1^\alpha x_2^{(1-\alpha)}$$ and I must use the implicit ...
Three Diag's user avatar
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Mixed gambles and risk aversion

The 1997 Quarterly Journal of Economics (QJE) paper titled "The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental Test" by Thaler, Tversky, Kahneman and Schwartz, says that ...
Ramandeep's user avatar
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Substitutable preferences vs. gross substitutes over indivisible items

I don't really have a background in economics. I'm trying to understand the relationship between these two terms, if they are related at all. The definitions that I understand are here: Substitutable ...
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How do I prove 2 indifference curves have the same properties?

I understand questions a) but I'm completely stumped at c). What do they mean by U'=1 having same properties as U=10?? And w,for questions b and c, what are they asking by "general expression for ...
Jess Franc's user avatar
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How special is the "expected value" operator in Von Neumann–Morgenstern utility theorem?

The Von Neumann–Morgenstern utility theorem states that For any VNM-rational agent (i.e. satisfying axioms 1–4), there exists a function $u$ which assigns to each outcome $A$ a real number $u(A)$ ...
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Relation between second-order derivatives and corner solutions

Imagine I have the simple maximisation programme: $$\max_{x,y}U(x,y)$$ $$\text{subject to: } B=x+y$$ $U(\cdot)$ satisfies the usual properties: it is increasing and concave in both arguments. This ...
ju_pi_car's user avatar
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Example of a utility function which yields inelastic demand function

I am looking for a example of a utility function which, when the utility maximisation problem is solved, results in an inelastic demand. The standard examples in textbooks always seem to have unitary ...
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Utility function for a combination of a normal good and necessary good

I am trying to formulate a decision problem for an agent involving their heating-energy consumption $c$. Let $x$ denote all other consumption. What would be a reasonable utility function to employ ...
Anthony's user avatar
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If utility function is convex, what can be said about preference relation?

It is known that if a utility function is concave, then it is quasiconcave, and the preference relation is convex. What can be said if a utility function is convex? I've found on the Internet then in ...
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If utility function is homogenous of order 1, then partial derivatives of demand function are equal

Prove that if $U(\alpha x)=\alpha U(x)$, then $$\frac{\partial x_i(p,w)}{\partial p_j}=\frac{\partial x_j(p,w)}{\partial p_i}$$ for any $i$ and $j$. I've proved that $x(p,\alpha w)=\alpha x(p,w)$, but ...
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Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent

I have been trying to use the contradiction method to prove this, but it does not seem to be working. Suppose $x^*$ is optimal in both EMP and UMP. Then $u(x^*) \geq u(x')$ for all $x'$ in $B_pw$. And ...
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Understanding consumption units normalisation by $u^\prime (c) $

It is frequently noted that if utility is given by $u(c)$, then the object $$ \frac{u(c)}{u^\prime (c)} $$ puts the utility in consumption units via the normalisation by $u^\prime(c)$. What is the ...
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Log_linearization

Can any one please suggest me how to log-linearize the utility maximization of the Ricardian households in a closed economy DSGE model. The equation is bellow :
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MCQ on income and substitution effects

Person A spends their income only on bread and cheese. Given a rise in the price of bread leaving income constant and the price of cheese constant, the consumer consumes less bread and less cheese. ...
secretrevaler's user avatar
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Change in Hicksian Demand of an Inferior Good when changing Utility

How can you rigorously show that Hicksian demand for an inferior good will decrease when utility increases? Thanks,
Peter Luu's user avatar
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How the saving rates were derived in Azariadis (1996)'s Impatience Trap?

The household maximizes his lifetime utility function according to $$ \max_{c_1, c_2} v(c_1, c_2) := \frac{1}{\beta(c_1)} \log c_1 + \log c_2 - A(c_1, c_2) $$ subject to $$ \beta(c_1) = \begin{cases} ...
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Basics of MRS. Interpretation and constant utility

I am sure this question has been asked before but I didn't know what to search for since its a quite long question. Say, I have a utility function U = sqrt(x)*sqrt(y) and the MRS = y/x. Say I have y = ...
tony13s's user avatar
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Why is monotonic preference and monotonic utility function non-decreasing?

Obviously a monotonic function can be either nondecreasing or nonincreasing: However, in Economics, a quick google search gives: I am interested in the history or the motivation behind the econ ...
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Example to Demonstrate that with Uncountably Infinite Outcomes We do not Have A Representing Utility Function [duplicate]

Suppose we define $\Omega$ = $\mathbb R_+$. The preference relation $\succeq $ is defined as $$(x_1, x_2)\succeq(y_1,y_2)\iff x_1>y_1 \text{ or } [x_1=y_1 \text{ and }x_2\geq y_2]$$ where $x_1, x_2,...
Luka's user avatar
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The sufficient condition for unique interior solution in utility maximization problem

Suppose the utility function is continuous, differentiable, strictly increasing and strictly quasiconcave. Whether the utility maximization problem has unique interior solution? If not, is there any ...
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Quasiconvexity of the indirect utility function for Cobb-Douglas utility

I've recently started Mas-Colell's, Green's and Whinston's Microeconomic Theory. In section 3.D, the authors define the indirect utility for a price vector $p$ and wealth $w$ as the utility derived ...
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Proving Expected Utility Theorem

I am struggling to understand the proof of the second step in the Expected Utility Theorem, particularly the part that deals with preferences over weighted sums of lotteries. The statement I am trying ...
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In Debreu's representation theorem of ordinal utility, is the assumption of "second countability" necessary?

Debreu's representation theorems Debreu 1959 states that: second countability, continuity, and weak ordering sufficiently implies the existence of real (continuous) utility function. The second and ...
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How to get a Certain Consumption Equivalent using Epstein-Zin preferences?

In many asset pricing models we use CRRA preferences and Epstein-Zin preferences. Let's say I have an agent that lives $T$ periods with CRRA preferences: $$ V_0 = \sum_{t=0}^{T} \beta^t \frac{C_t^{1-\...
phdstudent's user avatar
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1 answer
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How to calculate direct utility from indirect utility in this exercise?

A consumer has an indirect utility function given by $$v(p_1, p_2, R)=\frac{R}{p_{1}+p_2}$$ Where $p_1$ and $p_2$ denote the prices of the two goods consumed by the individual and $R$ the income. How ...
Arthur Pavezzi's user avatar
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How do I determine the degree of substitution affect the change in per capita consumption of a good?

Suppose there are two people living together. They have the same utility function (CES) $$u(x,h)=(x^\rho+h^\rho)^\frac{1}{\rho}$$ where $x$ is a type of good, $h$ is housing. The price of good is $p$, ...
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How to approach this problem of utility?

An individual has the following utility function: U(x, y) = 2xy + 3y, where x and y represent the quantities consumed of goods X and Y, respectively. The budget constraint is given by R = px + qy, ...
MOHAMED SALHI's user avatar
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How to find the indirect utility function and the expenditure function through this interesting utility function?

The utility function seems innocent: $u(x_1,x_2)=(x_1^2+x_1)x_2$. I want to find the indirect utility function and the expenditure function, but I've encountered some problems. Here's what I've got: $$...
Ludwig Gershwin's user avatar
1 vote
1 answer
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How do I use total derivatives of an implicit function to solve this problem?

Suppose a consumer has a utility function $u(x_1,x_2)$, where $u_1>0, u_2>0, u_{11}<0,u_{22}<0,u_{12}=u_{21}>0$. The prices are fixed. The consumer's income comes from working and the ...
Ludwig Gershwin's user avatar
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Quasiconvex and quasiconcave utility function

I saw that the model of the quasi-convex utility function is similar to the concave utility function and also the quasi-concave utility function is similar to the convex utility function. How can ...
Huy Lê Thanh's user avatar
2 votes
1 answer
372 views

Utility Maximization of a quasi-linear utility function

I am dealing with a quasi-linear utility function. For example $U=(x_1x_2)^{0.5}+cx_3$ with constrain $w\ge x_1+2x_2+px_3$.By taking c, w and p as constant, I function that by using Lagrange ...
Paul Huang's user avatar

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