Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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Demand and Utility
A consumer has an endowment vector $w$; at prices $p$ his demand for the first good exceeds his endowment; $x_1^+(p; pw)>w_1$ then a small increase of $p_1$ will lower his utility.
Logically, it ...
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Derive utility function from expenditure function [closed]
How can I obtain utility function from expenditure function e(p1,p2,u) = u*min(p1,p2)
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Utility maximization derivative calculation [closed]
What is the derivative function to solve the utility?
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1answer
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Utility functions and positive monotone transformations
We let $g(z)$ be a strictly monotonous function so:
$$\frac{dg(z)}{dz}>0$$
Consumer 1 has preferences given by the utility function $u(x_1,x_2)=ln(x_1)+2ln(x_2)$, while consumer 2 has preferences ...
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1answer
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Quadratic utility: monotonicity and risk aversion
I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility ...
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Show LNS function [closed]
O have the following utility function.
$$ u(x,y) = y- a(x -b) ^2 $$ where $a>0$
This function is locally nonsatiated. Well, in mathematical terms, how can I show it?
LNS definition
$x,y\in X$ there ...
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1answer
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Compare taxes Cobb-Douglass and more
Let a utility function for a consumer be defined as $u(x_{1},x_{2})=x_{1}^{1/2} x_{2}^{1/2}$. With the budget $x_{1}p_{1}+x_{2}p_{2}=m$. With values $p_1=p_2=1, m=32$. The state now adds a tax of unit ...
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2answers
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which type of goods maximum utility function represent?
I am not sure, which type of goods does the maximum utility function represent i.e., $U(X_1, X_2) =\max(X_1, X_2)$.
As the $U(X_1, X_2) =\min(X_1, X_2)$ represent the complementary goods, and $U(X_1, ...
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1answer
25 views
Elasticity of intertemporal sustitution with composite CRRA function
In the usual CRRA $\frac{c^{1-\sigma}-1}{1-\sigma}$ function we have that the intertemporal elasticity of sustitution $\partial\frac{c_{t+1}}{{c_{t}}{\partial r}}$ is $\frac{1}{\sigma}$.
But how can ...
2
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1answer
38 views
Proof on weak axiom of revealed preferences
I read the following statement.
ā A utility maximizer with strictly convex and strongly monotonic preferences
satisfies weak axiom of revealed preferences.ā
How can I prove or show this? I cannot ...
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1answer
26 views
Measuring and assigning utility numbers
I was recently introduced to the concept of cardinal utility. In real life, how do we assign these utility levels? For example if i wanted to assign numbers to my own utility indifference curve for ...
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1answer
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Homogeneous Utilities: Anything other than CES?
Does there exist any homogeneous utility function, i.e., $u(\lambda \mathbf{x}) = \lambda u(\mathbf{x})$, that is not a special case of the CES (or nested CES) family of utility functions or its ...
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1answer
107 views
Determining subgame perfect Nash equilibriums
Question
Three houses share exclusive access to a beach, but it is dirty due to trash washed ashore. A beach clean-up exercise costs $100$, but has a value of $200$ to each household. A clean-up ...
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2answers
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How was CES utility function derived?
Is there any book/papers that I can refer to the proof (derivation) of the CES utility function?
Or if anyone could help me with the derivation, I will be so much grateful to you.
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1answer
37 views
Solving Utility Maximization with Lagrangian
I know how to solve the 2 variable constrained optimization problem using MRS = MRT, but I also want to make sure I understand how to do it with the Lagrangian method.
So if I have the following ...
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1answer
46 views
Can an irrational function be a utility function?
Given some irrational preferences, that can be represented by a function. If the function does not satisfy rationality (transitivity, completeness), does this imply it is not a utility function.
I ...
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1answer
603 views
Mathematical Notations that I Never Understand While Reading Articles or Dissertations
I have some problems when I reading mathematical notations. For example:
$$\mathrm{E}_{0}\left\{\sum_{\mathrm{t}=0}^{\infty} \beta^{t}\left[\mathrm{u}\left(\mathrm{C}_{\mathrm{t}}, \mathrm{M}_{\mathrm{...
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2answers
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Showing utility function gives preferences that are rational and convex
Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$
Are these preferences rational and are they convex/...
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1answer
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What may the alpha mean in the context of indifference curves? How to solve such questions? [closed]
The question is as follows:
A consumer has a budget of 3000 units. He uses it to buy 2 goods: bread and cheese. Cheese costs 30 units/kg, and bread costs 3units/kg. The indifference curve is ...
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1answer
163 views
Is it accurate to state that an economist cannot assign a true numerical value for utility?
Investopedia article - What is the utility function and how is it calculated?
https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp
Article describes ordinal ...
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2answers
66 views
Marginal Rate of Substitution for perfect complements
I have come across the following problem:
Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function:
u(x1, x2) = min(x1, x2).
The solution is that ...
2
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1answer
63 views
HARA preferences details
I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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1answer
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Why utility should be bounded (or unbounded)?
For Expected Utility and SEU, people make axioms to ensure that the utility is bounded. However, I personally believe that the utility function must be unbounded, especially if we are considering ...
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2answers
52 views
indifference curve
Suppose my preferences are such that I like more of both goods, but only up to a
point. After I have 5 units of both goods, thatās as good as it gets, and Iām indifferent if I
get more.
how do u draw ...
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1answer
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Comparing utility functions [closed]
I'm doing an econ course after not having any math or micro for a few years, now I'm totally missing the basics again.
I'm wondering how to show that utility functions are an equivalent to each other:
...
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1answer
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Strictly increasing but not convex preferences
Is it possible to have preferences that is strictly increasing but not convex?
Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't ...
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1answer
45 views
The efficient frontier in mean variance criterion
The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given varianceļ¼Why do the optimal portfolios in the effcient frontier, is ...
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1answer
39 views
Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions
Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you.
If $u(x)$ is a homothetic utility, then show ...
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0answers
39 views
Quasi-linear utility. Deriving demand
I was trying to derive a general demand for the good $x$ for this quasi-linear function $u(x,y) = y + 2\sqrt{x}$ subject to standard budget constraint $p_x x + p_y y \leq M$
Using Kuhn-Tucker ...
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0answers
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MWG_3D4_C, why the solution seems in reverse?
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 is ...
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1answer
152 views
Convex Preference but Convex Utility
Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
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Marginal rate of substitution interpretation
I am trying to interpret the marginal rate of substitution stidied in an article. The article in question is Burbidge, J. B., Robb, A. L., 1980. Pensions and retirement behaviour. The Canadian Journal ...
2
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1answer
58 views
When the global optimal is outside of the constraint set, what will be the demand?
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
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2answers
89 views
What are the correct utility functions?
It is common to talk about utility functions. For example in a universe with only two goods, we might assume each person (or group of people) carries a function $u(x,y)$ in their heads. When offered ...
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How do I figure out whether the ICs are convex or concave?
Question: Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences.
(a) Sketch an ...
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0answers
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Effect of a productivity shock on the real exchange rate within a two period model
So if we have a two period model, tradable goods and nontradable goods, where consumers tend to maximize utility, then we have the following Euler equation:
$$\frac{ u' (c_1) }{P_1} = (1+r)\beta \frac{...
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3answers
105 views
Relation between demands of $x, y$ and $z$
Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such ...
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0answers
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Calculating risk interest rate within a two period model
I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility ...
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2answers
112 views
How do I solve the Envelope Theorem condition in Microeconomics?
I am preparing myself for a MSc in Economics and don't understand why, according to the Envelope Theorem, when deriving a utility function $ u(Īø, q(Īø), r(Īø)) = B(q-r) - C(\frac{q}{Īø})$, its derivative ...
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1answer
332 views
Why do many papers not write the actual utility function?
Why do many papers write the intertemporal maximisation problem for the household as
\begin{equation}E_{0} \sum_{t=0}^{\infty} \beta^{t} U\left(C_{t}, N_{t}\right)\end{equation}
and then do not write ...
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1answer
25 views
Expenditure function. Prove that this set is bounded
I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ ...
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2answers
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Is it considered acceptable or unacceptable to use currency as a measure of utility?
There will always exist at least one economist who condones measuring utility in US dollars and another who does not. However, I am wondering which way the majority of contemporary economists lean.
...
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2answers
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Prove that budget constraint is Lower Hemi Continuos (LHC)
I need to prove that the following constraint is LHC.
$B=\{x \in R^n : px\leqslant pw)$
But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
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2answers
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Remove Linear Good From Quasi-linear Utility Function
Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $
What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
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1answer
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How is the defintion of the mean preserving spread (MPS) not too general?
The mean preserving spread is defined as follows:
Consider two lotteries g and h. Let $x_g$ und $x_h$ denote the corresponding random variables. Then h is a mean preserving spread (MPS) of g, if:
$...
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1answer
45 views
Does the duality of utility maximization and cost minimization hold in practice?
I recently learned about the relationship between utilization maximization and cost minimization.
Are there studies on whether this duality holds in real life?
Any information on this topic for a ...
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1answer
75 views
Differentiability of the utility function and indifference curves
Comment on the following affirmative:
In the traditional consumer model, the hypothesis of differentiability of the utility function and of convexity of preferences, assure the indifference curves ...
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1answer
120 views
Mathematics of the income and substitution effects
I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the ...
3
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2answers
112 views
Additional components in utility functions (behavioral economics)
I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines.
For example, Thaler (1983) describes a utility function that could be ...
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0answers
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What would we say on the utility of risk and its consequences?
Anything has its risks and anything has its utility or desutility. The risk aversion causes a looking for safer alternatives in the market which maximizes utility in a trading off between risk and ...
