Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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How come a representative consumer with quasilinear utility need not economize?
Suppose a representative consumer has the following quasilinear utility function:
U_i(x_1,x_2)=ax_1+ax_2-(1/2)*[(x_1)^2+(x_2)^2] + k
where a>0 is a utility parameter, x_1 and x_2 are the goods, and ...
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0answers
25 views
King–Plosser–Rebelo Preferences and Additively Separable
The wiki of King–Plosser–Rebelo preferences says that the utility function has the multiplicatively separable form $$u(C, L)=\frac{1}{1-\sigma_{c}} C^{1-\sigma_{c}} v(L)$$ and "in the limit case ...
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47 views
Understanding utility function curve and marginal rate of substitution
This example appears in a different question, but there is something I don't understand.
Maybe this question is better suitated for algebra stackexchange.
John’s utility function for food (f) and ...
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1answer
42 views
Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$
I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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47 views
How are weak preferences different to strict preferences/indifference?
Given a utility function $u(\cdot)$ and two bundles $x$ and $y$.
Assuming $u(x)=u(y)$.
I am to prove or disprove that $x \succcurlyeq y$.
Now I'm confused by this.
We say $x$ is strictly preferred to $...
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2answers
282 views
Fundamental question on marginal utility
I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional "happiness" ...
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108 views
Demand for minimum of $4$ different goods
The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$.
Find the demand.
So far I have observed that it is ...
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1answer
31 views
Adding scaled CRRA utility
Suppose our utility function is the usual CRRA utility with $\gamma=2$ so that:
$$u(C) = \frac{C^{1-\gamma}}{1-\gamma} = -\frac{1}{C}$$
Now suppose there are 2 goods, A and B, available for ...
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1answer
60 views
Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation
Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$
$$
\frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...
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175 views
Economic theory journals for a refinement theorem about utility function representation
I would like to ask which are the (mathematical) economics journals that publish papers about economic theory and that focus mainly on the mathematical aspects of it. Let me be more precise. If I have ...
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36 views
Unsolveable Demand/Utility Problem?
A consume has a preference relation on $\mathbb{R}^4_+$ with a utility function defined as
$$ U(x_1,x_2,x_3)=(\ln(3x_1+2x_2+x_3))^3$$
Find the demand at prices $p=(1,1,1)$ and wage $4$.
Attempt
I ...
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1answer
34 views
Concept of Utility in demand systems
I have seen that researchers use different utility function in demand systems estimation such as Stone Geary. What is the role of these utility functions? What are utility function other than stone ...
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1answer
68 views
Utility function and homogenous of degree zero
I've a utility function which is given by
($x_i$-$b_i$)$^{c_i}$ $\sqrt{x_2}$
. What values of b and c can I input to ensure Homogenous of degree zero in prices and wealth? I think c will be positive....
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1answer
116 views
Are the goods in additively separable utility functions normal goods?
Inspired by this answer.
To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a ...
3
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1answer
106 views
Expected utility theory (Lottery notation)
A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences
$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$
...
3
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1answer
162 views
Question about Social Welfare Function and Social Profile
What are the meanings of a social welfare function and social profile? How are they related?
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1answer
56 views
Derive demand function from utility [closed]
Never encountered such a problem as I am new.
$$U(x_1,x_2)=(a\ln(x_1)+b\ln(x_2))^n$$
and $a,b,n>0$ with income $w>0$ and prices $p_1,p_2>0$.
Find the demand function.
Attempt
I am thinking ...
3
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1answer
52 views
The Price and Demand Index in Homothetic Kimball Utility
Suppose with Kimball preferences, utility $Q$ from consuming $\left\{q_{\omega}\right\}_{\omega \in \Omega}$ is implicitly given by $$\int_{\omega \in \Omega} Y\left(\frac{q_{\omega}}{Q}\right) d \...
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1answer
62 views
The Intuition of CES Utility
Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$
1 The indirect ...
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2answers
128 views
Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?
As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$:
$$
QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}
$$...
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1answer
20 views
How do I determine PED from price consumption curve with slope of zero?
Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1.
By ...
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1answer
58 views
Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?
Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income.
Now, I haven't heard of the Slutsky equation yet nor the income/...
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2answers
211 views
Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income?
I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\...
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1answer
43 views
Marginal Utility vs Cost of production
I have a confusion.
Marginal utility is always decreasing and people will not be happy to pay 2 times of price for 2 times of a coffe but I guess the price of producing 2 times of coffe will be the ...
4
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1answer
63 views
Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?
I'm studying the optimal choice of consumers with regards to taxation.
I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax:
If the ...
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2answers
39 views
Social welfare in terms of preferences
How does one define a social welfare in terms of individuals’ preferences $\succeq_i$?
If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\...
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1answer
71 views
Why is the derivative of a monotonic transformation of a utility function assumed to always be greater than 0?
I'm looking into utility functions and their relation to indifference curves.
Now, I understand a positive monotonic transformation does not change the order (it's a rank-preserving transformation).
I ...
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1answer
64 views
Demand function for partially subsumable products
I am struggling with this question that should be simple for economists (I am not an economist at all):
There is a market with a limited number of (heterogenous) consumers with two firms, each ...
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1answer
50 views
Utility maximization: pollution and housing prices
A factory releases a toxic pollutant which causes two types of damage to a representative area resident whose utility function is $U(S,H,x)= a \cdot \log(S) + b \cdot \log(H) + c \cdot \log (x)$ where ...
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2answers
66 views
Multi dimensional Auction in economics
I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
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83 views
Ordinally Separable Utility Representation
Let $X_i$ be a separable, compact, Banach space.
Definition: A weak order $\succeq$ on $X=\prod_{i=1}^NX_i$ has an ordinally separable representation if there exists $u_i: X\rightarrow \mathbb{R}$ and ...
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1answer
35 views
Trouble Understanding the Integral Underlying Random Utility Models
Given a utility function, $U_{nj} = V_{nj} + \varepsilon_{nj}$, it makes sense that we can find the probability the decision maker $n$ chooses alternative $i$ as:
$$Pr(U_{ni} > U_{nj} \forall j \...
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2answers
63 views
How are real income and utility the same thing?
The textbook I'm using, "Microeconomic Theory: Basic Principles and Extensions", treats utility and real income as the same thing in the chapters on compensated and uncompensated demand. I ...
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1answer
67 views
Modern descendants of Frank Ramsey's paper “A Mathematical Theory of Saving”?
I haven't studied economics, but I'm interested in applied ethics, and I came across Frank Ramsey's paper "A Mathematical Theory of Saving". I thought his application of calculus to a ...
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1answer
187 views
How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?
I have a question that asks:
"Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
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1answer
39 views
How to Represent as a Payoff Matrix
I'm trying to represent the following as a pay-off matrix.
I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
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1answer
69 views
Can I rename a utility function based on its properties?
A big name researcher gives a name to a specific utility function 30 years ago. Now I am writing a paper and feel that a new name might be more suited because of the properties associated with the ...
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1answer
209 views
Comparing & contrasting decision problems and normal games
I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.
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Looking for an universal utility function
I'm trying to build a computer simulation of an economy which separate simulation for each household and I'm trying to figure out what utility function should I use to model the households behavior. I ...
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1answer
97 views
Necessary and sufficient conditions for the existence of a utility function
I was reading Jehle and Reny, Advanced Microeconomic Theory, where they discuss in detail, the choice problem of a consumer. The Consumption Set (or Choice Set) $X$ is a subset of $R_+^n$, is closed ...
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2answers
235 views
Arrow-Debreu Theorem of Existence: Non satiation
Let $n$ be the number of consumers and $m$ be the number of commodities.
The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
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Von Neumann–Morgenstern implications for repeated strategic games
I am currently studying game theory and have just begun looking at repeated strategic games.
In my lecture notes, it states that "preferences are unique up to an affine transformation", ...
2
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1answer
41 views
Is there a financial hypertrophy ? Could you make a case for finance?
I've the impression that finance is in hypertrophy. But I'm not an expert on it, so I'd like those who are more knowledgeable than I am to do a [steelman][1] of it.
The things that make me thinking ...
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0answers
94 views
Social Planner problem: two period
The production function is $F(K_t,N_t)=AK_t^\alpha N_t^{1-\alpha}$ and depreciation $(\delta)$ is equal to 1. The given preferences are as follows: $$U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(...
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1answer
47 views
Lagrangian multiplier and optimal bundle
I would like to know where I am wrong (if I am) and why I am wrong here please:
If a consumer has an income of 600 euros to spend for good x (Px = 10 euros) and good y (Py = 5 euros).
What is the ...
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1answer
39 views
Marginal Utility Meaning [closed]
I'm revisiting some old topics from introductory economics and I am not quite sure I have convinced myself of the theory behind marginal utility. I have a few simple questions if anyone could please ...
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2answers
64 views
Nested/Recursive Dynastic Utility Functions
I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain ...
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0answers
21 views
functional form for a consumption shock
In a DSGE model, how can I add a disturbance/shock in the consumption of households?
For example given my utility function
$$ U(C,H) = \frac{C_t^{1-\theta}}{1-\theta} - \frac{B}{\eta} H_t^\eta,$$ ...
0
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1answer
42 views
Interpersonal comparison of utility
What are the criteria which have been proposed to deal with the problem of interpersonal comparison of utility?
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33 views
Utility function parameters
I have the following utility function:
u($x_1$,$x_2$)=($x_1$+$b_1$)$^c$($x_2$+$b_2$)$^{1-c}$
I'm asked to explain what $b_1$, $b_2$ and $c$ stand for, maybe for c is like a weight of every good. but I'...
