Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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Solve consumer’s problem [on hold]
Suppose a consumer consumes three goods, his utility function is given by $$u=min\{x+y,x+z\}$$
Solve the consumer’s problem i.e. find the optimal consumption bundle. No other information is given in ...
3
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1answer
55 views
Why Certainity Eqivalence in PIH only holds for quadratic utilities
In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was ...
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How do I perform utility transformations on a function to match given functions in this specific example? [closed]
EDIT: Corrections were made to the problem and now this question is irrelevant. Sorry if this took up anyones time.
We're given a list of functions in which one of the functions has the same ...
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1answer
49 views
Can a continuous preference be represented by a discountinuous function?
I can think of some examples, but what can be an outline of the proof?
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Image of binary relation
From the book:
"a binary relation $R$ associated to each element $x$ of $X$ some elements $y$ of $X$. We denote by $R(x) = \{y \in X : x R y\}$ the image of $x$ through $R$"
but then is an example:
...
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1answer
27 views
Exercise where lagrangian is needed?
I teach a general equilibrium class in my university and I want to have an exercise that is not too difficult where the Lagrangian multiplier is needed. I was under the impression that with Cobb ...
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0answers
17 views
Optimal trajectory of consumption/leisure/work and path integral (variational calculus) approach to total lifetime utility maximization?
Is there connection between the total lifetime (discounted) utility maximization and path integral (functional integral, Feynman integral, variational calculus) approach to the selection of optimal ...
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Quasi-linear Optimal Consumption Bundle
I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by
$$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$
and $p_1 = 8, p_2 = 4, I = 30$.
What I have so far ...
0
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1answer
50 views
Calculating income and substitution effects
Consider a simple quasi-linear utility function of the form $U(x,y)=x +ln(y)$. For this problem, assume
that you have “enough” income, so that the optimal consumption bundle is where: $x,y >> 0$....
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0answers
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What is the difference between $>$ and $≻$ in microeconomics?
As far as understood from the textbook the $≻$ (succeeds symbol) represents the preference of a consumer and the $>$ (greater than) is used to represent a number value (such as the utility). Is ...
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1answer
47 views
Prove that $u$ is a utility function for $\succsim$
If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$.
Is it sufficient to prove that the ...
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1answer
42 views
The relationship between indirect utility and expenditure functions
I am trying to understand the fact that $e(p, v(p,y)) = y$. There is a proof in the text Advanced Microeconomic Theory (Jehle and Reny) that states the following:
Because $u(·)$ is strictly ...
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1answer
46 views
Proof that utility is nonincreasing in prices
The following is a proof that the indirect utility function is nonincreasing in prices, but I can't understand the last step. How do they conclude that $v(p_1, y) \ge$ from the previous reasoning?
...
2
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1answer
41 views
Existence of maximum utility with two bads
I am working with a consumption set $X = R_+^2$ and preferences that are complete, transitive, continuous and strongly monotonically decreasing. The economy is characterized by the presence of two ...
1
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1answer
40 views
What is the concept of ordinal utility?
I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used.
If that is so, how can one define a mathematical function for utility which gives a ...
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0answers
26 views
Non-existance status of differences in utility
Suppose that you have four alternatives and $u(x)-u(y)$ vs $u(x')-u(y')$.
Is this a meaningful comparison?
If for example we discover $u(x)-u(y) \ge u(x')-u(y')$,
somehow there is an ...
2
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2answers
49 views
Ruling out boundary solutions in Utility Maximization
Solving the basic Utility Maximization Problem, i.e.
\begin{align}
max_{x\geq 0} u(x) \\
s.t. \,\,\, p^Tx\leq w
\end{align}
we get the Kuhn-Tucker first order condition
\begin{gather}
\frac{\...
4
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2answers
58 views
A question about Lagrange multiplier(when $\lambda=0$)
I need help in a maximization problem(finding the optimal investment portfolio).
where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars.
$C^s$ is consumption (or wealth) of an ...
1
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2answers
195 views
hicksian demand of perfect complements [closed]
As the title states, I want to know how to derive the hicksian demand of perfect complements $\text{min} \, \{x1,x2\}$. Thanks in advance.
Also, no price is given, or budget. my main question is ...
0
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0answers
33 views
Consumer Theory - Utility / Costs / Preference
I have the following question:
Violet buys two goods, toys and pens. We do not observe her preference but we
know it satisfies the three assumptions, completeness, transitivity, and more is better. ...
3
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2answers
75 views
Continuous function in microeconomics
In the following picture two preference relations are defined -
Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. ...
3
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1answer
44 views
quasiconcave vs convex function
I have been struggling trying to understand the difference between a quasiconcave and a convex utility function. As far as I understand a function can be both at a certain point, but is not clear to ...
3
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1answer
60 views
separable utility function and cross price effect
Suppose that consumer's utility function for three goods is separable, that is,
$U(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ ...(i)
where $f_i$ is increasing and strictly concave, i=1,2,3. ...
1
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1answer
15 views
advanced mathematical treatement of revealed preference and utility theory?
I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel.
What would be suggestions for this? Specifically I'm interested in conditions ...
3
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1answer
52 views
Interpretation of Interesting Utility Function
Solving introductory microeconomics problems I have come across the following type of utility function:
$$ f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{...
2
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1answer
72 views
Lagrangian: when to discount budget constraint?
I am getting a bit confused about setting up the Lagrangian in intertemporal constrained optimization problems. The confusion is as to when is the one-period budget constraint multiplied by the ...
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2answers
56 views
What is a good way to generate realistic utility curves?
I am aiming to program a basic simulation of a simplified economy to look at the impact of various interventions.
The economy will have N groups of homogeneous consumers and M producer / employer ...
0
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2answers
56 views
Utility and consumption tax
If I have a model with taxes on consumption denoted $\tau$ should I write the utility function as $u(c)$ or $u((1-\tau)c)$? Thanks
3
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3answers
75 views
modelling disutility from over consumption
In introductory economics courses the concept of marginal utility is illustrated through simple examples like how much benefit one gets from eating another slice of pizza (i.e first slice provides 100 ...
0
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0answers
18 views
Is delivery-capability (in economics) a probability?
A dealer with a large, but finite stock counts for 1 year
a = the number of all purchase inquiries that reach him this year
and
b = the number of purchase inquiries that he can deliver on the ...
0
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3answers
102 views
Is the utility of money *actually* logarithmic?
Apologies for asking what is probably a basic question from someone that is not in the economics field.
But I was playing around with the idea of determining how a group of people could split a bill ...
2
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0answers
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Finding savings in an Overlapping Generations model
I have not seen this question asked anywhere, so I'm posing it here in case anybody else (hopefully) can help me get to the answer. In a nutshell, my question is: how do we arrive at the saving ...
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0answers
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Relation between Epstein Zin and Power Utility
I found this graph in Campbell and Viceira 2001 at page 35-36 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Campbell_Viceira.pdf) which is used to explain the relation between Epstein-...
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0answers
25 views
survival probability and integration by parts
I am trying to integrate by parts by using an indicator function. However, I am not really sure if it is a correct way to change the bounds of integral with indicator functions. I am trying to deal ...
2
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0answers
33 views
The use of preference relations in choice theory and the $\succsim$ symbol
At least as from Edgeworth and Pareto we think about utility in mathematical terms. My question twofold
(i) about the start of the usage of binary relations to model preferences in economics, and ...
2
votes
1answer
38 views
Construct utility function for a risk-averse agent
I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
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1answer
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Would a very cheap renewable energy source be harmful economically?
This question is not on whether these devices work or not but so much as if they did work. What if electricity can be made so cheap that everyone could afford it ti the point there was no demand for ...
2
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1answer
37 views
Continuation value versus utility in asset pricing
Is there a difference between continuation value ($V_t$) and utility ($U_t$) except for a possible scaling / difference in units? My question refers to the consumption-based asset pricing literature.
...
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Utility and functions
A text I read posits that utility functions tend to be unstable, if the utility people draw out of goods depends on the consumption of the particular comparison group. Can you explain why this ...
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0answers
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Production choices in Hayek's theory of information-bearing prices
As I understand the work of Hayek, he asserts that prices encapsulate the true societal worth of the item being sold by integrating the compound need for all of the ingredients and work which go into ...
4
votes
1answer
64 views
Relative risk aversion, a property of period or lifetime utility
This question is to be understood in the context of consumption based asset pricing.
I'm wondering whether relative risk aversion is a property of the period utility function, which is simply a ...
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0answers
26 views
Deriving Single Good Demand Curve
came across a problem set that I had no clue how to tackle, but looks painfully simple.
It's a market for electricity where households utility is represented by:
U(E) = aE - 2mL2 (Household Utility)
...
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0answers
32 views
Natural borrowing/debt limit and other borrowing constraints
When confronted with the simple household consumption maximization problem under uncertainty (and with Arrow security sequential trading)
$$\max_{\{c_t(s^t),a_{t+1}(s^t,s_{t+1})\}_{t=0}^{\infty}}\...
1
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1answer
49 views
Do we really need accurate utility functions?
Knowing that a utility function's primary purpose it to be used as a tool to rank consumption bundles, I was wondering:
"do we really need to be concerned with accurate identification utility ...
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0answers
16 views
Lender Return/Contribution per loan as function of Borrower score
I have been browsing existing economic/financial economics literature looking for a model of a lender's profit (return /contribution) per loan as an explicit function of the loan amount and borrower's ...
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1answer
84 views
Utility Maximisation Subject to Income and Time Constraints
The consumption of economic goods often takes time. Consider, for example:
Transport services, eg flights, rail journeys;
Leisure goods, eg watching a film, visiting a park.
I would like to explore ...
4
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1answer
103 views
Money Metric Utility Function: Budget constraints become Utility Functions?
Im currently reading up on the "money metric utility function" (also known as the minimum income function or direct compensation function).
By definition it is defined as:
$$m(\text{p},\text{x})\...
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1answer
57 views
Compare utility functions
I recently joined an econ class. I am so lost on how to prove their equality. As a math standpoint, these are completely different equations. Please help!
...
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1answer
29 views
Characterising utilitarianism and altruism in economics
This question is a quantitative analogy to this question on philosophy.SE. Within the framework of economic decision-theory using utility functions, how do you characterise the moral principles of ...
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1answer
114 views
Maximization with disposable income
Consider a welfare system u dear which a single cash transfer(guaranteed income ) is given to every citizen. Then for each dollar the person earns the payment is reduced to by a where 00 you get a ...
