Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
694
questions
3
votes
1
answer
54
views
What is the economic intuition of prudence in the static case?
How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)?
I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
- 43
1
vote
1
answer
25
views
Has the Arrow-Pratt measure a lower bound with DARA utlity?
Say I have the following utility function:
$$u(x,w)=f(w+x)$$
This utility exhibits decreasing absolute risk aversion ($f'>0$, $f''<0$ and $f'''>0$). $x\in R_+$ is the control variable and $w\...
- 43
2
votes
0
answers
30
views
Which utility functions generate constant (but arbitrary) price/income elasticity of demand functions?
I want to estimate a demand function, and for convenience, I would suppose it has constant price and income elasticities: $\varepsilon$ and $\eta$, let's say. That is, demand $x_i(p, w)$ would be ...
2
votes
1
answer
24
views
Prove strict monotonicity of utility function
I have the following utility function: $$ u(x_1, x_2, x_3) = med(x_1, x_2, x_3) $$ Given that $UMG_{i}$ ≥ 0, the utility function represents a strictly monotonic preference. Does this assertion make ...
3
votes
2
answers
104
views
What is the budget constraint when we assume a common utility function?
Let's consider an exchange economy with two identical consumers. The
common utility function is:
$$u^i (x_1, x_2) = x_1^α x_2^{1-α} \;\;\; \text{for} \;\;\; 0 < α < 1.$$
Society has 10 units of ...
2
votes
1
answer
54
views
Willingness to sell a lottery ticket vs. willingness to buy a lottery ticket
I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would ...
- 31
2
votes
1
answer
39
views
Linear Engel Curve
How to prove that if the Engel curves (expenditures as a function of wealth) are linear in wealth, then the indirect utility function has the form $v_{i}(p,a_{i})=\alpha_{i}(p)+\beta(p)a_{i}$ for an ...
- 21
3
votes
1
answer
58
views
Universal Basic Income (UBI) policy proposals optimal hours worked and consumption
can someone please help me check my work for this question? I want to make sure I did it correctly.
Question:
Work:
0
votes
0
answers
15
views
What are the conditions to determine whether demand function is rationalizable?
A consumer chooses a bundle (z, z, . . . , z) where z satisfies $z Σp_k = w$.
The book (Rubinstein's) states that the demand function x(p,w) can be rationalized if there exists a preference such that ...
2
votes
2
answers
85
views
What does it mean if the derivative of the Utility function (at the optimal bundle) is 0?
It states in my book that under strict monotonocity, the derivative of U(x*)=0 can be possible although it's unlikely to happen.
What does this exactly mean?
0
votes
0
answers
36
views
What does differentiability of Utility function at an optimal solution x* mean?
I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other ...
1
vote
1
answer
70
views
Help with checking work for preferences over consumption and leisure question
I was wondering if anyone could help me check my work for the following question, and if I am wrong, help me correct my mistakes?
Question:
Work:
-1
votes
0
answers
35
views
Help with checking work for utility preferences question
I was wondering if anyone could help me check my work for the following question, and if I am wrong, help me correct my mistakes?
Question:
Work:
Part a.
Part b.
1
vote
1
answer
24
views
Are homothetic additively separable preferences always equivalent to CES?
Are homothetic additively separable preferences always a monotonic transformation of CES preferences?
In technical language, the question is the following:
Let $n>1$, and let $f:\mathbb{R}^n_{\ge 0}...
- 222
0
votes
1
answer
35
views
Can strict preference be represented by Utility function if not complete?
The definition states that a Utility function represents the preference relation because the relation on R satisfies transitivity and completeness. Yet, strict preferences (and indifference ...
1
vote
2
answers
187
views
What is an example of utility function where the proportion of one goes to zero?
I would like an example of an utility function with 2 goods where the proportion of one goes to zero (and the other goes to one).
I am thinking of a problem where the household receive an endowment y ...
2
votes
1
answer
52
views
Can a preference relation not satisfy monotonicity and still be represented by an Utility function?
The book I am working with (Microeconomics Theory by A. Rubinstein) states that:
"In the case that preferences are represented by a utility function, preferences satisfying monotonicity (or ...
1
vote
1
answer
32
views
Can the following statement be rationalized if it yields a choice function?
A person choose an alternative to maximize another person's suffering.
I thought we could define a sort of relation where the person suffers more from x than y. And if we can always do this, we can ...
1
vote
1
answer
27
views
Can the following behavior be rationalized if it yields a choice function?
The decision maker has an ideal point in mind and chooses the alternative closest to it.
I am not sure if I am right, but in order to rationalize it, we first have to construct a choice function. So, ...
3
votes
1
answer
86
views
Kuhn-Tucker(KT) conditons EMP
How should I formally solve the expenditure min.problem (EMP) by using KT conditions?
Since I should follow the notation of the Mas-Colell, I should write:
$\min~$ $p \cdot x$ , s.t. $u(x) \ge u$
...
- 71
0
votes
0
answers
36
views
Why does SoCalGas use a commodity price that is currently 10X the market?
SoCalGas charges separately for transportation, taxes, and commodity. In January 2023, SoCalGas's commodity portion was \$3.45 per therm, or $34.50 per million BTU. But the US wholesale price in that ...
- 101
0
votes
1
answer
99
views
Quasiconvex Constraints in Maximisation
Why do we have to have Quasi-convex Constraints for constrained maximisation? I think i'm missing something pretty simple as this feels like a basic question:
My current Logic: If both the objective ...
- 343
2
votes
1
answer
72
views
Quasi-convex constraints using monotonic functions
I believe i have a major misunderstanding surrounding quasi-convex constraints in maximisation, when using monotone functions. Can you help me spot my errors please?
The definition of a quasi-convex ...
- 343
0
votes
0
answers
27
views
how to solve two period uility funcion on DSGE model, or if not how to solve it using other model?
I want to build two overlapping generations within an infinite horizon model in DSGE. I wonder can DSGE do it or if it can't which method can help to sovle it? Can you suggest any reading material ...
- 1
1
vote
1
answer
36
views
Are other 'variables' in demand functions always fixed?
My question is whether our demand functions e.g. Hicksian (compensated) demand, are ever functions of 3 or more variables, or if the other price variables and utility are always fixed, and hence just ...
- 343
2
votes
1
answer
52
views
Integrating over the Y Axis: (∆CS)
The traditional formulae for consumer surplus is: $\text{CS} = \int_{0}^{x_0} [x(p_x,\overline{p_y}, \overline{m})]dx - x_0P_{x_0}$.
This is the area under the Marshallian demand curve, that is only ...
- 343
1
vote
1
answer
85
views
Calculating the substitution effect with the derivative
Substitution Effect (SE) for a price increase of $P_x$ to $P_x'$ can be written as:
$h(P_x', P_y, U) - h(P_x, P_y, U) = ∆h$, where $h$ is Hicksian demand. Correct?
The Slutsky equations decomposes a ...
- 343
0
votes
1
answer
25
views
Compensating Variation - Interpreting the formulae
Assume $U(x,y) = x^{1/2}y^{1/2}$ s.t. $P_xx + P_yy = m$
And a price increase from $P_x$ to $P'_x$:
$U_0 = \frac{M}{2(P_xP_y)^{1/2}}$
Compensation variation formulae is: $\frac{M + ∆M}{2(P_x'P_y)^{1/2}...
- 343
0
votes
0
answers
42
views
Compensating Variation for $U = (xy)^{1/2}$ and $U = xy$
I want to check my calculations for these compensating variations regarding an increase in $P_x$ to $P'_x$.
Below I have used $-∆M$, this is how my course first laid it out but I appreciate that it's ...
- 343
2
votes
1
answer
57
views
Why do we not stick to utilities in calculating supply and demand?
Common microeconomics models give that MC must equal MR in the optimal position for the consumer, therefore, the marginal utility must equal its price. But this is where a mistake has been made, what ...
- 23
0
votes
2
answers
63
views
Decoding Endogenous vs Exogenous - Parameter vs Decision Variable - and Independent vs Dependent
this is a topic that i feel is very implicit in a lot of economics, but is some times brushed over in interest of getting strait to the model or the maths. But often i realise i don't actually know ...
- 343
0
votes
1
answer
74
views
Ruling out corner solution in portfolio maximization problem
I am new to the econometric world.
I have a portfolio maximization problem
$$
\max \sum_{i}^ n a_{i} x_{i} \quad \text{s.t.} \quad \sum_{i}^n a_{i}=1, a_{i} \geq 0.
$$
I solved the problem but I had a ...
2
votes
0
answers
24
views
How to model the payoff (or utility function) of the information provider?
After a thorough look in the literature of information design like Bergemann and Morris and Kamenica and Gentzkow I am still not so sure how the utility gain or payoff of the information provider/...
- 132
0
votes
0
answers
39
views
Deriving Demand for Exponent Term for Quasilinear Utilities
Consider a quasilinear utility function: $u(x, y) = x+4 y^{.5} \quad \text{s.t.} \, I=P_{x}x+P_{y}y$. I know how to calculate the demand for good $x$, beginning with
\begin{align*}
&\cfrac{\...
3
votes
1
answer
79
views
How can I solve a Utility Maximization problem using the Lagrangian method where the Utility formula has an exogenous constant $a$?
The utility function is given by: $$u(x, y) = 2x^{\frac{1}{2}} + 2ay^{\frac{1}{2}}.$$
The optimal bundle should be expressed as a function of $a$. Other variables are given by:
$$\begin{eqnarray*}\...
- 31
4
votes
1
answer
58
views
Calculating the Compensating Variation with $M^2$
We can calculate the compensating variation (CV), which (to my understanding) is the amount of money we would need to give back to a consumer to keep them at the same level of Utility after a price ...
- 343
4
votes
3
answers
180
views
How to determine convexity or concavity of an indifference curve?
I am at my wits end. Maybe one of you can explain it to me.
A utility function is given: $U(x,y)=\sqrt{x^2−y^2}$ and we should determine whether the indifference curve is convex.
From the lecture ...
- 41
0
votes
0
answers
11
views
Known approaches to identify sub-portfolios in an investors' portfolio choice
I'm looking for several days already and i haven't found a satisfying idea how to approach the following problem:
I'm interested in identifying mental accounts in the form of sub-portfoios in an ...
- 303
0
votes
1
answer
63
views
What economic theories describe the phenomenon of zero marginal utility when a resources is given at zero cost?
(I am not looking for the law of diminishing marginal utility, even though it is related)
Which economic theory or theories describe the following problem? When a resource is made available at 0 ...
- 101
3
votes
2
answers
175
views
How to handle multiple lagrange multipliers in a maximization problem?
Let's assume a standard household maximization problem of the form:
\begin{align}
\underset{C_t}{max} \sum_{t=0}^{\infty} \beta^t U(C_t)
\end{align}
subject to a standard Budget constraint:
\begin{...
1
vote
0
answers
36
views
Are there any ``sophisticated'' mathematical modelling where they solve for the utility function?
Are there any references in literature of any ``sophisticated'' mathematical modelling where they solve for the utility function under specific conditions using differential equations theory?
In such ...
- 132
1
vote
2
answers
89
views
How to correctly calculate my real salary?
My salary is $900 after taxes. This is quite a large salary for my country. And when my parents found out about it, they said that I earn a lot.
But in my opinion it is not so, because in order to do ...
- 185
0
votes
1
answer
36
views
Finding consumed quantity using marginal utilities
I was asked the following problem : for an individual, the ratio between the marginal utility of orange juice and marginal utility of apple juice is constant and equal to $0.5$. The two goods cost 3\$ ...
- 97
2
votes
0
answers
38
views
Relation between complements and substitutes (for multiple goods)
I am a little bit curious about the following problem:
If we have multiple goods (at least 3 or more)... And we know that $x_1$ and $x_2$ are substitutes and $x_1$ and $x_3$ are also substitutes, does ...
- 680
0
votes
0
answers
27
views
Decomposition of preferences into set of CES functions
CES function as a tool
Hello everyone,
I have this idea: CES function basically tells us what is the elasticity of substitution between two (and more) goods, therefore giving us the exact complement/...
- 680
2
votes
1
answer
54
views
State dependent preferences vs state independent preferences in utility theory
I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What ...
- 146
1
vote
1
answer
66
views
Integral in front of utility function
I have a problem understanding the integral in front of the modified Ramsey problem of the DICE model. So U the utility of one household is determined by u(c) the instantaneous utility and the rest of ...
- 11
1
vote
1
answer
32
views
Asymmetries in Equilibrium Utility
In this lecture, the professor says that all Nash Equilibria have the same utility in non-atomic selfish routing, whereas this is not guaranteed in atomic selfish routing. It is unclear how general ...
- 389
0
votes
0
answers
54
views
example of risk neutral or risk loving utility function
i"m looking for an example of either risk loving or risk neutral utility function. what i mean is like for risk averse, we have the HARA utility function. is there a utility function that exhibit ...
0
votes
1
answer
54
views
crra as special case of hara
I've been looking for an explanation why the HARA function as shown below:
can be this CRRA function below?
I need to know what kind of special case that CRRA has compared to HARA. Hope my sentences ...