Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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questions
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How are real income and utility the same thing?
My book, "Microeconomic Theory: Basic Principles and Extensions" treats utility and real income as the same thing in the chapters on compensated and uncompensated demand. I would like to ...
2
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1answer
56 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 ...
2
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1answer
101 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_+...
0
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1answer
32 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 ...
1
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1answer
67 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
202 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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115 views
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 ...
4
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1answer
63 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 ...
5
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2answers
231 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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0answers
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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
40 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
83 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: $$U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(...
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1answer
43 views
Lagrangian multiplier and optimal bundle
I would like to know where I am wrong (if I am) and why I am wrong here please:
If a consumer has an income of 600 euros to spend for good x (Px = 10 euros) and good y (Py = 5 euros).
What is the ...
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1answer
38 views
Marginal Utility Meaning [closed]
I'm revisiting some old topics from introductory economics and I am not quite sure I have convinced myself of the theory behind marginal utility. I have a few simple questions if anyone could please ...
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2answers
57 views
Nested/Recursive Dynastic Utility Functions
I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain ...
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0answers
21 views
functional form for a consumption shock
In a DSGE model, how can I add a disturbance/shock in the consumption of households?
For example given my utility function
$$ U(C,H) = \frac{C_t^{1-\theta}}{1-\theta} - \frac{B}{\eta} H_t^\eta,$$ ...
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1answer
41 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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0answers
31 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'...
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0answers
66 views
How to derive the Indirect Utility Function and Marshallian Demand from Homothetic Preferences
I need to prove the following relationships:
1 - If preferences are homothetic, then the indirect utility function can be written as
$v(p, w) = v(p) · w$.
2 - If preferences are homothetic, then the ...
4
votes
1answer
61 views
Interpreting the Reference Outcome in Thaler (1985)
On page 18 of Thaler 1985 on Value-functions $V(\cdot)$, he makes an example about an individual expecting some outcome $X$, who instead obtains $(X + \Delta X)$ which he then defines as the ...
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0answers
38 views
What is the usefulness of Cobb Douglas functions? Why do we use them so often?
Hard to find much explanation as to why we generally use CD functions so often.
My understanding is that it is usually well behaved when used for utility functions and preferances, since it is
convex,...
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0answers
45 views
Labor Supply- how to do comparative statics?
Consider an economy with a competitive industry where the representative firm's production function takes the form of a Cobb Douglas production function $Y=z K^{\theta} L^{1-\theta}$.
$z$ is an index ...
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1answer
57 views
max{x1,x2} where P1not=p2
I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ...
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0answers
22 views
Marginal utility and convex utility function
If we have a convex utility function, like the quadratic one, does the law of diminishing amrgnial utility still apply or do we have that the partial derivative of utility with respect to, say ...
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1answer
80 views
Find Pareto optimal allocations and the core for the following economies
Find Pareto optimal allocations and the core for the following economies.
There are two consumers and two goods. Utility functions are $u_1(x_1,y_1)= 10x_1-(y_1-2)^2$ and $u_2(x_2,y_2) = 10y_2 − (x_2 −...
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2answers
106 views
What is the service equivalent of an economic 'bad'?
In general conversation, the terms "goods and services" are often used together. In economics, these terms have the following meanings:
Goods:
In economics, goods are items that satisfy ...
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1answer
55 views
Essential goods: How does one restrict the utility function?
I understand that solutions on boundary of the set under consideration when doing constrained optimization are often problematical. Usually it is said that we assume that goods are essential to insure ...
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0answers
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Is unobserved heterogenity in mixed logit models variable specific?
I have a mixed logit model with travel cost, travel time, and mode constants. If I only randomize travel cost and keep fixed coefficients for travel time and mode constants, will the model capture ...
5
votes
2answers
108 views
Utility function for introductory microeconomics
What are the utility functions standardly used in introductory microeconomics courses. My own list would include
Perfect substitutes: $U(x,y) = ax+by$
Perfect complements: $U(x,y) = \min(ax,by)$
Cobb ...
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0answers
31 views
graph of dependent income
I would need help with the following problem about consumer theory. Let us say that $X$ is the amount of days at the sea and $Y$ is the amount of days on the cottage. We have some utility function $u(...
0
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1answer
44 views
Indifference Curve Analysis [closed]
I would like to analyse how COVID-19 has impacted the aviation industry by looking at how the demand for airlines + holidays has fallen via an indifference curve analysis. However, I'm not sure where ...
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2answers
67 views
setting of Lagrangian function
Consider a simple consumer's problem:
Max $u(X)$ s.t. $\sum_i^l p_i x_i\leq \sum_i^l p_i w_i$
$w$ is initial endowment.
We can set the Lagrangian function to solve this problem.
$L=u(X)+\lambda ( \...
3
votes
1answer
86 views
How can I prove that a utility function does (or does not) satisfy diminishing MRS?
I have this CES utility function:
$$U(f, c) = (f^\alpha + c^\alpha)^{1/\alpha},$$
with $\alpha > 0$.
The problem set asks does it "satisfy the principle of diminishing marginal rate of ...
4
votes
1answer
59 views
Is there a name for this type of CES look-alike utility function?
I do not know whether the following utility functions are used a lot but I was wondering whether there was a common name for this type CES like utility function
$$u(z) = \left[ \left( \sum_{j \in J_1}...
2
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1answer
50 views
Set of consumption over all period is convex in $\mathbb{R}^T_+$?
Today in class, the professor said that the set of all consumption $c(S)$ is non-empty, compact and convex subset of $\mathbb{R}^T_+$. i.e. we know $\sum \limits_{t=1} ^T c_t = S$ where $c_t$ is ...
4
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1answer
91 views
Perfect substitutes and Lagrange
How does one solve utility maximization of perfect substitutes using Lagrangian function?
Consider the problem
$$\max_{x,y} ax +by $$
subject to the constraint that
$$px + qy \leq I$$
where $a,b,p,q,...
1
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1answer
60 views
Complicated utility function
I am trying to answer this past paper question on microeconomics and a rather complicated utility function question. The question is below as well as my answer.
In my answer, I use the fact that the ...
0
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0answers
33 views
Max of the tax provenue [duplicate]
I have this utility function:
$$u(c,l)=c-\frac{\eta}{\eta+1}(24-l)^{\frac{\eta+1}{\eta}}$$
where c is consumption and l is sparetime.
Then I also think we must have the condition: $$pc+wl=24w$$ where ...
2
votes
1answer
76 views
Proving that the utility is concave
Consider a household which solves the following problem:
$$v(k,r,w)=\underset{c,l\in B{(k,r,ω)}}{\ {max}} \{u(c,l)\}$$
where $u : R_+^2 \rightarrow R$ is a strictly concave, twice continuously ...
0
votes
1answer
45 views
When is expenditure function non-decreasing?
I have to find parameters m and d for which expenditure function is non-decreasing and homogeneous of degree 1.
My expenditure function is:
I think that I should find ∂e/∂p which has to be >= 0 but ...
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1answer
41 views
Is the expected utility the inverse of the utility function?
Can somebody explain to me if that it's true and also graphically explain it?
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1answer
55 views
Effect of price on 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.
I was discussing ...
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1answer
73 views
Walrasian demand with a twist of Leontief function
A consumer has the utility function $u(x_1; x_2) = \min(x_1; x_2) + 5 \max(x_1; x_2)$.
Find its Walrasian demand $x^*(p; w)$.
I've tried searching it up when we have two Leontief functions summed ...
2
votes
1answer
52 views
Expenditure function
Let $u (x) = \prod_{{i\leq n}}$ $(x_i-m_i)^{a_i}$, where $m_i\geq$0 and $a_i\geq$0, Σ$_{{i\leq n}}a_i=1$ show that the expenditure function $e(p,u)$ is linear in $u$.
Based on the definition of the EF,...
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1answer
51 views
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 ...
2
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1answer
67 views
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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1answer
51 views
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 ...
2
votes
2answers
171 views
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, ...
0
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1answer
34 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
69 views
Proof on weak axiom of revealed preferences
I read the following statement.
“ A utility maximizer with strictly convex and strongly monotonic preferences
satisfies weak axiom of revealed preferences.”
How can I prove or show this? I cannot ...
