Questions tagged [utility]

Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.

Filter by
Sorted by
Tagged with
3
votes
2answers
39 views

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
votes
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
votes
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
votes
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
vote
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 ...
1
vote
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.
4
votes
0answers
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
votes
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
votes
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 $i \in [n]$. ...
1
vote
0answers
22 views

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
votes
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 ...
3
votes
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(...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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
votes
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?
0
votes
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'...
0
votes
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 ...
0
votes
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,...
0
votes
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 ...
0
votes
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. ...
0
votes
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 ...
1
vote
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 −...
5
votes
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 ...
1
vote
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 ...
1
vote
0answers
13 views

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 ...
1
vote
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
votes
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 ...
2
votes
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
votes
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
votes
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
vote
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
votes
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 ...
-2
votes
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?
2
votes
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 ...
1
vote
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,...
0
votes
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
votes
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 ...
1
vote
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
votes
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
votes
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 ...

1
2 3 4 5
11