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Questions tagged [utility]

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

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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
360 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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41 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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172 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 ...
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Question on consumer theory

The story of my question is I have multiple question. (1) when John doesn’t work in the underground economy at all , t=0, how can I find the optimal value of $l$ and consumption bundle and his ...
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400 views

Question about budget constraint and utility maximization [closed]

I have also following budget set $$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$ where y is income. Assume that there are two stories. The agent can shop in both of them. The first store ...
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888 views

Show that First order conditions are necessary and sufficient for utility maximization

I have a budget set $$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$ where $y>0$ is income. Assuming the preferences are strictly monotonic and convex, I want to show that first order ...
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1answer
136 views

How to write budget constraint if the agent sell the goods that buy

Della’s utility is $U(G,R)$ G is the consumption of gasoline per week R is the the consumption of other goods Just help me to write down budget constraint. I think that $$R*1+(G-20)*10+20*1=...
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Utility maximization question setting up.

Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$ Assume the agent's income is $y=5$. The price of one unit ...
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60 views

Homothetic preferences [duplicate]

I want to prove that if a utility function that represents $\succsim$ has constant marginal elasticity of substitution (MRS) in proportional expansions along rays, that is: $$ MRS(x,y) = MRS(\alpha x, ...
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Homothetic preferences and utility functions

I know that if you have homothetic preferences and a utility function that represents it, then this utility function must present constant Marginal Rate of Substitution (MRS). My question is whether ...
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1answer
92 views

Utility Function in Consumer Credit

I have been studying the area of unsecured consumer credit (consumer loans and credit cards) and credit scoring. My question is: can we have a utility function (either a lender's or borrower's utility)...
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1answer
359 views

Intuition Behind the Definition of Prudence?

I'm having trouble seeing why an agent is said to exhibit "prudence" when u'''($\cdot$) > 0. How does having a utility function with a strictly positive third derivative make an agent act "prudently"? ...
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1answer
426 views

Derive utility function with both substitutes and complements

I know that in the 2-good world it is easy to derive the demand functions from a utility function for imperfect substitutes or complements, but what if I have N goods that include many combinations of ...
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1answer
332 views

Determining the elasticity of Hicksian Demands

If we have Hicksian (compensated) demand functions, how can we determine the income elasticity and own price elasticity? Is the procedure the same as for Marshallian (uncompensated) demands?
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2answers
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How can I motivate a dynamic model using utility and consumer preference where only one good is affected by past consumption?

I've been looking how I can motivate the model I want to estimate using a utility optimization framework. Basically, I want to write a model using two goods: x and y, in two periods: 1 and 2, where ...
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1answer
316 views

Reservation utility

I am self-studying contract theory using Bolton and Dewatripont (2005). It is meant for grad students, which might be why I am having a difficult time understanding basic terminology. Here is the ...
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1answer
129 views

relation between the demand function and the marginal utility function

Can one say that the demand curve equals the marginal utility function? I have one course where this is stated. However, the demand curve dan be derived from combining the utility function with the ...
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1answer
363 views

Bliss point utility doubt

Why is the bliss point utility function convex even though it has concave portions to it ? According to Nicholson and Snyder (authors of Microeconomic theory - Basic principles and extensions) a ...
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General Equilibrium allocation holding fixed a consumer's utility

I'm having some issues with solving this general equilibrium exercise. The way I started off is by assuming that since consumer 2's utility is fixed, he will have a fixed utility function. Then ...
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1answer
494 views

Existence of competitive equilibrium between max utility function and min utility function

u1(x1,y1)=max(x1,y1) ω1=(0.2,0.2); u2(x2,y2)=min(x2,y2) ω2=(0.8,0.8) The utility functions for two individuals and their endowments are given above for a two person two good economy. My question is ...
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1answer
1k views

How to Calculate Marginal Utility

Imagine a scenario where an agent is faced with two purchasing options, each with an individual utility function. Let us say option $A$ offers $m$ units of $P$ per £, and option $B$ offers $n$ units ...
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1answer
150 views

Putting a Price on Happiness

When I was in college, a classmate of mine working two jobs mentioned that his/her job working at at a local fast food restaurant was causing undue stress and dissatisfaction. My response was to ask ...
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1answer
193 views

Modelling Bounded Utility Functions

I'm trying to work out how to model a utility function that is bounded below some level. More precisely, given a specified limit $L$, I want to work out how to ensure that the utility of any outcome $...
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3answers
529 views

Multivariable Utility functions

For a highschool economics/mathematics interdisciplinary essay I will use the Lagrange multipliers and deriving formulas that find the maximum. Could some one maybe suggest any (utility) functions ...
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Finding out an optional consumption without calculation [closed]

I need help with this task. The utility function is U(a;b)=3a+2b. The prices for the goods a and b are equal. Explain what an optional consumption of the consumer would be without calculating. ...
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757 views

MRS for quasi-linear preferences

I'm having difficultly understanding what my professor taught in class. I thought, like cobb-douglas, when finding $U_1$ we take partial derivative with respect to $q_1$ and hold everything else ...
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1answer
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Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$. Are there intuitive interpretations of the numerical values of these ...
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1answer
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Homogenous of degree one in utility function.

Question My solution is as follows. Please check my solution. If I make a mistake, please tell. I am really not sure about my solution. Thank you U(x) is homogenous of degree one i.e. u(...
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What's the relation between deadweight-loss and alpha in Cobb-Douglas?

I'm studying for an exam and facing a question about the relationship between the $\alpha$ of the Cobb-Douglas function and the loss of utility of imposing taxes. If I have understood correctly, ...
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2answers
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Why does local non satiation imply the constraint is binding?

Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$. I don't understand why this implies that $px^* = m$...
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1answer
166 views

Implications of differentiable demand function on the utility function properties

Suppose you know that the (Marshallian) demand function $x(p,m)$ that satisfies the consumer's problem of utility maximization is such that $\frac{\partial x_i(p,m)}{\partial m}$ is always well-...
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1answer
240 views

How to compute the utility function when risk aversion is equal to 1?

How to compute the utility function when risk aversion is equal to 1? If the utility function of consumption is set as, $\frac{C^{1-\sigma} - 1}{1-\sigma}$. Is it meaningful as $\sigma$ is equal to 1?...
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363 views

Utility function must be continuous for $V(p, e(p,u) )$ to hold?

Most utility functions we work with are already continuous, so I thought it was understood that it must continuous. But how would I show that if the utility function is discontinuous the identity V(p, ...
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1answer
368 views

Ordinal utility and monotonic transformations

If u(x) is an ordinal utility function that represents the (weak) preference relation R, then (a) any strictly monotonic transformation of u(x) also represents $R$, or (b) any monotonic ...
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151 views

Intertemporal choice with no income flow in the second period

Question: Suppose Mr X maximises his utility for two periods, his total utility is given by log $c_1$ + $\beta$ log $c_2$ where $\beta$ $\in$ ( 0,1) and $c_1$ and $c_2$ are his consumption for ...
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1answer
247 views

Verify Indifference curves of two utility function to be the same

I'm being asked to verify that two utility functions, $U(x_1,x_2)$ and $V(x_1,x_2)$ have the same indifference curves and the same MRS. There is no problem in verifying the MRS to be the same, but ...
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1answer
160 views

Maximal Allais paradox

The Allais paradox, is an experiment set up as follows, where you are free to chose between gambles $A$ and $B$: (the table on wikipedia is much more readable if you prefer) Experiment 1 ...
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4answers
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Existence of utility representation of a rational but discontinuous preference

This is related to Do discontinuous preferences imply no continuous utility function? I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more ...
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2answers
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Do discontinuous preferences imply no continuous utility function?

I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function. I know that you can represent continuous ...
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1answer
408 views

Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth

I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), ...
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1answer
211 views

Preorder and multi-utility function

Let $\succeq$ be a preorder, i.e., it is reflexive and transitive on $X$. Prove that there exists an index set $N$ and a multi-utility function $u:X \rightarrow \mathbb{R}^N$ such that $x \succeq y$ ...
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1answer
113 views

Consumer utility optimization question

I am having diffculty with this question: Can we proceed using Lagrange here since the utility function is convex, or do we have to treat them as perfect substitutes? If latter or any other method, ...
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2answers
333 views

CRRA utility function with a scale parameter

I am wondering if it is possible to write down a following CRRA utility function ; $$u\left(c(t)\right)=a\frac{c\left(t\right)^{1-\sigma}}{1-\sigma}$$ where $a>0$ is a constant scale parameter. I ...
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1answer
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Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
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1answer
151 views

Interpretation of utility function

I am reading Lucas (1980) and I am a bit confused about the way he formulates the utility function. So there is one non-storable good that comes in $n$ colours and one unit of labor produces $y$ ...
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1answer
466 views

Specification form for household utility function

What determines the choice of the functional form to be adopted for the household CRRA utility function, when utility depends on consumption and leisure? For examples, we have these three functional ...
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1answer
70 views

What is one dimensional, ordered type?

I am reading papers about moral hazard. What is one dimensional, ordered type $\theta\in\Theta$? What is one dimensional, not ordered type $\theta\in\Theta$? Could you please give an example? ...
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Terminology for separability in price and value

Take an agent with mean-variance utility over something that is uncertain: $$ U(x) = \mu_x^\theta - \sigma_x^\lambda $$ $A\in \{0,1\}$ happens if $U(x)>0$, and $x$ is a random variable $$ A = \...
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2answers
173 views

Equivalence of definitions of continuity [closed]

One of the definitions of continuity is that the Upper Contour Set and the Lower Contour Set are closed. I am trying to show that if preference is continuous and $x>y>z$, then there is some $\...