Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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What are the necessary and sufficient assumptions for indifference curves to be convex to the origin?
I thought this required (quasi-)concavity of the utility, but can this (e.g. declining MRS) occur with fewer assumptions?
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Visualizing the expenditure minimization problem
I can easily visualize the utility maximization problem
ie. $$v(\mathbf{p},m^{*})= \max_{\mathbf{x}} \ u(\mathbf{x}) \ \ s.t \ \ \mathbf{px}\leq m$$
Since it is pretty easy to graph the indifference ...
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4answers
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Is the market price objective?
Is the market price objective, does it exist independently of human consciousness, how do we treat the market price in economics and the philosophy of economics?
The market price is the current price ...
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Examples of Specificied Utility Functions
For the case of two goods, give examples of different two utility functions that satisfy all of
the following properties: 1. one utility is strictly concave in good 1 and the other is strictly
convex ...
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1answer
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Different ways of writing CIES/CARA utility
I frequently encounter the following two versions of writing CIES or CRRA preferences:
$$u(c_t) = \frac{c_t^{1-\theta}-1}{1 - \theta}$$
...and...
$$u(c_t) = \frac{c_t^{1-\theta}}{1 - \theta}$$
The ...
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0answers
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Consumer willingness to pay [closed]
Consumers can eat in a fast food outlet at price p1 and in a restaurant at price p2 (p1 < p2). Willingness to pay to eat out in a restaurant is w, where w is uniformly distributed on [0,100]. ...
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Utility of both players in St. Petersbourg paradox - behavioural economics
Im reading a paper by Karl Menger [1] about the St. Peterbourg paradox :
In the theory of probability, the "Petersburg Game" designates the
follow- ing gamei between two persons, A and B. ...
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0answers
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How to solve a general equilibrium problem with lexicographic preferences?
I have been unable to find a good example of this type of GE problem in our textbooks, and our professor has indicated that something like this may appear on our exam. So, here is a hypothetical ...
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1answer
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For any small perturbation dx, utility cannot change, or else, x* would not be optimal
I am having trouble understanding something that Varian says in "Microeconomic Analysis: Third Edition." For those of you who have the book handy, the question that I have regards something ...
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2answers
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Is this a case of nonseparable utility (across states of nature)?
There are two states of nature: summer (hot) and winter (cold).
I have a utility function indexed by states of nature: $u(\cdot;summer)$ and $u(\cdot;winter)$.
There are two good to choose between: ...
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How do thresholded incentives influence behavior?
I'm trying to understand how incentives can change crowds in terms of their work performance. I have metrics describing said performance and I'm trying to see how introducing incentives might change ...
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1answer
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Nonseparable utility across states of nature: an intuitive example
I am new to nonseparable utility across states of nature as found in some macro-financial models (discussed in this YouTube video lecture by John Cochrane). I do not find the notion intuitive. Could ...
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58 views
Utility Function Challenge
A utility function is given for two goods
Good 1 and Good 2
$$U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$$
Did I get this right? the marginal utility functions with respect to G1 and G2 will be ...
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1answer
43 views
What utility function represents an agent with a time-discount factor?
Consider an agent who has a fixed budget, and should decide how to split it between consumption today and consumption tomorrow. For simplicity, suppose there is no interest, and no borrowing/lending, ...
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2answers
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marginal utility and Marginal rate of substitution
While studying for my microeconomics class, I realized that I could not fully understand the meanings of Marginal utilities and marginal rate of substitution. Can anyone explain to me the difference ...
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how to solve such UMP where utility function is quasi-linear with cobb-douglas function as the non-linear part [closed]
U =$X_1+X_2^aX_3^{1-a}$ $a ∈[0,1]$
$s.t. p·x≤w , x≥0 $
I have tried FOC for x1 x2 x3 and λ, but I cannot get two pairs of equalities separately in order to express two unknowns as a function of ...
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1answer
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Binary choices in consumer theory
Back when I was a teaching assistant, we were teaching utility theory and how it relates to price determination. So we were looking at continuous goods (e.g. "food") so as to get marginal ...
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1answer
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certainty equivalent and lotteries [closed]
suppose an agent has $u(z)=-e^{-bz}$ where $b>0$ as her Bernoulli utility function and faces two gambles:
G1: win 1000 dollars with probability $\frac{1}{2}$ and zero with probability $\frac{1}{2}$ ...
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1answer
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CES utility maximization two goods two period
In an Arrow-Debreu economy, there are two periods and N identical agents.
In each period, the agent consumes two goods $c_{At}$, $c_{Bt}$ where $ t = 0,1 $ and has the endowments $(e_{a0},e_{b0},e_{a1}...
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1answer
62 views
Why is Deadweight Loss Bad for Society?
I have learned that in a perfectly competitive market in the absence of externalities, taxes will impose a deadweight loss upon society, due to reduced market participation by consumers and producers. ...
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0answers
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quasilinear utility maximization with non-negativity constraints
I have a utility function:
max $U = \frac{c_o^{1-\eta}}{1-\eta} + \frac{\beta}{2} c_{1a} + \frac{\beta}{2} c_{1b} $
subject to the budget constraint $p_0c_0 + p_{1a}c_{1a} + p_{1b}c_{1b} = p_0e_0 + p_{...
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comparing two lotteries
Suppose the prize space (in dollars) is $\mathbb{Z}$ = {1, 2, 3, 4, 5, 6, 7, 8} and consider choices by an agent
whose preferences (over lotteries) satisfy the von Neumann-Morgenstern axioms.
A risk ...
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0answers
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Lagrangian in Ramsey model
I struggle to write and solve Lagrangian in the Ramsey model.
I have the following individual preferences with a budget constraint:
and an additional constraint that is a no-ponzi condition:
How to ...
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0answers
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Market clearing price for a single good with two consumers with different utilities
Say I have a single indivisible good that is randomly allocated to one of two consumers. The first consumer's utility for the good is \$5 and the second consumer's utility for it is $10.
If the good ...
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1answer
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Can any three of the four vNM axioms (of expected utility theory) be satisfied without satisfying the fourth?
Is it true that any three of the four vNM axioms (of expected utility theory) can be satisfied without satisfying the fourth? Any examples which support such claim?
Basically I'd like to prove that ...
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1answer
29 views
Utility Maximisation With Infinity
Consider the following utility function.
$U(w) = \max x_{1}^{0.25}x_{2}^{0.25}(x_{3} +1)^{0.5} $
$s.t. x_{1} \geq 0, x_{2} \geq 0, x_{3} \in \{0,1\}$ and $1 \times x_{1} +1 \times x_{2} + 1000 \times ...
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0answers
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How do we show mathematically that the lump sum principle does not apply to perfect complements?
I want to show mathematically that the lump sum principle does not apply to perfect complements. I was able to show it applied with a specific Cobb-Douglas utility function, but I am not sure how to ...
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1answer
91 views
Log Linearising CES demand
I have been trying to log-linearise the demand function that follows from a standard two-good CES-utility maximamalisation problem. That is:
Maximise
\begin{eqnarray}
U(h,c)= \left(G_1^{\rho}+ G_2^{\...
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1answer
33 views
Failure of 1st welfare theorem with non-increasing utility function
I want to find an example that utility function is not increasing
but still satisfies that $u(x) \geq u(y)$ for all $x \geq y$
and 1st welfare theorem fails.
I want to prove this on edgeworth box not ...
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1answer
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How does this imply that a Pareto optimum maximizes a weighted average of utility functions?
I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me.
In the passage, Back is ...
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1answer
29 views
Risk seeking investors: Do they benefit from return at all?
Starring on the indifference curves for different types of risk preferences I ask myself why the risk seeking investor would be indifferent between an investment on the far left of his indifference ...
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Von Neuman-Morgenstern utility theorem apply only to linear utility functions?
Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...
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1answer
63 views
Calculate hicksian demand with utility function (with restriction)
$U(x_1, x_2) = 1/2 * x_1 $
I am trying to calculate the Hicksian demand when when $U(x_1, x_2) = 2$ and the value of the minimum expenditure when $p_1 = 9$ and $p_2 = 16$
For the hicksian demand I ...
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1answer
88 views
Calculate income and sustitution effect from utility funcion
Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $
$ p_1 = 3, p_2 = 8, m =120 $
$p_2$ changes from $8$ to $10 $
How can I calculate the income and substitution effect.
I first thought about calculating ...
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0answers
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CES utility with negative values
We know that the CES utility function approximates a Leontief utility function as in the following:
$$u(x_1,x_2) = (x_1^{-r}+x_2^{-r})^{-1/r}\overset{r\rightarrow\infty}{\longrightarrow}\min\{x_1, x_2\...
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2answers
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Why are utility functions typically assumed to be concave?
Why is it usually required that utility function be concave? Is it because concavity is a necessary (or sufficient?) assumption for a unique equilibrium?
Can someone please spell this out for me?
...
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1answer
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How do you measure the MRS for more than two goods?
For two goods, the MRS is defined as the amount of one good you would trade off for the other. Mathematically, $$\text{MRS} = \frac{dy}{dx}$$ where the amount of goods $X$ and $Y$ are denoted by $x$ ...
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2answers
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Is addiction a case of increasing marginal utility?
I got to know that alcohol addiction is a case of increasing marginal utility. My professor refutes me bluntly stating that once a person starts consuming he no longer remains to be a 'rational ...
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1answer
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MRS and IC : The language sounds contradictory
The MRS$_{xy}$ is defined as $\left(-\frac{dy}{dx}\right)$ and Nicholson/Snyder (NS) writes it as the amount of $x$ we can trade for $y$ while remaining equally well off.
However, the analytical ...
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1answer
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Question about Marginal Utility [closed]
The following statement is given as true and I cannot make sense why. It is the only information given.
"The $MRS$ of flour in 1kg bags for flour in 2kg bags is negative and constant."
I ...
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2answers
209 views
What is the problem with this opportunity cost example?
The "stand-up economist" Yoram Bauman used the concept of opportunity cost to make the following joke:
[S]omebody offers you a choice between a Snickers bar and a package of M&Ms. ...
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1answer
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How come a representative consumer with quasilinear utility need not economize?
Suppose a representative consumer has the following quasilinear utility function:
U_i(x_1,x_2)=ax_1+ax_2-(1/2)*[(x_1)^2+(x_2)^2] + k
where a>0 is a utility parameter, x_1 and x_2 are the goods, and ...
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1answer
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King–Plosser–Rebelo Preferences and Additively Separable
The wiki of King–Plosser–Rebelo preferences says that the utility function has the multiplicatively separable form $$u(C, L)=\frac{1}{1-\sigma_{c}} C^{1-\sigma_{c}} v(L)$$ and "in the limit case ...
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2answers
59 views
Understanding utility function curve and marginal rate of substitution
This example appears in a different question, but there is something I don't understand.
Maybe this question is better suitated for algebra stackexchange.
John’s utility function for food (f) and ...
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1answer
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Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$
I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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1answer
67 views
How are weak preferences different to strict preferences/indifference?
Given a utility function $u(\cdot)$ and two bundles $x$ and $y$.
Assuming $u(x)=u(y)$.
I am to prove or disprove that $x \succcurlyeq y$.
Now I'm confused by this.
We say $x$ is strictly preferred to $...
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2answers
299 views
Fundamental question on marginal utility
I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional "happiness" ...
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Demand for minimum of $4$ different goods
The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$.
Find the demand.
So far I have observed that it is ...
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1answer
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Adding scaled CRRA utility
Suppose our utility function is the usual CRRA utility with $\gamma=2$ so that:
$$u(C) = \frac{C^{1-\gamma}}{1-\gamma} = -\frac{1}{C}$$
Now suppose there are 2 goods, A and B, available for ...
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1answer
80 views
Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation
Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$
$$
\frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...