Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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Modeling risk aversion. Expected utility function
I want to model an Expected Utility Function for risk aversion but my problem is uncertainty in itself.
I want a function(a special case) $$f(x, y) =\left\{\begin{matrix} h(bx^{1-C}+ay^{1-C}),C\neq 1\...
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48 views
Framing Effect Risk-Aversion Risk-Pursuit
I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed.
I am trying to word.
200 dollars with 50% ...
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Rent dissipation meaning?
What is Rent dissipation? Please explain with an example.
I tried to search it on the internet about it. And I couldn't find anything in simple language. It was the esoteric language and was unclear. ...
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98 views
What would the indifference curve of min{√x,y} looks like?
The locus of kinks would follow x=y^2 but what would the arms look like?
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A case where the solution to Expenditure Minimisation Problem is not a solution to Utility Maximistion Problem
I am looking for a preference relation which satisfies the above property.
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Doesn't the concept of marginal utility speak to a cardinal utility function?
When we differentiate the utility function with respect to some input $x_i$, we get a number that tells us how "fast" the utility function is changing at some point with respect to $x_i$. Doesn't that ...
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Mean Variance Optimization in a Utility Maximization Framework
I'm struggling to gain a broad understanding of Mean-Variance utility theory as it relates to finding the efficient frontier of a group of assets which each have some return and variance.
The typical ...
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1answer
34 views
Opportunity Cost effect on benefits
My question is the following:
Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will ...
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54 views
utility maximization with nested Cobb–Douglas–CES preferences
I'm trying to understand the following paper: Hsieh & Ossa: A global view of productivity growth in China (2016). The pdf can be found here: https://faculty.chicagobooth.edu/chang-tai.hsieh/...
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Fixes of quadratic utility when probability of decreasing utility is large
In finance and specifically portfolio theory, a popular utility function is quadratic utility
$$
u(x)=x-\frac{\lambda}{2}(x-\mu_x)^2
$$
where $x$ is wealth and $\lambda$ is the parameter of risk ...
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30 views
Moral hazard, bubbles, and economies of scale in limited companies and organizations
http://eprints.lse.ac.uk/100058/1/Goodhart_CEPR_DP13494.pdf
What would be the disadvantage of limiting the liability to the product of the proportion of the company and the debt(a person with 2% of a ...
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Log-linearizing a non-separable utility function around the steady state
I've started reading Jordi Galí's Monetary Policy, Inflation and the Business Cycle (2nd ed., 2015). In section 2.5.2, Galí considers an example with the following non-separable period utility ...
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56 views
Maximin utility function
If someone has the attitude that they want to maximize their worst possible outcome (so they are maximally risk-averse), what does the utility function for that look like? Can this attitude be ...
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31 views
Are marginal utilities or utilities compared?
Consider decision making in an economic model. Suppose that there is some utility and it is a function of consumption and leisure where leisure is full-time work, part-time work, or full-time ...
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38 views
What is the trade-off between? Consumption and Leisure or Income and Leisure?
When first presenting the utility function and its arguments, textbooks typically start by stating that utility is a function of consumption and leisure. See for example https://sites.hks.harvard.edu/...
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Are there examples of Cost Benefit Analysis using diminishing marginal utility of income?
In Cost Benefit Analysis (CBA) constant Marginal Utility of Income (MUI) is usually assumed. This implies that a dollar received/earned is the same at low and high levels of income. In Social CBA, ...
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33 views
Change in the marginal utility of leisure with respect to a change in consumption
I am reading a paper that derives a theoretical retirement model. There is a utility function and a budget constraint forming an optimal control problem. The solution to this problem states that
\...
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Is a combination of Political economics and Game theory possible and beneficial?
By Political economics I do not mean the "economical" advice given by some people(see the Wealth of Nations by Adam Smith) but rather the heavily mathematized subfield of Economics studying and trying ...
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68 views
Showing that a preference relation admits a utility function representation
Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|...
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34 views
Proof: Risk averse; Certainty Equivalent smaller than expected value
I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds:
The certainty equivalent, $CE(\cdot)$, is ...
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2answers
54 views
The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?
I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality.
But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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Rotation of Quasilinear Utility
Let $u(x,y)=f(x)+y$ be a quasilinear utility. Now we rotate it by 45 degrees, (such that the $x-$axis becomes the direction of $(1,1)$)
$v(x,y)=f(x-y)+x+y$. Is $v$ also a quasilinear utility? What is ...
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Linear Homothetic Utility
A Homothetic Utility is where
$$
\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y)
$$ (or its monotonic transformation).
A linear Homothetic utility is defined as $$
\forall x,y, \forall ...
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1answer
34 views
If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?
Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?
$\succsim$ is a weak order over $\mathbb R^L$.
For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$.
We know that $D$ is always ...
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1answer
51 views
Meaning of $dF(z)$ in expected utility framework
Background: from a Microeconomics course,
$F$ is a cdf. In other words, if $F$ has a density function $f$, then
$$F(z)={\int_{-\infty}^z f(x) dx} $$
Write the Bernoulli utility function $u:...
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1answer
19 views
Gapminder's Dollar Street and the role of self-supply
I find it quite hard to get a clear picture of what the income numbers in Gapminder's Dollar Street tell. How to compare \$27 in Burundi with \$10,098 in China? What would it mean that the family in ...
2
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1answer
34 views
Obligations of a company
Any company may "feel" obligated towards several parties at once:
its shareholders
its employees
its customers
its partner companies (sub-contractors and suppliers)
its country and social environment ...
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1answer
64 views
robinson economy with production
Facing a little bit of a problem with this questions, did a similar one BUT the utility function was not linear and got MRS dependent on goods (was not just a number) - here I am at a loss.
The ...
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1answer
22 views
How does the notion of utility differ from that of value?
Is utility merely the notion of value in the subjectivist/marginalist (aka neoclassical) school?
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30 views
Aggregated demand of households given utility function
I have an utility function given,
$\ u_j(q_{j1},q_{j2} )=q^{3/4}_{1j}*q^{1/4}_{2j} $
$\ s.t.: y=p_1*q_{1i} +p_2*q_{2i}$
I do know that the for $\ q_{1j}$ the marginal prospensity to consume is 3/...
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1answer
94 views
WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?
Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$:
$$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$
Theorem (from Kreps 1988): for ...
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1answer
25 views
Is anyone familiar with the following basic resource sharing model?
Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics.
Let $T > 0$ be the total quantity of resources. For example, ad ...
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2answers
82 views
What are the units of utility?
I'm trying to show a result that involves utility and money (the latter is in dollars). I would like to know if it is safe to assume that the units of utility is dollars? After all, in auction ...
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1answer
67 views
Proof of monotonocity of preferences
Question from Intermediate Microeconomics by Hal Varian:
"We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve ...
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1answer
52 views
Utility maximization in a 2-good scenario with an option to buy a combo of the two
I am solving the following question:
Suppose that we live in a two good world, books (x) and movies (y), with utility function given by $u(x,y)=min(x+2y,2x+y)$. Prices of books and movies are 25 and ...
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82 views
Preference relations defined by $x_1^n + x_2^n$ converge to $\max\{x_1, x_2\}$
In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question:
Let $\succ_n$ be the preference relations defined ...
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How is the Euler Equation for Consumption derived from from intertemporal budget constraint and lifetime utility function in basic macroeconomics
I suspect that what I'm actually asking here is just a basic calculus question, which I have overwrought, but I wanted to ask it here to make sure before taking it to SEMaths.
In the Jones ...
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1answer
236 views
Demand derived from Cobb-Douglas utility, interpretation, check
I derived demand, given a Cobb-Douglas utility function but I am not really sure if I did it correctly. I am especially struggling with the sum signs and the subscripts of $i$ & $j$. It would be ...
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1answer
153 views
Utility maximimization for unusual Leontief utility function
The problem is basic utility maximization subject to a budget constraint with
$$u(x,y) = min\{x+y,4\sqrt{x},4\sqrt{y}\}$$
$$p_x = 1, p_y = 1, M = 4$$
I will have to first plot the Indifference ...
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2answers
71 views
Proof of Choice Coherence in Kreps (2013)
In the first chapter of Kreps (2013), there is a proof that the choice function satisfies choice coherence. Kreps writes:
I do not understand how the third sentence of (b) logically follows from the ...
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1answer
45 views
Optimal choice for a weird leontief function
Compute the optimal choice for a consumer with the following utility function:
$$u(x_1, x_2) =\max \{\min(2x_1, x_2), \min(x_1, 2x_2)\}$$
I'm familiar with computing optimal choice for perfect ...
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1answer
94 views
Solving for Pareto Efficient Utility Possibility Frontier using constrained optimisation
The economy is a one-good two individual endowment economy in which individual $i’s$ preferences are given by $𝑈_𝑖(𝑥_𝑖)=𝑥_𝑖$, for 𝑖∈1,2, and the feasibility constraint on the amount of x ...
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1answer
82 views
What is the assumption behind “indifference curve does not cross”?
If only weak-ordering and continuity is assumed, "ICs" can definitely intersect.
If we assume Monotonicity or convexity in addition to weak-ordering, then we can get "no cross of IC".
But those two ...
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231 views
Question about an economy with 3 components household, firm and government with functions given
I've spent considerable amount of time on this question, in vain. It is from one of the competitive exams for admission to a grad econ program. Help would be tremendously appreciated. Thanks.
An ...
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1answer
225 views
Quasi-Linear Functions
I understand that quasi-linear functions have a general form
$U(x_1,x_2,...,x_n,y) = f(x_1,x_2,...,x_n) + y$
and that for a quasi-linear function, the income effect with respect to the other ...
0
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1answer
73 views
Solution to maximization not Pareto efficient
In my economics class, we saw a proof that if an allocation $ ((\hat x_h), (\hat y_f)), h\in H$ (the set of households), $f\in F$ (the set of firms) is Pareto optimal/efficient, it must necessarily be ...
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1answer
422 views
Imperfect Substitutes and Utility Funcitions
The utility function for perfect substitutes is defined as U(X,Y) = aX + bY. If the two goods X&Y are imperfect substitutes what would be their utility function?
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What was “Pareto's proof of the immeasurability of utility”?
Wong (1978, 2002, Foundations of Paul Samuelson's Revealed Preference Theory), repeatedly refers to "Pareto’s proof of the immeasurability of utility". What was this proof?
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What are the definitions of the terms value, wealth, and utility in economics?
Are there any definitions for the following three terms that are widely agreed upon in economics?
Value
Wealth
Utility
In particular, are these terms identical? If not, what differentiates them?
I ...
