Questions tagged [utility]

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

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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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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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51 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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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
50 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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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 ...
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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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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(...
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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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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 ( \...
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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 ...
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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}...
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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 ...
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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,...
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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 ...
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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 ...
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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 ...
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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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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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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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60 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 ...
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1answer
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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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42 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 ...
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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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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 ...
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160 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, ...
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31 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 ...
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1answer
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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 ...
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Measuring and assigning utility numbers

I was recently introduced to the concept of cardinal utility. In real life, how do we assign these utility levels? For example if i wanted to assign numbers to my own utility indifference curve for ...
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Homogeneous Utilities: Anything other than CES?

Does there exist any homogeneous utility function, i.e., $u(\lambda \mathbf{x}) = \lambda u(\mathbf{x})$, that is not a special case of the CES (or nested CES) family of utility functions or its ...
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1answer
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Determining subgame perfect Nash equilibriums

Question Three houses share exclusive access to a beach, but it is dirty due to trash washed ashore. A beach clean-up exercise costs $100$, but has a value of $200$ to each household. A clean-up ...
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135 views

How was CES utility function derived?

Is there any book/papers that I can refer to the proof (derivation) of the CES utility function? Or if anyone could help me with the derivation, I will be so much grateful to you.
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1answer
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Solving Utility Maximization with Lagrangian

I know how to solve the 2 variable constrained optimization problem using MRS = MRT, but I also want to make sure I understand how to do it with the Lagrangian method. So if I have the following ...
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1answer
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Can an irrational function be a utility function?

Given some irrational preferences, that can be represented by a function. If the function does not satisfy rationality (transitivity, completeness), does this imply it is not a utility function. I ...
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611 views

Mathematical Notations that I Never Understand While Reading Articles or Dissertations

I have some problems when I reading mathematical notations. For example: $$\mathrm{E}_{0}\left\{\sum_{\mathrm{t}=0}^{\infty} \beta^{t}\left[\mathrm{u}\left(\mathrm{C}_{\mathrm{t}}, \mathrm{M}_{\mathrm{...
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Showing utility function gives preferences that are rational and convex

Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$ Are these preferences rational and are they convex/...
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What may the alpha mean in the context of indifference curves? How to solve such questions? [closed]

The question is as follows: A consumer has a budget of 3000 units. He uses it to buy 2 goods: bread and cheese. Cheese costs 30 units/kg, and bread costs 3units/kg. The indifference curve is ...
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Is it accurate to state that an economist cannot assign a true numerical value for utility?

Investopedia article - What is the utility function and how is it calculated? https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp Article describes ordinal ...
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Marginal Rate of Substitution for perfect complements

I have come across the following problem: Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function: u(x1, x2) = min(x1, x2). The solution is that ...
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1answer
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HARA preferences details

I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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Why utility should be bounded (or unbounded)?

For Expected Utility and SEU, people make axioms to ensure that the utility is bounded. However, I personally believe that the utility function must be unbounded, especially if we are considering ...
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indifference curve

Suppose my preferences are such that I like more of both goods, but only up to a point. After I have 5 units of both goods, that’s as good as it gets, and I’m indifferent if I get more. how do u draw ...
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Comparing utility functions [closed]

I'm doing an econ course after not having any math or micro for a few years, now I'm totally missing the basics again. I'm wondering how to show that utility functions are an equivalent to each other: ...
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1answer
31 views

Strictly increasing but not convex preferences

Is it possible to have preferences that is strictly increasing but not convex? Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't ...
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The efficient frontier in mean variance criterion

The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance,Why do the optimal portfolios in the effcient frontier, is ...
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1answer
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Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions

Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you. If $u(x)$ is a homothetic utility, then show ...
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Quasi-linear utility. Deriving demand

I was trying to derive a general demand for the good $x$ for this quasi-linear function $u(x,y) = y + 2\sqrt{x}$ subject to standard budget constraint $p_x x + p_y y \leq M$ Using Kuhn-Tucker ...
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MWG_3D4_C, why the solution seems in reverse?

I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...). It is about exercise 3.D.4, the full statement of the exercise is ...
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182 views

Convex Preference but Convex Utility

Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
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Marginal rate of substitution interpretation

I am trying to interpret the marginal rate of substitution stidied in an article. The article in question is Burbidge, J. B., Robb, A. L., 1980. Pensions and retirement behaviour. The Canadian Journal ...

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