Questions tagged [utility]

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

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Does Varian define the MRS differently/ as negative?

Varian defines the MRS as the slope of the indifference curve. However, Snyder/Nicholson (and apparently Wikipedia) define the MRS as the negative of the slope. Does Varian use a different definition, ...
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Are standard discrete choice models based on ordinal utility or cardinal utility?

Suppose we model consumer's choice between three brands Honda(choice 1), Toyota(choice 2) and BMW(choice 3) using a standard discrete choice model, with the utility of choice $j\in\{1,2,3\}$ being ...
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2 votes
1 answer
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Does a neoclassical production with constant returns to scale implies type of Cobb-Douglas

Assume the neoclassical production function $$F(K,L)\colon [0,\infty) \times [0,\infty) \to [0,\infty)$$ twice continuously differentiable, i.e., F is montone increasing and concave, i.e., $$ \partial ...
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4 votes
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Proving Pareto-efficiency with MRS

Given three people with the same utility function: $$ u_A(x_1,x_2)=u_B(x_1,x_2)=u_C(x_1,x_2)=\sqrt{x_1x_2} $$ Prove that the following allocation is Pareto efficient: $$ x_A=(2,2),\: x_B=(3,3),\: x_C=(...
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How Can I Model Demand Elasticity?

Can demand elasticity be determined by examining the distribution of marginal utility across a potential customer base? For example, if the distribution of marginal utility among potential customers ...
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3 votes
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Economic interpretation of assumption on utility function

Suppose $u\colon \mathbb{R}_{>0} \to \mathbb{R}$ is a utility function, twice continously differentiable, $u' > 0, u'' < 0$, and the classic Inada conditions hold, i.e., $\lim_{c \to \infty} ...
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1 answer
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Are these preferences locally non satiated? U(x1,x2)=(x1-1)/(2-x2)^2

I got this utility function representing certain preferences. Are these preferences locally non satiated? Can somebody please explain me with the exact definition of local non satiation why these ...
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utility maximization problem

Consider a simple two-period model in which consumer utility is a function of consumption over two periods.At this time, the utility function of the consumer is assumed as follows. u(x1,x2) = x1 times ...
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Simple utility maximization problem in a spatial equilibrium model

I was going through the conceptual framework in the following paper https://scholar.harvard.edu/files/shleifer/files/human_capital_qje_final.pdf Gennaioli, N., La Porta, R., Lopez-de-Silanes, F., &...
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What conditions imply convex utility set?

given a convex consumption set $X$, and utility function of $N$ agents: $u_1,\cdots,u_N$, under what condition, the utility set $U=\{u\in\mathbb{R}^N:\exists x\in X s.t. u_i(x)=u_i\forall i\}$ is ...
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Is the linear probability model consistent with utility maximization?

We know that Logit/probit models are consistent with utility maximization in the sense that the model implied probability of choosing option $1$ equals the probability that option $1$ has larger ...
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3 votes
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Concave utility functions solution example

In the following post an example is given of the corner solution for a concave utility function. I tried solving it but got stuck. I have no idea how these types of problems are solved so if you could ...
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Can the topological assumption in Debreu's representation theorem of cardinal utility be altered from "connected separable" to "second countable"?

Theorem (Debreu 1959 page 9, 10) Let $X$ be connected separable topological space endowed with product topology. If $\succsim$ is independent and at least three factors are essential, then there exist ...
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Does Debreu's representation theorem of ordinal utility require Hausdorff topology?

By Debreu's theorem of ordinal utility, any continuous weak order on $X$ is represented with a continuous utility function, if $X$ is a second countable or connected separable topological space. My ...
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Constrained optimization to find utility maximizing allocation

I am trying to find the allocation of goods X and Y in order to maximize utility between two consumers. The two utility functions are: $$ U1 = xy^5 $$ $$ U2 = 10xy $$ There are 8 of good X and 8 of ...
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Net utility intuition

Let us assume that a utility funciton is $U=C-L,$ or utility is consumption less leisure. Suppose $C=10,$and $L=2.$ We get $U=8.$ My question is: which 2 utility units are being subtracted from $C?$ ...
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What are some examples of goods/services whose utility functions have local maxima?

I'm a calculus teacher trying to construct a realistic example of a smooth utility function $U(x,y)$ that has a local maximum at some point $(x_0,y_0)$. This requires two goods, X and Y, such that the ...
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Constant relative risk aversion for wealth spanning from negative to positive

I am modeling scenarios that could involve wealth for all real numbers and I am assuming constant relative risk aversion. I need to model the scenarios for different risk aversion levels, but I can't ...
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What is the discounted (4%) difference in health outcomes between Treatment A and Treatment B using ICER, QALY and utility value?

I'm studying health economics and have been racking my brain trying to find the right answer to this problem, but I keep getting it wrong no matter what I do. I haven't had any trouble calculating ...
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4 votes
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What assumptions can be made to ensure convexity in this optimization problem?

This question is a continuation of the question I asked at: How can I show convexity of this value function? Where I came to the conclusion that more assumptions are required to show that the ...
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4 votes
1 answer
189 views

How can I show convexity of this value function?

I have set up an optmization problem as follows: $$V(A)=\max_{l, C} \quad u(C,l)$$ Where the only constraint is as follows: $$C=f(l,A)$$ Here $u$ is the utility function which captures social welfare. ...
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1 vote
3 answers
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risk aversion and the law of diminishing marginal utility

I see many plots where x is wealth and y is utility. If a person is risk averse, he has a concave line on the plot. If the person is risk neutral, her line on the plot is straight. On the other hand, ...
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Graphing Indifference curve & Budget constraint for substitute goods

I have two 'goods' - inpatient and outpatient healthcare units. In this scenario, the two goods are substitutes and I have graphed what happens when there is a decrease in the price of inpatient ...
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Convex Preference in Nash Equilibrium

Arrow Debreu (AD) uses the convex preference (A4 among their four assumptions, also see the assumption IIIc in AD 1954 ECTA) to make general equilibrium (GE) exist, unique, and well-behave. What ...
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How can I formulate the following optimization problem?

I want to set up an optmiization problem for global warming in which a planner determines how much carbon dioxide gas is emitted. Let's say we reduce this problem down to two periods, then I ...
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Why do we optimize utility from X1 according to itself?

In lecturer's notes we have a utility function $U_i = X_i^A * (1-L_i)^{1-a},$ $ 0< a< 1$, $ i = 1,2 $ $MP_1 = w_1 $ $MP_2 = w_2$ $X_1 + X_2 = w_1 * L_1 + w_2 * L_2$ And we need to form a ...
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1 vote
1 answer
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Lagrangian when ICs are tangent to the budget line

Suppose the graph below shows three Indifference Curves such that $t > s > r$, and the budget line $p_1x + p_2y = I$. I was wondering if we set the Lagrangian as $\mathcal{L}= U(x,y) - \lambda (...
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1 vote
0 answers
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Risk Premium for Prospect Theory-like value function

I am curious how to calculate the following risk premium for a utility function that is not linear in $w$. What i'm asking is the following: Consider an agent with utility function $u$, initial wealth ...
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How does marginal utility and marginal product differ?

The marginal utility is, in plain English, the additional benefit (utility) that an individual gets by consuming an additional unit of a good or service. According to the Law of Diminishing Marginal ...
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2 votes
1 answer
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Is Epstein-Zin utility a generalization of dynamic expected utility (DEU)?

Epstein-Zin (EZ) utility is the solution to: DEU is relatively simple: $\sum_t \delta ^t\mathbb E[u(c_t)]$. Is DEU a special case of EZ? How are those two models compared? Since EZ is a solution of a ...
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1 vote
1 answer
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Is it possible to get a demand function as function of income and utility from this log linear indirect utility?

I have this indirect utility function: $$v=-c\frac{p^{(-β+1)}}{(-\beta+1)}+\frac{y^{(-\gamma+1)}}{(-\gamma+1)}$$ with constraint Y = c + pq I have posted before about getting the utility function from ...
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1 vote
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What is the typical utility function of the standard loglinear demand function?

What is the typical utility function of this demand function? $$x_1 = \ln(x_2) - \beta \ln(p_1) + \gamma \ln(y).$$ With budget constraint $y = p x_1 + x_2.$
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What the name of a demand function that is both a function of income and utility?

I am working with a model that includes a demand function that follows this proces: We have utility function and budget constraint. Good x1 has price p and good x2 is normalised. p = dU/dx1/dU/dx2 ...
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2 votes
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How to derive utility function from indirect utility and Marshallian demand?

c is composite good with normalised price, q is good with price p. y is income. I have this indirect utility function: $$v=-c\frac{p^{(-β+1)}}{(-\beta+1)}+\frac{y^{(-\gamma+1)}}{(-\gamma+1)}$$ And ...
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Price Offer Curve for a U(q1,q2)=max{q1,q2} Utility Function

Can someone help me understand how to draw out the price offer curve, or price consumption curve (PCC), for a U(q1,q2)=max{q1,q2} function? There's no information about this in my textbook and it's ...
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3 votes
2 answers
54 views

Help solving utility optimization problem from Connelly 1992 (Economics)

I am working through a paper by Connelly 1992 in RESTAT and I'm hoping to get some assistance in working through the optimization problem that she sets up. I apologize that it might be simple for many ...
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1 vote
0 answers
56 views

Perfect substitutes mathematical definitions not equivalent

Statement: Consider goods $X$ and $Y$ (and we denote the quantities of by the same notation) such that they are perfect substitutes with the substitution ratio $1:n$. Assume the basic axioms ...
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Mathematical definition of perfect substitutes

If $X$ and $Y$ are perfect substitutes such that a unit of $X$ can be replaced by $n$ units of $Y$, how do we get the mathematical equation from it? I know the equation is of the form $ax+by$ (and $U =...
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0 votes
1 answer
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Marginal utility meaning and properties

Consider goods $X$ and $Y$ such that the marginal utility of a unit of good $X$ is always that of $n$ units of good $Y$. $X$ and $Y$ are perfect substitutes. Question 1: What does the above mean ...
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1 vote
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How to measure utility functions in the stock market

i am looking for some articles on how to identify and estimate utility functions in the stock market. My own search results yielded some papers by Blackburn and Ukhov https://www.researchgate.net/...
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Convergence of different models for the disposition effect?

I am struggling with the following problem: in a paper, Markku Kaustia (2012) https://www.jstor.org/stable/40930477 found that Prospect Theory does not explain the disposition effect. A similar study ...
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What is a simple demand function that allows for different price and income elasticities than 1 and -1?

Cobb-Douglas utility functions assume price elasticity of $-1$ and income elasticity of $1$. Are there any utility functions with two goods that lead to a demand function, where you have the choice of ...
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In consumer theory, shouldn't necessity good and neutral good be different ? What will be the IC and utility function for both?

Necessity good for example salt, which regardless of income has to be consumed at certain quantity. But neutral good for example is Suppliments for a healthy person which regardless of income he/she ...
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1 answer
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How do I get to this demand function in the monocentric city model?

I need to get this resulting price and quantity (housing): It's pretty clear that the denominator of the quantity function is just the price function. From this utility function: And this constraint:...
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-1 votes
1 answer
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Representing a Lexicographic Preference in a Natural X Natural Choice Space With Utility Function

my current thinking is i have to dis/prove two things cardinality continuity but im not sure about how it would apply since the above is a natural X natural choice space I know cardinality of ...
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0 votes
1 answer
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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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1 vote
1 answer
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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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2 votes
4 answers
2k views

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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1 vote
1 answer
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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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1 vote
0 answers
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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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