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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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### 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 ...
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, ... 1answer 1k views ### 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 ... 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)... 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"? ... 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 ... 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? 2answers 78 views ### 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 ... 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 ... 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 ... 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 ... 0answers 76 views ### 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 1answer 49 views ### 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. ... 1answer 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 ... 1answer 72 views ### 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 ... 1answer 3k views ### 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(... 0answers 104 views ### 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, ... 2answers 4k views ### 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... 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-... 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?... 1answer 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, ... 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 ... 0answers 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 ... 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 ... 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 ... 4answers 3k views ### 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 ... 2answers 1k views ### 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 ... 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), ... 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 ... 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, ... 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}$$where a>0 is a constant scale parameter. I ... 1answer 3k views ### Are Cobb-Douglas preferences homothetic? Our lecture defined a preference to be homothetic, if the following is true:$$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$Cobb-Douglas preferences can be ... 1answer 151 views ### Interpretation of utility function I am reading Lucas (1980) and I am a bit confused about the way he formulates the utility function. So there is one non-storable good that comes in n colours and one unit of labor produces y ... 1answer 466 views ### Specification form for household utility function What determines the choice of the functional form to be adopted for the household CRRA utility function, when utility depends on consumption and leisure? For examples, we have these three functional ... 1answer 70 views ### What is one dimensional, ordered type? I am reading papers about moral hazard. What is one dimensional, ordered type \theta\in\Theta? What is one dimensional, not ordered type \theta\in\Theta? Could you please give an example? ... 0answers 44 views ### Terminology for separability in price and value Take an agent with mean-variance utility over something that is uncertain:$$ U(x) = \mu_x^\theta - \sigma_x^\lambda $$A\in \{0,1\} happens if U(x)>0, and x is a random variable$$ A = \...
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 \$\...