# Questions tagged [utility]

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

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### Why is the nature of graph of utility function different from indifference curve?

I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that ...
1answer
475 views

### A question about MWG Exercise 3.D.4

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 ...
0answers
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### Does quasilinear preference contain rationality, monotonicity or other assumptions?

I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first ...
1answer
140 views

### Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?

Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer: Suppose we have a preference ordering $\succeq$, which is ...
1answer
113 views

### How to find change in the optimal choice with a utility function in general form?

Suppose the utility function is represented as $U(x_1,x_2;I)$, where $I$ is the level of information the consumer possesses. How to find the change in the optimal choice of $x_1$ as price of $x_1$ ...
1answer
50 views

### Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ...
2answers
491 views

### Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
1answer
102 views

### Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?

According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
0answers
114 views

### How to prove that the walrasian demand function $x(p,w)$ is continuous in $p$ and $w$?

If the utility function $u$ is continuous and satisfies local nonsatiation, and walrasian demand function $x(p, w)$ is a function (i.e. always map to only single values), how to prove that $x(p,w)$ is ...
1answer
109 views

### Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle?

In the context of Walrasian demand: Suppose u is continuous, satisfies local nonsatiation, and is strictly quasi-concave, each $w(p, x)$ contains a single consumption bundle. The proof I got from a ...
1answer
133 views

### Deriving demand function in case of multivariable utility functions with min and max structures

Suppose I have utility function like this: $u(x_1,x_2,x_3)=min\{x_1,a-x_1\}\times min\{x_2,b-x_2\}+x_3$ where a and b are real numbers and $x_1\in [0, a]$ and $x_2\in [0,b]$. What will be a procedure ...
2answers
147 views

### Algebraic approach towards convexity

I have a function: $u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
1answer
196 views

### Why does quadratic utility function imply $\mu-\sigma$ preference?

Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
2answers
189 views

### Utility function_maximazation [closed]

A consumer is deciding about her hours ($h$) and consumption ($c$), her preference over bundles of work and consumption are as follows: $U(c,h)= c + \sqrt{24-h}$ The consumer would get an hourly wage ...
2answers
125 views

### Is there any evidence for consumer utility-maximising behaviour, at individual or market level?

Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence. Is there any evidence that some consumers do ...
0answers
107 views

### derive value function from utility function

We have the utility function. $$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$ And I am trying to find the value function. $U$ is utility function. $c_t$ is consumption at ...
1answer
131 views

### Strictly increasing function transformation

I have utility function given by: $U(x_1, x_2) = \begin{cases} x_1+x_2 & \text{if$x_1+x_2<6$} \\ 6 & \text{if$6\...
3answers
268 views

### utility function always negative

In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?
0answers
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1answer
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### 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 ...
1answer
35 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 ...
2answers
250 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 ...
1answer
38 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?
1answer
48 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/...
1answer
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### 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 ...
1answer
61 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 ...