# Questions tagged [preferences]

Binary relations that reflect which states of the world an agent considers to be most desirable. Preferences are a fundamental ingredient in the axiomatic study of consumer choice decision theory.

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### What is the purpose of the local non-satiation assumption in the first welfare theorem?

The profit maximization assumption implies $$\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i$$ Okay so this just says if the agent is utility maximizing / rational, then if he doesn't ...
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### Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
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### Consumption-Leisure Elasticity

The macro-literature insists on a consumption-leisure elasticity of 0 to match the balanced growth fact of constant labor supply. Is there any paper that tries to evaluate this elasticity using ...
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### What is the observable definition of "preference" by Frisch?

To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations! How to define ...
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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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### 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 ...
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### MATLAB code: Plot utility function and budget constraint

how do i plot these? i have this utility function: $$U(x_1,x_2)=\log(x_1)+\beta \log(x_2)$$ and this budget constraint: $$p_1 x_1+p_2 x_2=R$$ where $R=3, p_1=0.5, p_2=0.5$ i dont know how to plot ...
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### $a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?

$\succsim$ is a continuous and local non-satiate weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (...
637 views

### Non-homothetic CES preferences: demand derivation

I am struggling a little with the derivation of the goods demand and price index when preferences are CES and not homothetic. I am optimising the allocation of a Dixit-Stiglitz aggregator, so the ...
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### Definition of strictly convex preference

Let $x,y\in X$. Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that: $x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?
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### Show that if $\succsim$ is continous on $X$, then the sets $\precsim (x^0)$ and $\succsim (x^0)$ are closed

For a set to be continuous, it's contour sets must be closed. Since we can define $$\succsim x^0 = \{x, x^0 \in X: x \succsim x^0 \}$$ and $$\precsim x^0 = \{x, x^0 \in X: x \precsim x^0\}$$ it ...
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### Is it possible and logical to have an upwards sloping budget line?

The question I have is, for example, say Garry has two goods, cookies he pays 1 to consume a cookie and a maximum of 10 can be consumed, whilst he gets PAID 2 to consume vegetables. Garry is also ...
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### Reference request: modeling firms that act to create demand for their products

(I don't have an economics background; apologies if my terminology is confusing.) It seems like there is often a situation where a firm can take actions to create demand that did not already exist. ...
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### What is the usefulness of Cobb Douglas functions? Why do we use them so often?

Hard to find much explanation as to why we generally use CD functions so often. My understanding is that it is usually well behaved when used for utility functions and preferances, since it is convex,...
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### Binary relation on the set $X = \{v, w, x, y , z\}$ that is asymmetric and transitive but not negatively transitive

So I am trying to find a binary relation on the set $X = \{v, w, x, y, z\}$ that is asymmetric and transitive but not negatively transitive, and is quite tricky. Will $R = (v, w)$ be asymmetric and ...
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### Ordering of bundles for which the axioms of transitivity, continuity, strong monotonicity and convexity are valid

Let there be two bundles which are obtained from the sequences $x^n = (x_1,x_2)= \left( 2 + \frac{1}{n},5 \right)$ and $y^n = (y_1,y_2) = \left(4 + \frac{2}{n}, 5 \right)$. Is it possible to obtain an ...
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### Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
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### Heckscher-Ohlin with heterogeneous preferences

could someone really help me out I would need to show a situation in which the Heckscher-Ohlin result does not necessarily hold when preferences are heterogeneous. Does someone have an idea how I ...
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### How are preferences related to relative prices?

For instance, across regions of a country or between countries. Is that different preferences for food lead to distinct relative prices in different regions or countries? Or is it the other way ...
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### Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out..... Is there is a hierarchy of preference, and within each level of choice do we reset the ...
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### Revealed preference if we know that the decisionmaker is rational?

In standard revealed preference, we don't assume that the agent has rational preferences over a choice set $X$, and we can then ask: under what conditions can $X$ be rationalized by a rational ...
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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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### Inferior and normal good and the change in price of those goods

In general, We know that if a good is normal, then as your income increases, then demand of that good increases as well as price is fixed. Similarly, if a good is inferior, then as your income ...
Suppose that a binary relation satisfies only: Independence axiom: $L≿L′⟺α\circ L+(1−α)\circ L′′≿α\circ L′+(1−α) \circ L′′$ Reduction to simple lotteries: For all $g$, $g~g'$, $g'$ is the simple ...