Questions tagged [walrasian]

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Walrasian demand with a twist of Leontief function

A consumer has the utility function $u(x_1; x_2)$ = $min(x_1; x_2)$ + $5max(x_1; x_2)$ Find its Walrasian demand $x^*(p; w)$. I've tried searching it up when we have two Leontief functions summed ...
30 views

Demand and Utility [closed]

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. Logically, it ...
36 views

Prove the equation

Let $$x^0=x^*(p^0,w)$$ then $$v(p,px^0)$$ is minimized at $$p=p^0$$ What theorem are we supposed to use in order to solve this, because I am a bit lost. Thanks in advance for all the suggestions/help....
19 views

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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 ...
2k views

Pareto optimal and Walrasian equilibrium [closed]

There are 100 units of good 1 and good 2 in a economy. Consumer 1 and consumer 2 have 50 units of each good. Consumer 1 only wants good 1 whereas consumer 2 only wants good 2. Note: Neither of these ...
1k views

Finding a walrasian demand function

If I have a sum utility function like this $U(y) = \sum_{j=1}^J u(y_j)$ where $u$ is convex. Is there then a way to find walrasian demand for such a function without using calculus or do you need to ...
399 views

Doubt regarding Walrasian equilibrium with complements for both agents

There are two goods $1,2$ and two agents $1,2$. Both have the utility function $u_{i}=\min({x_{1i},x_{2i}})$ for agent $i$ .The endowments are $(1,3)$ and $(3,1)$ for agent $1$ and $2$ ...
443 views

How does Brouwer's fixed point theorem relate to Walrasian equilibrium?

I am trying to understand Walrasian equilibrium and its connection to fixed points, especially how we can apply Brouwer’s fixed point theorem to the notion of Walrasian equilibrium. I understand the ...
122 views

Whether the demand in the panels satisfies the weak axiom

The Walrasian demand function $x(p,w)$ satisfies the weak axiom of revealed preference if the following property holds for any two price wealth situations $(p,w)$ and $(p',w')$: If $p•x(p',w')\le w$ ...
Show that $x(p,w)=w\cdot x(p,1)$ with homothetic preferences
Someone gave me a proof of this, but I am not sure if it is correct. Let $B(p,w) = \{x: p\cdot x \leq w\}$ (the budget set). Then: \begin{align} x(p,w) &= \arg \max_{x\in B(p,w)} u(x)\\ &=\...