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 ...
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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 ...
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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....
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Walrasian Equilibrium

Need help solving last two parts of this problem. We’ve solved for the general equilibrium but not sure how to go from there. The endowments of two consumers are given by $w_1 = (40,80)$ and $w_2 = (...
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Becker Social Pricing and Lack of Smooth Demand

I was reading an article on Becker Social Pricing, where your demand for a good depends on other people's demand for the good. So basically this paper is meant to be a primer into explaining why some ...
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28 views

Find equilibrium price using excess demand function

Consider an economy with two agents. There are two goods, x and y. Agents' preferences are Leontif ones as follows: $u_1(x,y)=\min(x,4y)$ and $u_2(x,y)=\min(x,y)$. Initial endowment for 1 is (2,4), ...
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44 views

Unique competitive equilibrium in an exchange economy

I was working on the following excercise: In an exchange economy $\varepsilon$ with two goods and strictly monotone, continous and strict concave utility functions, suppose all demand functions are ...
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267 views

Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$

I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me. Problem Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$ What I did ...
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127 views

What is the difference between solving for utility maximization separately or aggregately?

I derived the Walrasian equilibrium for an economy of two consumers with their respective utility functions (u1, u2) and initial endowments but later on I am asked to maximize (u1+u2). Does anyone ...
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115 views

General Equilibrium Involving Production

I need a little conceptual clarification. For a standard $N*K*M$ general equilibrium model, would an allocation, say, $y^k$ be Pareto Optimal if it does not solve $max(py^k)$? I understand that the ...
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60 views

Question about the relationship between Weak Axiom and Slutsky Matrix

We know that if a differentiable Walrasian demand function $x(p,w)$ satisfies Walras' law ($p^Tx=w$), homogeneity of degree zero ($x(\alpha p,\alpha w)=x(p,w)$), and the weak axiom of revealed ...
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60 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 ...
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61 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 ...
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190 views

What is the Walras law vs first welfare theorem

As far as I know, both of the first welfare theorem and the Walras law are closely tied to the invisible hand. what is the difference between them? thank you very much for your help
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Walras's law in a Fisher market

Walras's law is stated for an exchange market: each agent comes to the market with a certain endowment of each commodity, a price-vector is determined, and the demand of each agent is the best bundle ...
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202 views

Blocking Coalitions

For $n$ individuals, can a blocking coalition only be formed by at least $n/2$ individuals? For example, if there are 6 individuals, can less than 3 individuals form blocking coalitions?
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2k views

What is excess demand/ excess supply?

I've been reading up on Walras' Law and thought I understood it pretty well. However one of my friends asked me point blank what is an example of excess demand or excess supply is and I had some ...
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861 views

Convexity of Walrasian Demand

A follow up to my previous question: Given $u(x) = (x_1-b_1)^\alpha (x_2-b_2)^\beta(x_3-b_3)^\gamma$ and ending up with from a maximization that $$x(p,w) = (b_1, b_2, b_3) + (w - (b \cdot p))\...
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104 views

MRS in Walrasian equilibrium price expression?

I have the utility function $U^A=\alpha ln(x^A)+\beta ln(y^A)$ for consumer $A$ and $U^B=\gamma ln(x^B)+\phi ln(y^B)$ for consumer $B$. They are endowed with $\omega^h_x$ and $\omega^h_y$ of $x$ and $...
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91 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 ...
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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 ...
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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 ...
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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 $2$ ...
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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 ...
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1answer
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 $p•x(p',w')\le w$ ...
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1answer
2k views

Perfect Complements - Walrasian Equilibrium

For a homework , I struggled to solve the following question but couldn't go further: endowment of person 1 = (30,0) endowment of person 2 = (0,20) utility ...
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257 views

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)\\ &=\...