Questions tagged [walrasian]

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Walrasian Equilibrium in A Simple Assignment (Matching) Model

I am reading Acemoglu 1996 and the Walrasian allocation in section II makes me confused. The setting is following. The economy lasts for two periods and consists of two types of agents, firms and ...
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36 views

What does it mean “non-Walrasian” or “quasi-Walrasian”?

In a recent NBER workshop, Robert Hall started a discussion with his first slide summarizing the macro literature. I am not very familiar with either DMP model or New Keynesian model and have no idea ...
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298 views

General Equilibrium with Perfect Substitutes

I came across the following problem: The quantities of an economy’s only two goods are denoted by $X$ and $Y$; no production is possible. Ann’s and Ben’s preferences are described by the utility ...
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1answer
32 views

How can a “producer face a limited market as regards sales and yet a highly competitive market as regards price”?

Kaldor (1972): it is evident that the co-existence of increasing returns and competition—emphasised by Young and also by Marx, but wholly excluded by the axiomatic framework of Walrasian economics—is ...
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1answer
86 views

Walras Law in a production economy with fixed costs

Consider a price taking firm with fixed costs $fc \geq 0$: \begin{align*} \Pi &= \max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\} \end{align*} A representative household owns this firm:...
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2answers
264 views

Finding Cobb-Douglas Hicksian Demand using Duality

I'm trying to follow the in-text examples from Mas-Colell. I can confirm I have the correct first order-conditions and hence the Marshallian demand functions for Example 3.D.1: $u(x_1,x_2) = x_1^\...
4
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1answer
71 views

Correct and complete characterisation of the Walrasian demand function

I would like to propose to you the following problem and my proposed solution. In particular, I am unsure in how to correctly characterize the Walrasian demand. Can you please have a look at it and ...
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142 views

General Equilibrium: Two Consumers with Perfect Substitutes and Perfect Complements Utility Functions

I am attempting to solve a general equilibrium in pure exchange economy problem where the first consumer has an endowment of $(3, 4)$ and a utility function of $U(x) = 3x + 5y$. The second consumer ...
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1answer
57 views

Effect of price on utility

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. I was discussing ...
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1answer
89 views

Walrasian demand with a twist of Leontief function

A consumer has the utility function $u(x_1; x_2) = \min(x_1; x_2) + 5 \max(x_1; x_2)$. Find its Walrasian demand $x^*(p; w)$. I've tried searching it up when we have two Leontief functions summed ...
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1answer
48 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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1answer
44 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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50 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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1answer
69 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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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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1answer
86 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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2answers
301 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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233 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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55 views

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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1answer
122 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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1answer
251 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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168 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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3k 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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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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98 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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1answer
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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1answer
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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1answer
471 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
127 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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467 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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1answer
3k 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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1answer
285 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)\\ &=\...
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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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1answer
985 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))\...