# Questions tagged [walrasian]

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### How to find a Walrasian equilibrium for this production economy?

Consider a production economy with 2 consumers and 2 firms. There are 3 goods: leisure $l$ and two goods $x,y$. The utility function of both consumers are $u_i(l_i,x_i,y_i)=l_i(x_i)^2(y_i)^2$ and the ...
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### Pure exchange economy: What if a consumer can set prices?

I'm trying to solve the following problem: Consider an exchange economy with 2 consumers and 2 goods. First, consumer A sets the price, then consumer B maximizes utility according to the price. Then ...
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1 vote
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### Endowment of an agent

I was going through the Shapley-Folkman-Starr Lemma (https://simons.berkeley.edu/sites/default/files/docs/3605/simons2.pdf) and I came across the term "endowment" of an agent. My assumption ...
71 views

### For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation is a walrasian equilibrium

I have a two-person exchange economy Each agent has the following utility $u_i(x_i,y_i)=v(x_i)+y_i$ for agent $i=\{A,B\}$ Assume that $v$ is strictly concave and increasing function that has a ...
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### Edgeworth Economy and Walras equilibrium

I have been given an Edgeworth Economy with to consumers A and B. Their preferences are given with the utility functions: My question is, how do I find the walras equilibrium? I tried starting out ...
1 vote
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### When is an allocation in the core of an economy but it's not a Walrasian equilibrium?

So I was given this problem where both agents have Cobb-Douglas utility functions and I'm asked to find an allocation that's in the core but not a Walrasian equilibrium. Isn't the core of an economy ...
293 views

### How to solve a general equilibrium problem with lexicographic preferences?

I have been unable to find a good example of this type of GE problem in our textbooks, and our professor has indicated that something like this may appear on our exam. So, here is a hypothetical ...
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### Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

I am given $U(x,y,z) = x^\frac{2}{3}y^\frac{1}{3} + z$. I am asked to solve the following: (i) Prove the convexity of these preferences (convex, strictly convex or neither?) (ii) Solve for the ...
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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 ...
1 vote
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### 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 ...
1 vote
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### 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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### 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 ... 107 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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1 vote
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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 ...
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### 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 ...
2k 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 ... 600 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 ...
1 vote
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### 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 $p•x(p',w')\le w$ ...
1 vote
588 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 $2$ ...
1 vote
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### 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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### 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)\\ &=\...
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))\...