Questions tagged [walrasian]
The walrasian tag has no usage guidance.
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How do I find the Walrasian equilibrium price?
Consider a production economy with 1 consumer and 2 firms. The consumer's utility is $u(x,y)=xy$. The first firm makes $x$ using capital and labor according to the production function $x=k^\alpha l^{1-...
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How to find a Walrasian equilibrium for this economy?
Consider a production economy with 2 goods, 1 and 2, two consumers A and B, and 2 firms $\alpha,\beta$. The consumers' utility functions are
\begin{align}
u_A(x_1^A,x_2^A)=x_1^A+x_2^A-\frac{1}{24}(x_1^...
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How do I argue that the Walrasian equilibrium is unique?
Consider an economy with 1 consumer and 1 firm. There are only 2 goods, leisure $l$ and corn $c$ and the consumer is endowed with 24 hours of leisure. The consumer's utility function is $u(c,l)=cl$. ...
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Exchange economy with trade
Consider an exchange economy with 2 goods $x,y$ and $n+1$ consumers $0,1,\cdots,n$. Consumer 0 has utility function $u_0(x,y)=x^\alpha y^{1-\alpha}$ and endowment $w_0=(1,0)$. Other consumers $1,\...
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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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How to find the General Equilibria allowing for infinitesimal prices?
I know there can’t exist a usual Walrasian Equilibrium when both agents have the same lexicographic preferences:
If both agents had the preferences
$(x,y) \succeq (x’,y’) \iff:$ $x > x’ \text{ or } ...
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Robinson Crusoe Economy Question
Question:
Hypothetically, Robinson Crusoe is stuck on an island and can choose between working on gathering coconuts or leisure. The utility function is:
$U(C,L)=C^{2/5}L^{3/5}$
where C is the num of ...
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What is the budget constraint when we assume a common utility function?
Let's consider an exchange economy with two identical consumers. The
common utility function is:
$$u^i (x_1, x_2) = x_1^α x_2^{1-α} \;\;\; \text{for} \;\;\; 0 < α < 1.$$
Society has 10 units of ...
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Why is there a Walrasian Equilibrium if excess demand goes to infinity as price goes to 0?
In one exercise, we have to argue that a Walrasian Equilibrium exists and the solution says that if we can see that excess demand goes to infinity as price goes to 0, and as price goes to infinity, ...
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Finding demand function in Walrasian equilibrium
Maybe the title doesn't reflect what I mean perfectly but basically, I wanna derive demand functions from those two utility functions:
where $x_{11}$ is the consumption of good 1 by agent 1 and $x_{...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
user20317
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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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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^\...
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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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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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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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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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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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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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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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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 $u(x) = \min\{x_1, x_2\}$, but the addition of $x_3$ confuses me.
Problem
Derive the demand function $x(p,w)$ from $u(x) = \min\{x_1, x_2\} + x_3$.
What I ...
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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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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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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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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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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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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 ...
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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 ...
user11861
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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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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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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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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)\\
&=\...
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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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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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