# Questions tagged [walrasian]

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### How do I argue that "prices aggregate beliefs" in this Walrasian equilibrium?

Consider an $n$ person economy with only 1 good and 2 states of nature $r,s$. Consumer $i$'s utility function is $$u_i(x_{ir},x_{is})=\pi_i \ln x_{ir}+(1-\pi_i)\ln x_{is}$$ where $\pi_i\in (0,1)$ is ...
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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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### 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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### 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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