Questions tagged [general-equilibrium]

In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall (or "general") equilibrium.

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Learning Resource Question - Computable General Equilibrium Modelling

Several years after graduation, I would like to learn some practical computable general equilibrium (CGE) modelling such as a CGE that can handle distributional outcomes. Does anyone know of open-...
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Existence of a Walrasian Equilibrium

I was wondering how to tackle part b of this question. I've already completed part a) using the usual method of equating the MRS (kink point for the second utility function) then looking at ...
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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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Competitive equilibrium for an economy with a consumer and a producer

A representative agent’s preference over consumption $(c)$ and labour supply $(l)$ is given by the utility function $$ u(c_D, l_S)= c_D^a .(24-l_S)^{1-a}$$ Production of the consumption good $c$ is ...
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Understanding a paragraph in Debreu's Theory of Value

I wish to understand the following paragraph (from section $2.7$ of Debreu's Theory of Value): Imagine that a certain good circulates as money at location $s$, at date $t$, and let $k$ be the index ...
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What does it mean when an economist talks about "equilibrium"

In economics, there are many equilibrium concepts, like equilibrium under perfect competition, Monopolist equilibrium, competitive equilibrium, general equilibrium, nash equilibrium, equilibrium price,...
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Changes in TFP and wage rates across firms

Assume that you have two firms, firm A and firm B. Firm A faces the production function: $$ Y_{A}=A_{A}F\left(K_{A},L_{A}\right) $$ and firm B faces: $$ Y_{B}=A_{B}F\left(K_{B},L_{B}\right) $$ Factors ...
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Perfect Competition, Zero profit rule and General Equilibrium

I'm reading a book where the definition of an equilibrium for a competitive economy is given as in Kenneth J. Arrow; Gerard Debreu (1954) Existence of an Equilibrium for a Competitive 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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How do I find the socially optimum and equilibrium value?

I am struggling with the following question. Could someone please explain how to do it? People are trying to go to the city centre. A bus takes 1 hour and will always take 1 hour, unaffected by ...
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How would a perfectly competitive industry respond to a macroeconomic demand shock in the long run?

In microeconomics, we are taught that in a perfectly competitive industry, the long-run industry supply curve is horizontal. This is because new firms would enter or exit until the profit is driven to ...
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In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?

The following is what I understand, so far. If we measure labour in the $x$-axis and capital in the $y$-axis, the slope of diagonal of the box is the capital-labour ratio $K/L$ in the economy. Let $A$ ...
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Is this really a valid description of AS&AD after lockdown?

I understand that in the short run AS decreased (supply chains) and AD increased (stimulus, post-lockdown behaviour). But what's up with the lines in the long-run? Also is this even a valid way of ...
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Can a 'general equilibrium' involve externalities?

The textbook definition of 'general equilibrium' requires that 1) each individual's utility depends only on their own consumption bundle 2) each firm's profits depend only on their own production plan....
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Non-existence of general equilibrium with quasi-linear utility

I recently came across an interesting example of why general equilibrium need not exist with quasi-linear utility (in case anyone is interested, I'm posting this at the end). To make the example work, ...
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Say's law of markets: theory and empirics

Good morning everyone, since I've just finished to read the book "A Treatise on Political Economy" by the french economist J.B. Say and since I've read about his famous "law of markets&...
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What should I learn from heterodox economy? [closed]

As a graduate and master student, everything I've learned and I'm learning is from mainstream economy which in some parts seems like propaganda. Most of theories comes from the hypotesis of perfect ...
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Failure of 1st welfare theorem with non-increasing utility function

I want to find an example that utility function is not increasing but still satisfies that $u(x) \geq u(y)$ for all $x \geq y$ and 1st welfare theorem fails. I want to prove this on edgeworth box not ...
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Equilibrium in an endowment economy

Consider an endowment economy with 2 agents with the same preferences defined by $\sum\beta^tlog\ c_t$ where Agent 1 has the following stream of endowments: $(w_0,w_1,w_2,w_3,...) = (2,1,2,1,...)$. ...
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Is there any macroeconomic model based on Olson's collective action theory?

I've recently learned about Olson's Collective Action Theory and I'm interested in mathematic models of economies that follow the theory's axioms. I tried finding a general equilibrium macro model ...
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First and Second-Best

Why are environmental instruments like Pigovian-taxes or the Coase-Theorem viewed as first-best solutions, while taxes or tradable permits are viewed as second best? How do they differ, and what makes ...
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Does aggregate CRS imply firm-level CRS?

Suppose that a production set $Y \subset \mathbb R^I$ has the following two properties: Constant returns to scale: $\forall y \in Y, \alpha \geq 0$, we have $\alpha y \in Y$. Separability: For some $\...
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GE with an intermediate good

intro I'm looking at a simple model with 1 consumer, 2 goods and 2 firms. I'm trying to get a price vector [p0, p1] that makes it work. By makes it work, I mean, ...
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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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Finding the pigou tax that supports a pareto efficient allocation as walrasian equilibrium

I have a two consumer economy with utility functions $u_1=x_{12}-x_{21}$ and $u_2=x_{21}x_{22}$. I am asked to find the Pigou tax $t>0$ on agent 2's consumption of good 1, such that the allocation $...
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Finding the set of pareto efficient allocations with externalities

I have a two-agent exchange economy where utility functions are given by: $u_{1}=x_{12}-x_{21}$ and $u_2=x_{21}x_{22}$. I am looking to find the set of pareto efficient allocations. Since utility ...
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Effect of change in endowments on prices in Walrasian equilibria

I have a two-good, two-consumer exchange economy. $(\omega_{i1}, \omega_{i2})\in \mathbb{R}_{+}^2$ denote consumer $i$'s endowments of commodities 1 and 2 for $i\in\{1,2\}$. Utility functions are ...
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Proving local non-satiation in arbitrary metric space

I have a pure exchange economy where every consumption set $X_i$ is non-empty and convex and every preference relation $\succeq_{i}$ is strictly convex. I am asked to show that preferences are locally ...
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Aggregation of the closure property of a production set

Consider an economy with finitely many goods $I$ and factors $F$. For each good $i$, let $Y_i \subset \mathbb R^I \times \mathbb R^F_{\geq 0}$ denote a production set for $i$. Assume each $Y_i$ has ...
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Gale's version of the Rubinstein-Wolinsky (1985) model

Likely to be a very stupid doubt. I am reading Douglas Gale's book "The Strategic Foundations of General Equilibrium", which presents a brief version of "Equilibrium in a Market with ...
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Quantity restriction in model with fixed factor of production

I'm trying to see the effect of a restriction on production in a model where one factor of production is perfectly elastic and the other is fixed. Specifically, suppose the production function is Cobb-...
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What will giffen goods and Veblen goods peform in general equilibrium model?

I'm a beginer of microeconomics. According to consumer behavior theory, a consumer possesses a set number of money as budget constraint at first. And their is negative income elasticity of demand and ...
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What are the best theoretical or empirical defenses of equilibrium analysis in economics?

An Anarchist FAQ (see Wikipedia page here) focuses its opposition to mainstream economics by criticizing equilibrium analysis. The FAQ notes that, [Equilibrium analysis] is essentially a static tool ...
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5 votes
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Arrow-Debreu Theorem of Existence: Non satiation

Let $n$ be the number of consumers and $m$ be the number of commodities. The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
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Economics behind reverse auctions with occasional non-profiting suppliers

I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
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Monotonicity and continuity implies that all bundles are weakly preferred to 0

Suppose a consumer has a preference ordering $\succsim$ on $X$ that is complete. Show that if preferences are continuous and monotone, then $x\succsim0$ for any $x\in\mathbb{R}_{+}^{N}$, where $0$ is ...
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Comparing 2 equilibrium values (competitive vs centralized): can I compare only 1st derivative of objective function?

I have a rather complex model where analytical solutions do not seem achievable (I also tried symbolic solving in Matlab and Python and could not find any) so that I cannot get an explicit expression ...
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Offer curves in general equilibrium

I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it? I can understand the Pareto set and contract curve but when it ...
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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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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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2 votes
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Meaning of «intertemporal substitution effect dominates the income effect»

Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, ...
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1 vote
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LM curve from money demand

Let $M^d (Y,r)=a+bY-cr$ where $M^d = M/P$ is the money demand in the economy. $a,b,c>0$. Derive $LM$. My try $M/P=a + b Y - c r$ $b Y = -a + \frac{M}{P} + c r$ $Y = -\frac{a}{b} + \frac{M}{b P} + \...
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1 vote
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GDP in equilibrium

I have to find the GDP in equilibrium for a IS LM model. It is given that $M^d (Y,r)=M_0+M_1Y-M_2r$ and $M^d=M/P$, $M_0,M_1,M_2>0$ and $M^d$ is money demand. my solution so far I have found that $...
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Find pareto optimal allocations

Consumer 1: $U_1(x_1,y_1)=x_1y_1$ Consumer 2:$ u_2(x_2,y_2)=min\{x_2y_2 , 4\} $ Initial endowments e1=(1,4) and e2=(4,1) I want to find Pareto optimal allocations and show its edgeworth box My ...
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Question on General Equilibrium: how to write offer curves?

QUESTION: Consider simple two-person, two-good economy in which agents’ utility functions are given by $U_1(x_{11}, x_{21}) = min\{x_{11}, x_{21}\} $, and $U_2(x_{12}, x_{22}) = min\{4x_{12}, x_{22}\}...
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Market with changing number of goods and services

In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run. Over time,...
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1 vote
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preference convexity and existence of equilbria

Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of ...
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Competitive equilibrium with production

Consider an economy with four goods, two individuals and two firms. Firm 1 produces good $x$, firm 2 produces good $y$. Consumers' utilities are $u_1(x,y,z,w)=\min\{x,2y\}$ and $u_2(x,y,z,w)=\min\{2x,...
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Bothersome Mean/Variance Analysis

I'm currently writing my thesis in which I compare a series of ESG General Equilibrium models. I fell over this proof in Pastor, Stambaugh, Taylor Sustainable Investing in Equilibrium (2019) page 42. ...
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Regression approximation for the rate of change in occupancy rate of residential market with respect to price

I have historical data on occupancy rates for a given neighborhood, along with characteristics and other local economic variables. I am looking to estimate the regression equation with occupancy rates ...
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