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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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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1answer
32 views
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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36 views
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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22 views
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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31 views
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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40 views
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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1answer
135 views
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, ...
4
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0answers
33 views
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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18 views
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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3answers
54 views
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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0answers
22 views
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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2answers
215 views
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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2answers
180 views
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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1answer
39 views
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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1answer
80 views
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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1answer
63 views
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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2answers
249 views
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 $i \in [n]$. ...
2
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0answers
23 views
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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1answer
37 views
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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109 views
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 ...
2
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1answer
99 views
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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1answer
376 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
91 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:...
2
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1answer
78 views
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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1answer
73 views
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} + \...
1
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1answer
92 views
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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36 views
Second welfare theorem and non-continuous preferences
Are there any monotonic and strictly convex preferences that are not continuous but the second welfare theorem does not hold for them?
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1answer
153 views
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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1answer
137 views
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}\}...
2
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1answer
86 views
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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162 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
61 views
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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1answer
56 views
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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1answer
58 views
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. ...
0
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1answer
60 views
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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0answers
35 views
Uniqueness of Arrow-Debreu Equilibria
I have been trying to figure out conditions on the preferences of traders in an exchange economy such that the equilibrium prices are unique but I cannot be sure since all sources seem to be ...
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0answers
44 views
Proof of excess community demand function in Sonnenschein (1973)
Consider the following passage in Sonnenschein (1973; full citation below):
Perhaps because I do not know much about the uniform Lipschitz condition, I do not follow his exposition after the first ...
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1answer
171 views
Are no arbitrage models and equilibrium models equivalent?
This YouTube video from WHU (starting from 3:50) claims that no-arbitrage models (such as Black-Scholes and HJM) are equivalent to equilibrium models (such as CAPM or C-CAPM).
He uses the Euler ...
2
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1answer
51 views
Why don't suppliers increase price after a positive demand shock?
Forgive me, I am new to economics. Suppose there's a demand shock in the pork market and D1 shifts to D2. Why not keep quantity supplied fixed at 220 and then raise prices to $3.70, instead of moving ...
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3answers
517 views
First welfare theorem and convexity
Are convex preferences needed for the first welfare theorem? It would see so. For example, we could have a situation in which B's indifference curve is non-convex, such that, at the equilibrium X, it ...
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1answer
113 views
Edgeworth box and identical tastes
If tastes are homothetic and identical, does this imply that the contract curve is the line connecting the lower left and upper right corners of the box?
My understanding: no, it does not. Consumers' ...
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38 views
Is an input-output model an equilibrium model?
I know the difference between CGE and input-output models.
But can an input-output model be called a equilibrium model?
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1answer
90 views
Deadweight Loss Due to Taxes Represented on a Graph of the Market?
Let's say a market is operating at equilibrium, with MSB=MSC, and a tax is imposed on the market. This would shift the supply curve to the left and cause a deadweight loss represented by the triangle ...
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0answers
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Identify the Pareto welfare weights
I am asked to identify the Pareto welfare weights from the FOC of the following problem
$max_{{x_1}{x_2}} U_1(x_1)\ st\ u_2=U_2(x_2)\ and\ x_{1n}+x_{2n}=yn$
The Langrangian is: $L=U_1(x_1)+\lambda_1(...
4
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1answer
232 views
Properties of Financial Markets in Real Life
When studying financial economics, three concepts appear everywhere
Equilibria (investors maximise utility, markets clear and aggregated demand equals aggregated supply)
Completeness (there are ...
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1answer
44 views
Financial Economics and International Economics
What is the difference of Financial Economics and International Economics? Why, How? What are the implications of these differences?
Will a model of international economics suddenly become a model of ...
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1answer
70 views
Simple General Equilibrium Model of Public Goods: Intuition?
We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $ y^{A*} $ & $ y^{B*} $ respectively. ...
