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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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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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, ...
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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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43 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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20 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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204 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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157 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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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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67 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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61 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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238 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 $i \in [n]$. ...
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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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35 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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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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92 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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302 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
86 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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67 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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61 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} + \...
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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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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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132 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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130 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}\}...
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84 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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143 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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56 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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55 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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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. ...
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log-linearize a forward looking variable (P/D) with recursive expression

I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, ...
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Determining a variable from empirical results obtained from regression analysis

For context, I am trying to estimate the excess supply and demand in the Commercial Real Estate market and the rental price adjustment mechanism following the change in vacancy. I found a paper titled ...
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56 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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33 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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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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162 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 ...
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1answer
47 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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484 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
111 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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84 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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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(...
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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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38 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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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. ...
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51 views

Pareto Set with strictly convex preferences

Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A $ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10). The contract curve's equation turns out ...
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45 views

Why is macroeconomics about general equilibrium?

In a fairly popular paper published a couple of years ago ("On the future of macroeconomic models"), Blanchard (2018) makes the following statement, among other "widely believed propositions": (i) ...
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Equations of “rational mechanics” and general equilibrium

Vilfredo Pareto, referring to the equations that determine equilibrium, wrote: These equations do not seem new to me, they are old friends. They are the equations of rational mechanics. This ...