Questions tagged [competitive-equilibrium]

The study of equilibrium when individual agents have no power to influence market-level variables like prices or quantities.

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Competitive equilibrium in a two-person economy with substitutes and complements

Recently came across this question on a microeconomics test and there was something that did not sit quite right with me. In an economy with two agents, A and B, and two goods, milk and honey, the ...
8 votes
1 answer
361 views

Pure exchange economy: Set of multiple equilibria endowments

Initial endowments which can result in multiple equilibria in a pure exchange economy are explained here. Given a pure exchange economy, that is given the utility functions (which fulfil the usual ...
1 vote
1 answer
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Finding the competitive equilibrium in an exchange economy with two perfect complements

I am currently in a Microeconomics class and have come across the problem described below. I have tried to solve the problem algebraically but only get to the intercept (x1a,x2a)=(8,4). I know that ...
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2 answers
146 views

Find the competitive equilibrium of the following economy

The following question was given as a part of a task in microeconomic theory course. It is not from some textbook and since I still haven't figured a way to solve it I will leave it here. Thank you in ...
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How is it possible to have perfect balance of supply and demand?

How is it possible to have perfect balance of supply and demand? That is, e.g. the right amount of workforce compared to the amount of work. Background (as asked by Giskard in the comments): It's ...
1 vote
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Competitive equilibrium: how to define histories on continuous space?

In the usual setup for the competitive equilibrium we have the agent solve: $$ \max_{\{c_i(h^t)\}} \sum_{t=0}^\infty \sum_{h^t} \beta ^t u(c(h^t)) \pi(h^t) $$ subject to constraints, where $h^t$ ...
2 votes
1 answer
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In GE, is price ever exogenous?

In general equilibrium models, is ever price exogenously given rather than endogenously determined in the equilibrium? Now, which price am I talking about? Consider an economy with production. There ...
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1 answer
56 views

Competitive Equilibrium how to determine subject to functions

Consider a 1-commodity, 2-consumers, 2-periods economy with S = 2, J = 1. The asset pays one unit (of the commodity) in state 1 and 2 units in state 2. q denotes the price of the asset at time 0. The ...
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Externalities, Pigouvian Taxes and Wikipedia

It states on Wikipedia: A Pigovian tax (also called Pigouvian tax, after economist Arthur C. Pigou) is a tax imposed that is equal in value to the negative externality. The result is that the ...
2 votes
2 answers
365 views

Exchange economy with two agents, what's the competitive equilibrium?

I'm currently doing this assignment but I'm keep getting stuck by this question. I put the Lagrange function for both agents and get the MRS / Price ratio but what should I do from there?
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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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Multiple Equilibria

I'm having difficulties solving for multiple equilibria for competitive exchange economies. Considering a quasi linear preference as such: $U_{A}(x,y)=x+100(1-e^{-y/10})$ $U_{B}(x,y)=y+110(1-e^{-x/10})...
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Long-run equilibrium number of firms is indeterminate when all firms in the industry share the same constant technology and factor prices are same

Why is the long-run equilibrium number of firms indeterminate when all firms in the industry share the same constant returns-to-scale technology and face the same factor prices? How to show it ...
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How to find the Walrasian equilibrium for non monotonic utility functions?

I just say Amit's comment on this question: The second welfare theorem without monotonicity so I got curious and tried to find both the contract curve for that particular problem, and the Walrasian ...
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How to solve the Bertrand model when marginal costs are different and not constant?

Find the equilibrium in the Bertrand model with two firms, with total costs given by: $TC_1(q_1) = \alpha q_{1}^2$ $TC_2(q_2) = \beta q_{2}^2$ Inverse demand is given by $P = A - Q$, where $Q = q_1 + ...
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1 answer
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How to find the competitive equilibrium?

Consider a $2$-good, $2$-person pure-exchange economy where $A$ is endowed with $(0,5)$ and $B$ is endowed with $(5,0)$. If the utility functions are $u_A = xy$ and $u_B = \min\{x,y\}$, what are all ...
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1 answer
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Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)

The one version of the Second Welfare Theorem states that: if there exists a competitive/Walrasian equilibrium and an endowment $X$ is Pareto efficient, then there is a price vector $\hat{P}$ for ...
1 vote
1 answer
323 views

Edgeworth Box (Non-Convex preference)

Consider a situation that agent A's indifference curves are concave, while B’s indifference curves are convex and both sets of indifference curves have exactly the same shape. A northeast movement ...
1 vote
1 answer
237 views

Production economy general equilibrium

I encountered the following economic model. Consider the following general equilibrium model with only two households, two consumer goods ($x$ and $y$) and two inputs (capital $k$ and labor $l$). ...
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Can budget lines of two agents containing equilibrium allocations be different?

Consider a pure exchange economy that has two goods and two agents (people). Suppose the initial endowments of person $A$ and $B$ are $(e_x^{A}, e_y^{A})$ and $(e_x^{B}, e_y^{B})$ (resp.) such that $...
4 votes
1 answer
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How do economists explain "If You Want to Win, Tell Your Team It’s Losing (a Little)." along with self-efficacy

How do economists explain: "If You Want to Win, Tell Your Team It’s Losing (a Little)." ? I read this article. And I learnt that— "The relationship between the score and the likelihood ...
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3 answers
171 views

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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Is it allowed to have a company that is not profitable?

In my old memories my teacher said that we can't have a company who are not profitable. The reason is to prevent unfair competition. Ex : Toyota sell car at 10 \$ during 2 years. Every other mark ...
3 votes
1 answer
643 views

Calculating price in a pure exchange economy

The problem is simple, I'm not really sure of my answer though. Consider an economy where there are two consumers and two goods: $$U_1(x_{11}, x_{21}) = x_{11}$$ $$U_2(x_{12}, x_{22}) = x_{22}$$ $...
3 votes
1 answer
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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 ...
7 votes
2 answers
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Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Consider a pure exchange economy with two goods ($x_1,x_2$) and two consumers $A,B$. Both users have an initial endowment, $(\omega_1^A,\omega_2^A)$ and $(\omega_1^B,\omega_2^B)$ respectively. A price ...
1 vote
1 answer
140 views

Arrow debreu equilibrium or Radner equilibrium and spot prices

Suppose there are 2 states, 2 goods and 2 consumers and consumers have identical expected utility function: $U^i (x)= \sum_{s=1,2} \pi_s (\ln x_{1s}+\ln x_{2s} )$ where $\pi=(1/3,2/3)$. Endowments are ...
9 votes
1 answer
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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 ...
5 votes
1 answer
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The Equilibrium Wage in Ricardian Trade Model

I am learning the Ricardian trade model by reading Eaton & Kortum 2012 JEP. The equilibrium is easy to understand when there are finite goods, as shown in their Figure 1. However, they then ...
2 votes
1 answer
305 views

Endowment economy

Consider an economy populated by two types of infinitely lived consumers, odd and even. There is mass one of each type of consumer. There is a single good in the economy. The economy starts at $t = 0$....
2 votes
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Show that the long-run supply curve of an increasing cost industry in perfect competition is upward sloping

Many intermediate microeconomics textbooks teach us that in perfect competition, the long-run supply curve of an increasing cost industry is upward-sloping. However, They usually give some hand-waving ...
2 votes
1 answer
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CES utility maximization two goods two period

In an Arrow-Debreu economy, there are two periods and N identical agents. In each period, the agent consumes two goods $c_{At}$, $c_{Bt}$ where $ t = 0,1 $ and has the endowments $(e_{a0},e_{b0},e_{a1}...
2 votes
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Computing the competitive equilibrium from the edgeworth box

Consider the following Edgeworth economy. There are two consumers $i \in {1,2}$ and two goods x and y. Consumer $i$ consumes $(x_i,y_i)$, where $x_i ≥0$ and $y_i ≥0$. Endowments are $ω_1 =(a,0)$ and $...
0 votes
2 answers
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Why is the number of firms in the short run fixed?

My textbook says that in perfect competition the condition of free entry and exit only applies to the long run equilibrium. Because in the short run no new firms can enter or old ones can leave the ...
6 votes
1 answer
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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, ...
4 votes
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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 ...
4 votes
1 answer
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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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1 answer
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free market equilbrium point, S=D confusion

I am confused over the concept of market equilbriums. let's say there is a firm X, who supplies 100 units in 1 week and the market demand is also 100 units, then Supply = Demand, and resources are ...
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Long run equilibrium price under perfect competition

I have a problem related to Ricardian rent. I have one firm, let's call it X firm, and all of the other firms in the market. All firms have to pay some transportation costs due to their land except ...
4 votes
1 answer
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Lecture notes competitive labor market with minimum wage

Can somebody recommend lecture notes that derive competitive labour market model equilibrium with minimum wages? This has been surprisingly hard to find, because most lecture notes use minimum wages ...
4 votes
1 answer
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Equilibrium with substitute goods

I am attempting to solve the following problem The demand functions for two substitute goods, the production cost of which equals $c_1$ and $c_2$, are $q_1 = a_1 + b_{11}p_1 + b_{12}p_2$ and $q_2 = ...
1 vote
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Leontif case for Edgeworth box

Consumer 1 has utility $u_1=min\{x_1,y_1\}$, Consumer 2 has utility $u_1=min\{x_1,2y_1\}$, their endowments are $w_1=(a,0)$ and $w_1=(b,0)$ and in this case $a=b$. I know the offer curves look like ...
0 votes
1 answer
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Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 agents [closed]

Consider a pure exchange economy with three commodities and two households with individual endowments $e_{1}=(1,2,3) \text { and } e_{2}=(3,2,1)$ respectively, and utility functions $u_{1}\left(x_{11},...
2 votes
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Pareto allocations and Competitive equilibrium

Consider the one-consumer one-firm economy. The consumer has preferences over leisure $l\in(0,L)$ and consumption good $x ≥ 0$ represented by utility function $u(x, l) = ax + l$, where $a > 0$ is a ...
3 votes
1 answer
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Identical aggregation

Assume the following: all firms are identical, i.e. at each time period $t$, $\forall i$, $j: F_{t}^j = F_{t}^i = F_t$ and the technology is CRS. All consumers have the same endowment of capital $\...
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How does "buy low, sell high" relate to supply and demand?

I'm taking introductory microeconomics, and I'm trying to consolidate my understanding by looking at some real world examples. In a perfectly competitive market, there are many consumers and suppliers ...
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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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Competitive wages under imperfect information

Do competitive wages always have to be defined by marginal productivity? Can we have competitive wages which are not based on productivity, when the information is not perfect? To put it in context, ...
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Short, Medium and Long-Run Profit Maximization

Suppose that, in a perfectly competitive industry, the firms' technology have the following cost function: $C(x) = 100 + 3x + 0.04x^2$. Assume the fixed costs are sunken. a) If the demand for the ...
4 votes
2 answers
341 views

Competitive equilibrium with IRTS

Suppose we have a static economy with one firm and one consumer. Consumer owns the firm and decides on how much to consume and to work: $$\max U(c,1-n_s)\ \text{s.t.} \ pc\leq wn_s+\pi$$ The firm is ...