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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Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 agents

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},...
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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 ...
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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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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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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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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 ...
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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 ...
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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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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 ...
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demand curve shift in a monopolistic competitive market

As more firms enter the market, the quantity demanded at a given price level will thus decline. Therefore, the perceived demand curve for any individual firm will continue to shift leftward until the ...
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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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Who is losing in an arbitrage?

When some entity takes advantage of an arbitrage opportunity, who is losing money? For example, when there are price differences across cryptocurrency exchanges and someone exploits an arbitrage ...
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Walrasian Equilibrium

Need help solving last two parts of this problem. We’ve solved for the general equilibrium but not sure how to go from there. The endowments of two consumers are given by $w_1 = (40,80)$ and $w_2 = (...
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Unique competitive equilibrium in an exchange economy

I was working on the following excercise: In an exchange economy $\varepsilon$ with two goods and strictly monotone, continous and strict concave utility functions, suppose all demand functions are ...
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why is market clearing price assumed in cournot model with homogenous products

In the cornout model two firms choose the amount of a product they wish to produce. It is assumed that the price that results is the market clearing price for the total supply. Is there a ...
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Competitive equilibirium of max utility functions

Apologies in advance if my terms aren't exact, I'm learning "Mathmatical Economoics" in the hebrew language and some of the terms don't translate well. I was given the following question: Two ...
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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 ...
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Heckscher-Ohlin with non homothetic preferences [duplicate]

Can someone tell me how I can show with an example that the Heckscher-Ohlin result does not necessarily hold when preferences are not homothetic. I was asked if it similar as a case in which the ...
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Heckscher-Ohlin with heterogeneous preferences

could someone really help me out I would need to show a situation in which the Heckscher-Ohlin result does not necessarily hold when preferences are heterogeneous. Does someone have an idea how I ...
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What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy

In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting. This may be rather ...
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264 views

Why is market equilibrium pareto efficient?

Let us assume that the current price $P$ is lower than the 'equilibrium price' $P^\star$ so that $Q$ is lower than $Q^\star$. If we move from this combination towards the equilibrium one, it may be ...
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Simulating a simple economy with … price-makers? arriving at competitive equilibrium

I'm new to economics and thinking about graduate study. My background is mathematics. I started reading a book on microeconomics by Mas-Colell, Whinston and Green. My goal is to understand how ...
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Equilibrium price determination in a 2 commodity framework

Following are the set of equations describing the demand and supply of two goods X and Y: Demand functions: $$X_d = a_1 - b_1P_x + c_1P_y$$ $$Y_d = a_2 - b_2P_y +c_2P_x$$ $a_1,~ a_2,~ b_1,~ b_2,~ ...
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Why is Walras equilibrium inefficient when we are dealing with public goods?

I know that when we have public goods we have that: $$MRT = MRS_a + MRS_b$$ Though I fail to understand why does this makes Walras equilibrium inefficient. Thank you very much for your help!
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Computing the competitive equilibrium given initial allocation

Suppose that there are two agents, 1 and 2, and two goods, honey (h) and lemon (l), and that the agents' preferences over these goods are defined by the following utility functions: $$u^1(x_h^1, x_l^...
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Walrasian Equilibrium intuition given prices and some initial allocation

Suppose we have two agents who are each assigned some initial allocation of two different goods, where the prices of each good are given. Also, suppose the utility functions for each agent are weakly ...
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Selling price of a widget at competitive equilibrium

Let's suppose that it costs producers a minimum of y dollars to produce a widget (it may actually cost more, depending on the producer, but that is the bare minimum). In a competitive equilibrium, ...
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What's the market equilibrium price for the used good?

On a perfectly competitive market, a buyer wants to buy a used good. He is willing to pay $30$ for a badly used good, and $60$ for a nicely used good. The seller is willing to sell a badly used good ...
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Market price, output that maximize the price and level of firm profit after applying a license fee

I'm currently working on a problem that says the following : At first we had a number N of firms in perfectly competitive industry,the exercice gives us the total cost and the Market Demand with p as ...
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A question about the exchange economy

The question I am given is the following: Consider an economy that has only three goods, mineral water, orange juice, and wine available in fixed amounts, and three agents, A, B and C. So in this ...
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Equilibria in non regular economies

We know that in regular economies general equilibrium theory predicts a finite and odd number of equilibria, using the properties of the excess demand function and the index theorem. How about the ...
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Finding individual utility

There are N agents living in an economy with two goods, $X$ and $Y$. Their preferences are described by the following utility function $u(X,Y) = 2 \sqrt{XY}$. Each agent is endowed with 1 unit of $X$ ...
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Necessary conditions for the existence of a competitive equilibirum

I got that in an exchange economy, conditions as preferences being continuous, strictly convex and strongly monotone and $\sum_i \omega_i\gg 0$ are sufficient conditions for the existence of a ...
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Competitive Market - Production & Number of Firms

The question is as follows: The inverse market demand for provision of gas services is given by p(y) = 1/(1+y), where p is the unit price and y measures output in appropriately scaled units. Suppose ...
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Assumptions for the existence of a Walrasian equilibrium

I have a problem set stating that a competitive equilibrium does exist under a series of assumptions on the economy. The question is "Show that the following six assumptions are needed for existence ...
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Is Cobb-Douglas the only output function corresponding to a competitive economy?

Apologies if this is a rather simple question, I appreciate any guidance. $$ Q(K,L) = AK^\alpha L^{\beta} $$ where A is a constant. Identify the conditions on $\alpha$ and $\beta$ for ...
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MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market

Suppose the Total Cost function of a firm in Perfect Competition is given by: $$C(q) = 450 + 15q + 2q^2$$ The market price is $P = 15$ per unit Determine the optimal quantity produced by ...
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Cournot equilibrium question

There are two firs in the market. They produce perfect substitutes at cost $c(y_i)=y_i/3$ for i=1,2. The demand function is $p=1-(y_1+y_2)$ Consider the Cournot competition where firms ...
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Do I understand the second welfare theorem correctly?

As far as I understand, the second welfare theorem says that all Pareto-optimal allocations can be reached by market equilibrium on free competitive markets. Yet it seems that this understanding is ...
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Rosen's unique equilibrium conditions: Multi dimensional strategies?

I was wondering if the uniqueness of equilibrium conditions in n-person games as published in Rosen's 1965 paper (J. B. Rosen. Existence and uniqueness of equilibrium points for concave n-person games....
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Relationship between IRS and Competitive equilibrium

If there are increasing returns to scale in both sectors (in a 2x2x2x2) production and consumption economy, then a profit maximizing allocation most likely involves the economy producing only one type ...
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General Equilibrium allocation holding fixed a consumer's utility

I'm having some issues with solving this general equilibrium exercise. The way I started off is by assuming that since consumer 2's utility is fixed, he will have a fixed utility function. Then ...
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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 ...
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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 ...
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How to find the market equilibrium by surplus maximisation when there is a consumer subside?

Let's assume a market with linear demand and supply functions, let's say $Q_d = 20 - 4p$ and $Q_s = -4 +8p$ respectively. We can easily find the market equilibrium by either setting $Q_d = Q_s$ (or $...
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Looking for a term that explains market participants that lie about their participation to gain access to said market

I'm Looking for a term that explains the behavior of a market participants that will lie or exaggerate how much or what they offer in order to gain access to a market that would otherwise be ...
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Simple equilibrium in monopoly question

Given an inverse demand function for hangars: $$P = 3 - \frac{Q}{16,000}$$ and constant marginal cost of $1$, what is the equilibrium price and quantity of hangars in a monopoly? In a perfectly ...
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Stone-Geary preferences and competitive equilibrium

Does anybody know if a competitive equilibrium obtains under Stone-Geary preferences; are there multiple equilibria problems; do such preferences admit an analysis with more than one type of ...
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Could markets compute equilibria?

It has been shown, for example in the papers Deng, Du, The Computation of Approximate Competitive Equilibrium is PPAD-hard Hirsch, Papadimitriou, Vavasis, Exponential Lower Bounds for Finding Brouwer ...