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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questions
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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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45 views
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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28 views
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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1answer
35 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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35 views
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:
$$X_d = a_1 - b_1P_x + c_1P_y$$
$$Y_d = a_2 - b_2P_y +c_2P_x$$
$a_1,~ a_2,~ b_1,~ b_2,~ ...
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35 views
Given a Walrasian equilibrium, compute all intitial endowments that lead to given Walrasian equilibrium
If you would be so kind to take a look at the following problem:*
Consider an economy with two agents Stan ($S$) and Laurel ($L$) and two goods: Cans of coke ($C$) and Pretzels ($P$). The total ...
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1answer
52 views
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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2answers
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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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1answer
53 views
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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1answer
65 views
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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1answer
39 views
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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1answer
45 views
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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3answers
406 views
Why wouldn't competition prevent “usurious” payday loan rates?
The current Wiki page on "Payday Loans" claims loans are priced above marginal cost. The justification is that
If a lender chooses to innovate and reduce cost to borrowers in order to secure a ...
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0answers
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On marginal arguments for equilibrium conditions
On the Saylor website's course on economics, there is the following sentence, which I do not understand.
"In a simple market under perfect competition, equilibrium occurs at a
quantity and price ...
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0answers
25 views
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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1answer
94 views
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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1answer
42 views
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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1answer
139 views
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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1answer
37 views
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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0answers
35 views
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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0answers
204 views
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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2answers
84 views
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} $$
where A is a constant. Identify the conditions on $\alpha$ and $\beta$
for ...
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1answer
262 views
MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market
Suppose the Total Cost function of a firm in Perfect Competition is
given by: $$C(q) = 450 + 15q + 2q^2$$
The market price is $P = 15$ per unit
Determine the optimal quantity produced by ...
6
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2answers
989 views
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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3answers
111 views
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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1answer
245 views
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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0answers
59 views
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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1answer
74 views
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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0answers
76 views
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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0answers
243 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 ...
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1answer
537 views
Competitive equilibrium in Leontief economies
Consider an economy in which all consumers have, possibly different, Leontief utilities. Since preferences are not strictly convex, it is not guaranteed that a competitive equilibrium exists. I found ...
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1answer
44 views
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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1answer
99 views
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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1answer
130 views
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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1answer
366 views
Maximisation problem in a multiproduct firm
I am currently reading the book "Microeconomics: Principles and Analysis" by Cowell on my own. I'm interested in the section of the multiproduct firm, but i'm confused with the use of the profit ...
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3answers
111 views
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 ...
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1answer
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Papers on time it takes to reach market equilibrium?
Are there any models which calculate the time (i.e. minutes, hours, days ect.) it takes for equilibrium to occur? I.e how long it takes for market forces to settle.
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1answer
813 views
No competitive equilibrium for pooling contracts
In class we dealt with insurance economics and, specifically, adverse selection due to information asymmetry. As one possible solution we considered pooling contracts, i.e. the same contract for both ...
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Equilibrium Uniqueness in a General Equilibrium Framework
I was wondering if anyone had any insight into the conditions that lead to a unique equilibrium in an exchange economy under a general equilibrium framework. More specifically, I know that the two "...
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1answer
78 views
Can heterogeneous prices be consistent with competitive equilibrium?
I do not want to put many constraints on the structure of the problem, except by defining a competitive equilibrium as such where firms are price takers in the factor and good(s) market, and, perhaps (...
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1answer
141 views
When to prefer maximisation of surplus and when instead to prefer minimising differences in price and q to find market equilibrium?
Two alternative approaches to compute a market equilibrium (in static analysis) are either to minimize the differences (either using abs() or a quadratic diff) between supply-demand quantities and ...
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3answers
758 views
Why labour, capital, and output levels cannot be pinned down in perfect competition?
Consider a firm producing with the following technology:
\begin{equation}
Y = AL^{\alpha}K^{\beta}
\end{equation}
Assuming that factors are paid their marginal contribution to output, it can be ...
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1answer
5k views
Number of firms in Long Run
In a competitive market, is it possible to know the change (increase/decrease) in number of firms in the Long run with a positive shift in demand for increasing costs case?
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1answer
1k views
Optimal production level for a typical firm in long-run
Assuming all firms have identical cost functions. Now suppose there is an increasing shift in the demand curve. As we all know that for increasing costs case, both average costs (AC) and marginal ...
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1answer
937 views
Competitive equilibrium in an exchange economy with lexicographic preferences [closed]
I am really stuck with this problem and not able to approach it. Any help will be much appreciated.
I tried to draw edgeworth box with initial endowment point. I do know that for competitive ...
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Competitive prices, tax and lump sum cash transfer in case of externalities
An economy is made up of two people. The utility functions are
$$u_1(x_{11},x_{12}) = x_{11}x_{12}$$
$$u_2(x_{21},x_{22}) = 2x_{21} + 2x_{22} −x_{11}$$
The initial endowments are $ω_1 = (1,0)$ and $...
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3answers
124 views
Does the price level in a competitive market have to be at the intersection of the Average Cost curve and the Marginal Cost curve?
I could see that if the price level is say lower than the intersection point , then firms won't be able to operate , but what is wrong with the price level being above the intersection point of the ...
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1answer
117 views
Dynamic programming problem with dimension over 1000
I am working on a project which need to solve a dynamic programming problem with dimension over 1000. In past literature, there exist several methods like Smolyak algorithm and Sparse grid method that ...
2
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1answer
235 views
Productive Allocative Efficiency (Competitive Equilibrium)
I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in ...
