Questions tagged [competitive-equilibrium]
The study of equilibrium when individual agents have no power to influence market-level variables like prices or quantities.
61
questions
0
votes
0answers
26 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:
$$X_d = a_1 - b_1P_x + c_1P_y$$
$$Y_d = a_2 - b_2P_y +c_2P_x$$
$a_1,~ a_2,~ b_1,~ b_2,~ ...
-3
votes
0answers
11 views
Trade equilibrium
Suppose there are two countries who need to transport their goods to each other ie form a trade. The cost to transport goods is a and b for the two countries respectively. How to find the maximum ...
0
votes
0answers
29 views
Given a Walrasian equilibrium, compute all intitial endowments that lead to given Walrasian equilibrium
If you would be so kind to take a look at the following problem:*
Consider an economy with two agents Stan ($S$) and Laurel ($L$) and two goods: Cans of coke ($C$) and Pretzels ($P$). The total ...
2
votes
1answer
41 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!
-1
votes
1answer
24 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^...
0
votes
1answer
41 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 ...
0
votes
1answer
44 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, ...
0
votes
0answers
18 views
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 ...
-1
votes
2answers
54 views
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 ...
0
votes
0answers
22 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 ...
1
vote
1answer
78 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 ...
1
vote
1answer
31 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 ...
1
vote
1answer
32 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$ ...
1
vote
1answer
37 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 ...
1
vote
0answers
31 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 ...
0
votes
0answers
152 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 ...
3
votes
2answers
79 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} $$
where A is a constant. Identify the conditions on $\alpha$ and $\beta$
for ...
1
vote
1answer
131 views
MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market
Suppose the Total Cost function of a firm in Perfect Competition is
given by: $$C(q) = 450 + 15q + 2q^2$$
The market price is $P = 15$ per unit
Determine the optimal quantity produced by ...
2
votes
1answer
195 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 ...
0
votes
0answers
53 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 ...
3
votes
1answer
109 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....
0
votes
1answer
71 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 ...
1
vote
0answers
69 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 ...
5
votes
0answers
225 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 ...
6
votes
2answers
862 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 ...
1
vote
1answer
39 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 $...
0
votes
3answers
106 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 ...
0
votes
1answer
90 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 ...
2
votes
1answer
128 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 ...
5
votes
3answers
110 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 ...
1
vote
1answer
85 views
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.
1
vote
1answer
706 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 ...
4
votes
0answers
309 views
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 "...
1
vote
1answer
73 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 (...
1
vote
1answer
945 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 ...
4
votes
3answers
703 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 ...
1
vote
1answer
4k 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?
2
votes
1answer
130 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 ...
2
votes
0answers
151 views
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}$$
The initial endowments are $ω_1 = (1,0)$ and $...
0
votes
2answers
292 views
Would you consider airport parking to be a monopoly or a monopolistic market?
If you look at it one way and group the different companies that offer parking, it could be a monopoly as that is the only place you can park. On the other hand, the different companies offer ...
2
votes
0answers
42 views
Demonstrating that markets yield productive and allocative efficiency to introductory students
Has anybody come across a nice, intuitive (i.e. neither formal nor technical) way to demonstrate how markets yield both productive and allocative efficiency?
I suppose the allocative argument ...
2
votes
1answer
2k views
Market equilibrium and pareto efficiency
How can I prove that the equilibrum point $D(p)=S(p)$ is pareto efficient?
The definition of pareto efficient: there is no way to make any person better off without hurting anybody else
$D(p)$ is ...
2
votes
1answer
114 views
Dynamic programming problem with dimension over 1000
I am working on a project which need to solve a dynamic programming problem with dimension over 1000. In past literature, there exist several methods like Smolyak algorithm and Sparse grid method that ...
2
votes
1answer
230 views
Productive Allocative Efficiency (Competitive Equilibrium)
I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in ...
3
votes
3answers
120 views
Does the price level in a competitive market have to be at the intersection of the Average Cost curve and the Marginal Cost curve?
I could see that if the price level is say lower than the intersection point , then firms won't be able to operate , but what is wrong with the price level being above the intersection point of the ...
3
votes
1answer
110 views
Refinements of Walrasian equilibrium
In Walrasian equilibrium there is a market clearing price, that is
$$
D(p) = S(p)
$$
or the supply is worthless, so you can have
$$
D(p) < S(p) \mbox{ if } p = 0.
$$
This can be summarized as
$$
p \...
5
votes
2answers
420 views
Does the concept of Nash-equilibrium conflict with the concept of market equilibrium in the lemon market
Consider a version of Akerlof's Lemon market with two types of sellers. One type sells Quality cars the other type sells Lemons. Buyers' reservation prices are $r_{B,Q}$ for a Quality car and $r_{B,L}$...
3
votes
0answers
305 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
1answer
468 views
What Does “Quantity” Represent When Looking at Supply and Demand?
There are several possible scenarios involving changes in supply and demand that people are supposed to memorize in AS Economics. For example, when Either Demand OR Supply Move on Their Own:
Rising ...
8
votes
1answer
473 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 ...
