Questions tagged [competitive-equilibrium]
The study of equilibrium when individual agents have no power to influence market-level variables like prices or quantities.
86
questions
4
votes
1answer
37 views
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-...
-1
votes
1answer
30 views
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 ...
0
votes
0answers
31 views
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 ...
1
vote
0answers
26 views
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 ...
4
votes
1answer
71 views
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 = ...
0
votes
1answer
38 views
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
0answers
45 views
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 ...
0
votes
2answers
83 views
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 ...
3
votes
1answer
53 views
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 $\...
0
votes
1answer
59 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 ...
0
votes
0answers
49 views
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
1answer
78 views
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 ...
-1
votes
2answers
76 views
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, ...
4
votes
2answers
124 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 ...
1
vote
1answer
57 views
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 ...
1
vote
1answer
52 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 ...
0
votes
1answer
53 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,...
4
votes
4answers
176 views
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 ...
0
votes
0answers
22 views
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 = (...
0
votes
0answers
50 views
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 ...
2
votes
1answer
25 views
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 ...
0
votes
1answer
133 views
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 ...
0
votes
1answer
42 views
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 ...
0
votes
0answers
30 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 ...
0
votes
0answers
60 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 ...
1
vote
1answer
56 views
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 ...
0
votes
1answer
299 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 ...
2
votes
0answers
46 views
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 ...
0
votes
0answers
40 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,~ ...
2
votes
1answer
96 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
141 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
98 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
48 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, ...
-1
votes
2answers
55 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
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 ...
1
vote
1answer
151 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 ...
0
votes
1answer
47 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
41 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
49 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
37 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
273 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
91 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} $$
where A is a constant. Identify the conditions on $\alpha$ and $\beta$
for ...
1
vote
1answer
2k views
MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market
Suppose the Total Cost function of a firm in Perfect Competition is
given by: $$C(q) = 450 + 15q + 2q^2$$
The market price is $P = 15$ per unit
Determine the optimal quantity produced by ...
2
votes
1answer
293 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
73 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
168 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
84 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
97 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 ...
7
votes
0answers
287 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 ...
7
votes
2answers
1k 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 ...
