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Questions tagged [competitive-equilibrium]

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How to calculate the ad valorem tax from a given equation?

Q = 140 - 10p, Q= 10p (1) A $2 tax is introduced that gives the new equation: Q = 140 - 10p, Q= 10p-2 (2) I know how to find Q and P, but I need to know the ad valorem tax (the %) that yields the ...
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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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1answer
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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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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, ...
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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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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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21 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
73 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
30 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
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 $X$ ...
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1answer
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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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136 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
76 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
118 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 ...
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1answer
180 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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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
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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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1answer
70 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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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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2answers
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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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1answer
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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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3answers
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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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1answer
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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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1answer
125 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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3answers
109 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
84 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.
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1answer
661 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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295 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 "...
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1answer
67 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
895 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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685 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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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
123 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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0answers
147 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 $...
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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 ...
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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 ...
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1answer
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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 ...
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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
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1answer
224 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 ...
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3answers
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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
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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 \...
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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 $r_{B,L}$...
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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: $$U_1(x_{11}, x_{21}) = x_{11}$$ $$U_2(x_{12}, x_{22}) = x_{22}$$ $...
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1answer
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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 ...
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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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Uniqueness of Competitive Equilibrium Conditions

I know that if a consumer has strictly convex preferences it may not guarantee uniqueness of CE. I believe that we need monotonicity of preferences as well but would like to hear any thoughts of this ...
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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 ...