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8 votes
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Perfect Competition, Zero profit rule and General Equilibrium

Parallel to Arrow and Debreu, there is the approach of Lionel McKenzie, in which no ownership is specified and all technology has constant returns to scale. In such a model, firms can make no profit. ...
Michael Greinecker's user avatar
7 votes
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Why labour, capital, and output levels cannot be pinned down in perfect competition?

Thus, the furthest we can go in terms of characterising the equilibrium in this economy/firm relates to the optimal capital-labour ratio. In effect, nothing can be said about the level of inputs and ...
Giskard's user avatar
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7 votes
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Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Yes. The Debreu version of the Sonnenschein-Mantel-Debreu theorem guarantees that excess demand has to satisfy very little restrictions if there are as many consumers as commodities. An explicit ...
Michael Greinecker's user avatar
6 votes

Who is losing in an arbitrage?

Nobody has to loose in an arbitrage. Economic relationships are not necessarily zero-sum (in fact often they will not be zero-sum). For example, if apples in city A are sold for ${\\\$}5$ and apples ...
1muflon1's user avatar
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6 votes
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Competitive equilibrium with IRTS

Here is an example where the two are actually compatible: The consumer's utility function $U:\mathbb{R}_+\to\mathbb{R}$ is given by $U(c,1-n_ns)=c-n_s$, the initial labor endowment is $1$ and $F:\...
Michael Greinecker's user avatar
6 votes
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In GE, is price ever exogenous?

This is an interesting question. There is a tradition of general equilibrium models (even if the phrase 'general equilibrium' needs to be specified) that assumes prices as exogenously given. They are ...
BakerStreet's user avatar
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5 votes

Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Here is another example with two consumers (A and B), two goods (X and Y): \begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, ...
Amit's user avatar
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5 votes
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Competitive equilibrium in Leontief economies

Strict convexity of preferences is not needed in existence results for competitive equilibria. Leontief preferences are quite well-behaved. They are continuous, convex, and strongly monotonic. If ...
Michael Greinecker's user avatar
5 votes

Is Cobb-Douglas the only output function corresponding to a competitive economy?

Let $a+b<1,\;\; a,b>0$. Pay the factors of production their marginal product: $$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$ So total payments to factors of production will be $$rK ...
Alecos Papadopoulos's user avatar
5 votes

Externalities, Pigouvian Taxes and Wikipedia

The Pigovian taxes are non-distortionary. For example imagine situation where government optimal spending is 100e and before Pigovian tax all 100e was raised through income tax which creates ...
1muflon1's user avatar
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5 votes

Who is losing in an arbitrage?

It's important to distinguish between the effects of arbitrage on: a) the direct parties to arbitrage transactions; b) other agents in the markets in which the arbitrage takes place. Suppose ...
Adam Bailey's user avatar
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4 votes

Could markets compute equilibria?

Computing an equilibrium is not needed for implementing it. This was the mistake of Lange and co. and was decisively rebutted by Hayek. If you want a mathematical formulation, simply take a tatonement ...
Fato's user avatar
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4 votes
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Is Cobb-Douglas the only output function corresponding to a competitive economy?

Any constant returns to scale function is compatible witha competitive economy. Cobb-Douglas is not the only one. Google CES production function. Also, product can be wasted or be an externality, so ...
chatGPT's user avatar
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4 votes
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Walrasian Equilibrium intuition given prices and some initial allocation

The "trick" of this question is that the fact that agents do not want to trade at the given prices does not mean the allocation is Pareto. The only thing you know is that if there is an allocation ...
Regio's user avatar
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4 votes
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preference convexity and existence of equilbria

Consider an economy with two commodities. Production is trivial, $Y=\{0\}$, there is a single consumer with endowment $(1,1)$ whose preferences are represented by the utility function given by $u(x_1,...
Michael Greinecker's user avatar
4 votes

Competitive equilibrium with IRTS

Note that: (i) exploitation of returns to scale is not without limits when $n_s \leq 1 $ (this actually excludes global returns to scale for any value of $(c,n)$) (ii) the firm can produce something ...
Bertrand's user avatar
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4 votes
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Lecture notes competitive labor market with minimum wage

In the Varian textbook Intermediate Microeconomics (I am guessing in most micro textbooks), the chapter on Equilibrium discusses price controls in the presence of a demand and supply function. You can ...
Giskard's user avatar
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4 votes
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Competitive equilibrium for an economy with a consumer and a producer

This is the utility maximisation problem of the consumer: \begin{eqnarray*}\max_{c_D, l_S} & \ c_D^a(24-l_S)^{1-a} \\ \text{s.t.} & \ pc_D = wl_S \\ \text{and} & \ c_D\geq 0 , 0\leq l_S\...
Amit's user avatar
  • 8,811
3 votes

Could markets compute equilibria?

Generally the fixed-points of Nash Equilibria in a market can also be reached by a dynamic process where actors myopically best-reply to the market result in the last period (see Milgrom and Roberts ...
IMA's user avatar
  • 176
3 votes
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No competitive equilibrium for pooling contracts

As one of the comments points out, there are many models of equilibria in insurance markets. But it sounds to me like you are referring to the Rothschild-Stiglitz (1976) paradigm. I will provide a ...
saturno's user avatar
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3 votes
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Why is Walras equilibrium inefficient when we are dealing with public goods?

In a competitive market for a private good (y) individuals may consume different quantities but the equilibrium condition requires that: $$ \frac{\frac{\delta u^{i}}{\delta y}}{\frac{\delta u^{i}}{\...
Ali's user avatar
  • 852
3 votes

Competitive wages under imperfect information

Still, not 100% clear whether I get the question right, but in models with constant returns to scale and decreasing marginal productivity (question to others, are these conditions even necessary?), if ...
Papayapap's user avatar
  • 1,843
3 votes

Quantity restriction in model with fixed factor of production

Summary The equilibrium wage will decrease. The reasoning is that, due to the output constraint, total labour demand will go down. Then because of the fixed labour supply (and the fixed price of ...
tdm's user avatar
  • 12.2k
3 votes

GE with an intermediate good

This is my attempt. The final result is a set of equilibrium equations, which I will not attempt at solving. The consumer: $$ \max \ln(x) + \gamma \ln(b) \text{ s.t. } p_1 x + w b = w L + \pi_0 + \...
tdm's user avatar
  • 12.2k
3 votes

CES utility maximization two goods two period

The problem can be solved using two stage budgetting. In stage 1 total income $m = \sum_t p_{at} c_{at} + \sum_t p_{bt} c_{bt}$ is allocated across periods. In stage two the optimal expenditure $E_t$ ...
tdm's user avatar
  • 12.2k
3 votes

Find the competitive equilibrium of the following economy

There will be no equilibrium. Both technology and endowment play no role in the argument. Assume there would be an equilibrium with price system $(p_1,p_2,p_3)$. Notice that all prices must be ...
Michael Greinecker's user avatar
2 votes

Number of firms in Long Run

Yes, it is possible. In the long run, firms enter until they break even. Suppose firms are symmetric. Then for each firm the break even condition is that the average costs equal the price. This is ...
BB King's user avatar
  • 6,158
2 votes

Does the price level in a competitive market have to be at the intersection of the Average Cost curve and the Marginal Cost curve?

One of the assumptions of perfect competition is that firms are price takers. Ultimately price is determined by the quantity of goods supplied, and with perfect competition, there are infinite (or an ...
Kitsune Cavalry's user avatar
  • 6,638

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