8
votes
Accepted
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.
...
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7
votes
Accepted
"Competitive equilibrium" vs. "General equilibrium"
Competitive Equilibrium
A competitive equilibrium ("Walrasian Equilibrium")'s defining characteristic is that it's competitive. It's about an equilibrium in which market forces (say, consumers, firms)...
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7
votes
Aggregation of the closure property of a production set
Doing this more abstractly, let $Y_j\subseteq\mathbb{R}^n$ be a production set for $j=1,\ldots,J$ and let
$$Y=Y_1+Y_2+\cdots+Y_J=\{y_1+y_2+\cdots+y_J|y_j\in Y_j, j=1,\ldots,J\}$$
be the aggregate ...
- 11.7k
6
votes
Accepted
Are no arbitrage models and equilibrium models equivalent?
...no-arbitrage models (such as Black-Scholes and HJM) are equivalent to
equilibrium models (such as CAPM or C-CAPM).
Short Answer Yes, for models where asset prices are assumed to be Ito ...
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6
votes
Proving local non-satiation in arbitrary metric space
First, you need a vector space in order for convex combinations to be well-defined. However, not every metric on a vector space works. Indeed, under the discrete metric, the result will trivially fail ...
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6
votes
Accepted
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 ...
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6
votes
Accepted
Robinson Crusoe Economy Question
If you want to find Pareto efficient allocation in this economy, then you can determine that by solving the following system for $(C, L, H)$:
$L+H=1$
$C = 8\sqrt{H}$
$\text{MRS} = \dfrac{3C}{2L} = \...
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5
votes
Does a General Equilibrium here require Pareto Optimality?
Competitive equilibrium is the price vector $(p_x, p_y, w =1, r)$ such that it solves the following system of equations:
Demand for $X$ = Supply of $X$
Demand for $Y$ = Supply of $Y$
Demand for $L$ =...
- 8,206
5
votes
Accepted
Why is the production possibility set convex?
Perhaps you are confusing two things.
If $Q_1$ and $Q_2$ denote the production of goods 1 and 2 in a single country and you are in the space defined by them given $L_1 + L_2 = L$ then it is indeed ...
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5
votes
What purpose does general equilibrium serve in practice?
Daron Acemoglu, in a paper called Theory, General Equilibrium and Political Economy in Development Economics, discusses the role of economic theory in empirical work in development economics, which ...
- 6,885
5
votes
Accepted
Properties of Financial Markets in Real Life
Equilibria: in the macroeconomic sense of aggregate equilibrium where all markets clear, markets are most likely never in any equilibrium but rather in constant flux between different equilibria, ...
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5
votes
Market with changing number of goods and services
I think the best candidate would be monopolistic competition as introduced by
Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity,
in which two models are introduced. ...
- 3,286
5
votes
Accepted
Find pareto optimal allocations
Set of Pareto efficient allocations is given by the dashed line in the Edgeworth Box. It is the set of feasible allocations satisfying $y_1 = x_1$ and $x_1y_1 \geq 9$
.
- 8,206
5
votes
Accepted
Walras Law in a production economy with fixed costs
Partial answer:
for simplicity let $P_c =1$.
The budget constraint: $c= wn + \Pi$
Simplify (plug in $\Pi$): $c= F(n)- fc$
Goods clearing: $c = F(n)$
The household's budget constraint is inconsistent w/...
- 340
5
votes
Accepted
How do I find the socially optimum and equilibrium value?
You need to think about what the total costs are and what the marginal costs are. The social optimum is where marginal costs are equal to the outside option which is riding the bus.
The story goes ...
- 3,286
5
votes
Accepted
Second welfare theorem
Here is a short argument due to Maskin and Roberts. I'll give it in the simpler context of a pure exchange economy.
Suppose you have a Pareto efficient allocation, and an equilibrium $(x,p)$ exists ...
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5
votes
Accepted
How to find the contract curve when both agents have linear utilities?
I rewrite the problem of maximization you wrote (I omit the endowments):
$\max x_A + y_A \;\;\qquad (1)$
subject to
$s x_B + y_B = \overline{U}\qquad (2)$.
This problem can be seen as a problem of ...
- 3,312
5
votes
Pareto efficient allocations for non-monotonic, quasi-linear utility function
Given the economy:
Utility functions: $u_A(x_A,y_A) = x_A - |y_A-\alpha_A|$, $u_B(x_B,y_B) = x_B - |y_B-\alpha_B|$, where $\alpha_A \geq 0$, and $\alpha_B\geq 0$ are given.
$\omega = (\omega_X, \...
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4
votes
Is the marginal cost the same for every firm in a perfectly competitive market?
No, the marginal cost curves are not necessarily the same for each firm in the market. However the values of marginal costs are.
To disprove the general claim that "The marginal cost curve of each ...
- 6,128
4
votes
Looking for discussion on equilibrium vs dynamic models in econometrics
Economists (most of them) build their models assuming most of the time stochastic dynamic equilibrium. So Economics does not contrast "dynamic" with "equilibrium" - it synthesizes them.
It is ...
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4
votes
Accepted
Recent economics theories that involve differential topology?
The main reason differential topology had some success in economics is that supplies powerful methods to show that something holds generically, mainly Sard's theorem and the transversality theorem. ...
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4
votes
Accepted
Is the convexity of production sets necessary for the welfare theorems?
Convexity of the production set is indeed not needed for the proof of the first welfare theorem but for the proof of the second welfare theorem. It is not a necessary condition though.
It is ...
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4
votes
Say's law stated in terms of general equilibrium theory?
How about Walras's law?
Walras's law is a principle in general equilibrium theory asserting that budget constraints imply that the values of excess demand (or, conversely, excess market supplies) ...
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4
votes
Accepted
Walras's Law V.S Say's Law- Is there a difference?
The way you have defined excess demand, it is only consumer excess demand. But Walras's law holds in any private ownership economy at all prices (at which demand and supply are well defined). Walras's ...
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4
votes
Accepted
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 ...
- 4,188
4
votes
First welfare theorem and convexity
Are convex preferences needed for the first welfare theorem?
No, convexity of preferences is imposed for other reasons. A general sufficient condition is local non-satiation, which says the agent can ...
- 2,619
4
votes
Accepted
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,...
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4
votes
Accepted
Arrow-Debreu Theorem of Existence: Non satiation
Converting my comments into an answer:
At the bottom of p.268, the authors say:
The set of consumption vectors $X_i$ available to individual $i$ $(=1,\cdots,m)$ is a closed convex subset of $R^l$ ...
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4
votes
Aggregation of the closure property of a production set
For a fully overview on the conditions for the sum of closed sets to be closed, see this note of Kim Border
Recession cones
I'll be working with subsets of $\mathbb{R}^n$. Let's start with some ...
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