4 votes
Accepted

How do I find the set of pareto optimal allocations?

In the economy you provided, set of feasible allocations is $\mathcal{F}=\{((x_1,y_1),(x_2,y_2))\in\mathbb{R}^2_+\times\mathbb{R}^2_+|x_1+x_2=2 \ \wedge \ y_1+y_2=1\}$ and is represented by points in ...
Amit's user avatar
  • 8,466
4 votes

Core in a replicated economy

In the economy provided in the question, competitive equilibrium allocations is equal to the set of efficient allocations. This along with the fact that the competitive equilibrium allocations always ...
Amit's user avatar
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2 votes

Exchange economy with two agents, what's the competitive equilibrium?

I’m going to change the notation to one I’m more comfortable with: Let the goods be $x,y$, the consumers $A,B$; and the respective endowments $(w_{x_A},w_{y_A}), (w_{x_B},w_{y_B})$. Let’s set as ...
Nicolas Torres's user avatar
2 votes
Accepted

Is there/can we define a notion of Giffen goods in pure exchange economies?

"Giffenness" may follow only from the preferences, you have to filter out endowment income effects. (Substitute a fixed monetary income $m$, for details, see e.g.; Varian's Intermediate ...
Giskard's user avatar
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2 votes
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General equilibrium with market power

Given a pure exchange economy: $u_A(x_A, y_A)=x_Ay_A$, $u_B(x_B, y_B)=x_By_B^2$ with endowments: $\omega_A=(80,150)$ and $\omega_B=(210,180)$ To find the equilibrium, we first find the price offer ...
Amit's user avatar
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2 votes
Accepted

Why doesn't this exchange economy have a walrasian equilibrium?

The economy you described does have a Walrasian Equilibrium when $n$ is even. The Equilibrium price ratio is $\dfrac{p_X}{p_Y}=1$. The corresponding equilibrium allocation is any allocation in which $\...
Amit's user avatar
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1 vote

Finding the competitive equilibrium in an exchange economy with two perfect complements

Given a pure-exchange economy with $u_A(x_A,y_A)=\min(x_A,2y_A)$, $u_B(x_B,y_B)=\min(2x_B,y_B)$ Endowment of A is $(k_X,k_Y)$ and of B is $(12-k_X,12-k_Y)$ Set of feasible allocations is $\mathcal{F}...
Amit's user avatar
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1 vote
Accepted

Edgeworth Box for exchange economy

Not quite. The line you have drawn turns out to be the contract curve, but from this figure it's not clear how you get this line, because the indifference curves for the two utility functions are ...
VARulle's user avatar
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1 vote

General equilibrium with market power

Not sure where you get lost. $u_B$ is Cobb-Douglas type, thus given a price vector $\textbf{p}$ and initial endowment $\textbf{w}^B$ it is easy to determine $x_1^B(\textbf{p}),x_2^B(\textbf{p})$. Once ...
Giskard's user avatar
  • 29.5k
1 vote

Exchange economy with two agents, what's the competitive equilibrium?

An allocation $((c^*_{a,1},c^*_{a,2}),(c^*_{b,1},c^*_{b,2}))$ is a competitive equilibrium allocation for the given economy supported by the price ratio $\frac{p_1^*}{p_2^*}$ if it satisfies the ...
mynameparv's user avatar
1 vote

Pure exchange economy: Set of multiple equilibria endowments

The following article: TODA, A.A. and WALSH, K.J., 2017. Edgeworth box economies with multiple equilibria. Economic Theory Bulletin, 5(1), pp. 65-80. though not focusing on the properties of the ...
Jovan Jezdic's user avatar

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