Question

Romeo and Juliet are the only two consumers in an economy with two goods $x$ and $y$, and Romeo's endowment is $\omega^R=(0,1)$ while Juliet's is $\omega^I=(1,0)$. They each choose their consumption levels of the goods independently. But because they are madly in love, they get satisfaction not only from their own consumption of the goods but also from the other's consumption of both goods: $$ \begin{gathered} u^R\left(x^R, y^R, x^I, y^I\right)=x^R y^R+x^I+y^J, \\ u^J\left(x^R, y^R, x^J, y^J\right)=x^J y^I+x^R+y^R . \end{gathered} $$ (a) Find the contract curve for this two-person Edgeworth box. (b) Find a Walras equilibrium. Is it Pareto efficient? Explain why or why not.

   Romeo and Juliet are the only two consumers in an economy with two goods $x$ and $y$, and Romeo's endowment is $\omega^R=(0,1)$ while Juliet's is $\omega^I=(1,0)$. They each choose their consumption levels of the goods independently. But because they are madly in love, they get satisfaction not only from their own consumption of the goods but also from the other's consumption of both goods:
$$
\begin{gathered}
u^R\left(x^R, y^R, x^I, y^I\right)=x^R y^R+x^I+y^J, \\
u^J\left(x^R, y^R, x^J, y^J\right)=x^J y^I+x^R+y^R .
\end{gathered}
$$
(a) Find the contract curve for this two-person Edgeworth box.
(b) Find a Walras equilibrium. Is it Pareto efficient? Explain why or why not.

Intermediate Microeconomics: A Tool-Building Approach

Samiran Banerjee 2nd Edition

Chapter 14, Problem 2

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Romeo and Juliet each have utility functions that depend not only on their own consumption of goods $x$ and $y$, but also on the other's consumption. Romeo starts with 1 unit of good $y$ and no units of good $x$, while Juliet starts with 1 unit of good $x$ and no Show more…

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Romeo and Juliet are the only two consumers in an economy with two goods $x$ and $y$, and Romeo's endowment is $\omega^R=(0,1)$ while Juliet's is $\omega^I=(1,0)$. They each choose their consumption levels of the goods independently. But because they are madly in love, they get satisfaction not only from their own consumption of the goods but also from the other's consumption of both goods: $$ \begin{gathered} u^R\left(x^R, y^R, x^I, y^I\right)=x^R y^R+x^I+y^J, \\ u^J\left(x^R, y^R, x^J, y^J\right)=x^J y^I+x^R+y^R . \end{gathered} $$ (a) Find the contract curve for this two-person Edgeworth box. (b) Find a Walras equilibrium. Is it Pareto efficient? Explain why or why not.

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