<p>I don't know why this got down-voted. I'll post my attempt anyway...</p>

<p>$MRS_A(x_A^1, x_A^2)=MRS_B(x_B^1, x_B^2)$</p>

<p>$\displaystyle\left.\frac{\partial{u}/\partial{x_1}}{\partial{u}/\partial{x_2}}\right|_{(x_A^1, x_A^2)}=\left.\frac{\partial{v}/\partial{x_1}}{\partial{v}/\partial {x_2}}\right|_{(x_B^1, x_B^2)}$</p>

<p>In addition, $x_A^1+x_B^1=\omega_A^1+\omega_B^1$</p>

<p>and $x_A^2+x_B^2=\omega_A^2+\omega_B^2$.</p>

<p>These 3 equations in 4 unknowns determine the contract curve.</p>

CC BY-SA 4.0
2018-08-01T19:23:41.063Z
How is this an attempt? Did you derive these equations or did you find them in a book?
Giskard
CC BY-SA 4.0
2018-08-01T19:25:30.763Z
Also, you seem to be missing the individual rationality conditions if you want to the define the contract curve.
Giskard
CC BY-SA 4.0
2018-08-01T19:54:57.967Z
@denesp My textbook says that the consumers will have to have the same MRS between each of the two goods. I just wrote that down as an equation. I don't know what you mean by individual rationality conditions.
Siddhartha
CC BY-SA 4.0
2018-08-01T18:54:14.393Z
2018-08-01T19:01:18.473Z
2018-08-01T19:01:18.473Z
Siddhartha
<p>If agent A has utility function $u(x_1, x_2)$ and agent B has utility function $v(x_1, x_2)$, what are the equation(s) that characterize the Pareto-efficient  allocation of goods in the Edgeworth box? Assume that the initial endowment of agent A is $(\omega_A^1, \omega_A^2)$ and the initial endowment of agent B is $(\omega_B^1, \omega_B^2)$.</p>

<microeconomics><pure-exchange-economy>
Pareto-optimal allocations in the Edgeworth box
Siddhartha
# Pareto-optimal allocations in the Edgeworth box

(Asked by: username_0 on 2018-08-01)

If agent A has utility function $u(x\_1, x\_2)$ and agent B has utility function $v(x\_1, x\_2)$, what are the equation(s) that characterize the Pareto-efficient allocation of goods in the Edgeworth box? Assume that the initial endowment of agent A is $(\omega\_A^1, \omega\_A^2)$ and the initial endowment of agent B is $(\omega\_B^1, \omega\_B^2)$.

**Tags:** microeconomics, pure-exchange-economy

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## 1 answers

### Answer by username_0 on 2018-08-01. Score: 0 | Accepted answer

I don't know why this got down-voted. I'll post my attempt anyway...

$MRS\_A(x\_A^1, x\_A^2)=MRS\_B(x\_B^1, x\_B^2)$

$\displaystyle\left.\frac{\partial{u}/\partial{x\_1}}{\partial{u}/\partial{x\_2}}\right|\_{(x\_A^1, x\_A^2)}=\left.\frac{\partial{v}/\partial{x\_1}}{\partial{v}/\partial {x\_2}}\right|\_{(x\_B^1, x\_B^2)}$

In addition, $x\_A^1+x\_B^1=\omega\_A^1+\omega\_B^1$

and $x\_A^2+x\_B^2=\omega\_A^2+\omega\_B^2$.

These 3 equations in 4 unknowns determine the contract curve.

> **Comments:**
> **username_1**: How is this an attempt? Did you derive these equations or did you find them in a book?  
> **username_1**: Also, you seem to be missing the individual rationality conditions if you want to the define the contract curve.  
> **username_0**: @denesp My textbook says that the consumers will have to have the same MRS between each of the two goods. I just wrote that down as an equation. I don't know what you mean by individual rationality conditions.  

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