In a pure exchange economy with two goods, (G ) and (H ), the two traders have Cobb Douglas utility functions Amos ' utility is (U a left(G a ight) alpha left(H alpha ight) 1 alpha ) and Elise 's is (U e left(G e ight) beta left(H e ight) 1 beta ) What are their marginal rates of substitution Betwe...

Amos marginal rate of substitution is M R Sa alpha 1alpha Ha Ga and Elises is M R ...

In a pure exchange economy with two goods, (G) and (H), the two traders have Cobb-Douglas utility

Question:

In a pure exchange economy with two goods, $G$ and $H$, the two traders have Cobb-Douglas utility functions. Amos' utility is $U_{a}=\left(G_{a}\right)^{\alpha}\left(H_{\alpha}\right)^{1-\alpha}$ and Elise's is $U_{e}=\left(G_{e}\right)^{\beta}\left(H_{e}\right)^{1-\beta}$. What are their marginal rates of substitution? Between them, Amos and Elise own 100 units of $G$ and 50 units of $H$. Thus, if Amos has $G_{a}$ and $H_{a}$, Elise has $G_{e}=100-G_{a}$ and $H_{e}=50-H_{a}$. Solve for their contract curve.

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