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Calculating price in a pure exchange economy

Let $\omega_1 = (\omega_{1}^X, \omega_{1}^Y)$, and $\omega_2 = (\omega_{2}^X, \omega_{2}^Y)$ be the endowment of the two consumers, respectively. Also, their utility functions are $u_1(x_1, y_1) = x_1$...
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