Statistics Solutions

[Solution] A pure exchange economy has three consumers and three goods. Consumers' utility functions and endowments are as follows:

Question: A pure exchange economy has three consumers and three goods. Consumers' utility functions and endowments are as follows:

\[\begin{array}{ll} u_{1}\left(x_{1}^{1}, x_{2}^{1}, x_{3}^{1}\right) & =\min \left\{x_{1}^{1}, x_{2}^{1}\right\} & \omega_{1}=(1,0,0) \\ u_{2}\left(x_{1}^{2}, x_{2}^{2}, x_{3}^{2}\right) & =\min \left\{x_{2}^{2}, x_{3}^{2}\right\} & \omega_{2}=(0,1,0) \\ u_{3}\left(x_{1}^{3}, x_{2}^{3}, x_{3}^{3}\right) & =\min \left\{x_{1}^{3}, x_{3}^{3}\right\} & \omega_{2}=(0,0,1) \end{array}\]
  1. Find the Marshallian demands of the three consumers.
  2. Find all the equilibria.

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