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The tutorial discusses an example involving two agents, A and B, with initial endowments of good one and good two, specifically two units of good one for agent A and three units for agent B. The Edgeworth Box representing these endowments is a rectangle of dimensions two by three. Both agents are assumed to have Cobb-Douglas utility functions, indicating that each agent prioritizes their own consumption. The key focus is on identifying efficient allocations and the contract curve by equating the marginal rate of substitution (MRS) of agent A with that of agent B, utilizing the properties of their identical utility functions to derive the necessary conditions for efficiency.