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The initial endowments for agents A and B are two units of good one and three units of good two, forming a 2x3 rectangle in the Edgeworth box. Both agents have Cobb-Douglas utility functions. Efficient allocations are found by equating the marginal rate of substitution of agent A with that of agent B, as their utility functions have identical format. This approach is crucial for determining the contract curve and ensuring each agent's satisfaction with their own consumption.