In a 2-good model, if individuals in a group all have tastes that are quasilinear in good 1, then we can treat the group as if it was a single representative consumer.

Question

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If all individuals in a group have quasilinear preferences, then their demand functions for good 1 will be the same, allowing us to add up their demand to obtain the total demand of the group. This total demand can be represented by a single representative consumer with the same preferences and demand function. Therefore, we can treat the group as if it was a single representative consumer.

In a 2-Good Model, If Individuals in a Group All