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Ariadne's preferences can be described by the utility function U(x, y) = (3x1/2 + 6y1/2)2. Elliott'sutility function is U(x, y) = x + 3y1/3.

(a) What are Ariadne's demand functions for goods x and y as a function of prices px and py andincome I?

(b) Ariadne has an income of $10. Her three sisters Bianca, Clara, and Diana have the samepreferences but incomes of $20, $30, and $40, respectively. What is the aggregate demand function of the four for good y when px = 1?

(c) What are Elliott's demand functions for goods x and y as a function of prices px and py andincome I?

(d) Elliott has an income of $10. His brother Frank has the same preferences but an income of $20.What is the aggregate demand function of the two for good y when px = 1?

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