Alice's utility function is U(x, y) = x²y. Steve's utility function is U(x, y) = x²y + 2x. Alice and Steve have the same preferences since Steve's utility function is a monotonic transformation of Alice's.

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Steve's utility function is not a monotonic transformation of Alice's because it includes an additional term, 2x, which changes the preferences. Monotonic transformations involve multiplying by a positive constant or adding a constant, not adding a term dependent on the variables.

Alice's Utility Function Is U(x, Y) = X2y

Alice's Utility Function Is U(x, Y) = X²y