Question

If a consumer has a utility function u(x1, x2) = X,X⁴ , what fraction of
her income will she spend on good 2?

Answer 1

The fraction of income spent on good 2 will depend on the relative prices of the two goods. If the price of good 2 is higher than the price of good 1, then the consumer will spend a larger fraction of her income on good 2. If the price of good 1 is higher than the price of good 2, then the consumer will spend a smaller fraction of her income on good 2.