Question: Suppose a person has a utility function U(x1, x2) = x 1 a +x 2 a , which she maximizes subject to her budget constraint,

Suppose a person has a utility function U(x1, x2) = x₁^a+x₂^a , which she maximizes subject to her budget constraint, px₁ + qx₂ = m, where p, q, m are all positive. Use the Lagrangian method to solve the maximization problem, and find the demand functions for the consumer. Show that the demand functions are homogeneous of degree zero in prices (p, q) and income (m).

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