Asuming 0 a y to the utility maximization problem max x

Question

Question: (a) Assuming 0 ≤ a^∗, y^∗) to the utility maximization problem max x + a ln y subject to px + qy = m

(b) Find the indirect utility function U∗(p, q, m, a) = x^∗ + ln y^∗, and compute its partial derivatives w.r.t. p, q, m, and a. Verify the envelope theorem (7).