QUESTION 3: 8 marks Consider the problem of a consumer who must choose between two types of goods, good A (a) and good B (b) costing respectively Pa and p, per unit. He is endowed with an income y and has a utility function u defined by: u(a, b) = ln(2a + 3√6) 2 marks 1 mark 1. Show that the consumer's utility function is quasi-concave. 2. Write down the maximization problem of the consumer. 3. Determine the optimal amount of good A and good B, a* = a(pa, Pb, y) and b*b(Pa, Pb, y) respectively. 2 marks 1 4. By how much and in what direction will the utility function change if the income changes by 1 unit? 1 mark 5. Find the optimal amounts of good A and good B the consumer will choose as well as the maximum utility she will get if pa = 32, p = 9 and y = 256. 2 marks