4. [20 marks] Avi (A) and Brad (B) live in an exchange economy where they consume cakes, x, and litres of beer, y. Both of their preferences are given by: u= aln(x) + (1 - a) ln(y) where 0 < a < 1. There are a total of n cakes and 3n litres of beer in the economy, where 3 > 0. a. Assuming Py = 1 and letting pr=p, show that there will be a constant equilibrium price, p* (a, 3), regardless of the initial distribution of x and y between Avi and Brad. What is this price? b. Consider a beer-heavy economy in which n = 10, a = 0.2 and 3= 8. Suppose Avi starts with all the beer, and Brad starts with all the cake. What will be the post-trade equilibrium? Who trades how much for what? Show the situation on an Edgeworth-box diagram with post-trade indifference curves. (Your diagram does not have to be 'to scale".)