Problem 4 (Competitive equilibrium) Consider a market with 40 identical consumers whose quasilinear utility from consuming an amount 3: of a good and an amount m of \"money\" is given by U(33, m) = Z + m. There are identical suppliers in perfect competition with cost function C(q) = 12/2. 1. Derive the aggregate demand function. 2. Determine the competitive longrun equilibrium. 3. Show in a diagramme that the competitive equilibrium maximises welfare