Problem 3 (Elasticity of demand) Consider the demand function D(p) = 2 / p6 and the supply function 8(1)) = pp where e > 1 and p > 1. 1. Find utility and cost functions consistent with the demand and supply function. 2. Show that the pointprice elasticities of demand and supply are constant and equal to e and ,0 respectively (constant elasticty of demand/ supply). 3. For given values 6 and p, calculate the competitive equilibrium price and quantity. 4. Illustrate your solution in a diagramme, and explain what happens as we vary elasticity of supply p, but keep 6 xed. Problem 4 (Competitive equilibrium) Consider a market with 40 identical consumers whose quasilinear utility from consuming an amount :c of a good and an amount m of \"money\" is given by U(:c, m) = Z + m. There are identical suppliers in perfect competition with cost function C(q) = q2 / 2. 1. Derive the aggregate demand functiOn. 2. Determine the competitive longrun equilibrium. 3. Show in a diagramme that the competitive equilibrium maximises welfare