Problem 3 (Elasticity of demand) Consider the demand function D(p) = 2 / pE and the supply function 8(1)) = p\" 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 6 and p 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