PLEASE THOROUGHLY EXPLAIN ALL PARTS.

1. (30 points). In a competitive market for a good, demand and supply are both continuously differentiable in all dimensions. Demand depends on the price of the good and the income of consumers, 1: QB (P,I ). The demand curve is downwardsloping. Supply depends on the price of the good and the interest rate, r: QS (P, r) . The supply curve is upwardsloping and supply is strictly decreasing in the interest rate. a) Around a competitive equilibrium, is the equilibrium price an implicit function of consumer income and the interest rate? b) If the interest rate increases, does the equilibrium price and quantity increase or decrease? Use the implicit function rule and illustrate your answer in a graph. 0) Suppose that the good is a normal good. If income increases, does the equilibrium price and quantity increase or decrease? Use the implicit function rule and illustrate your answer in a graph. d) Suppose instead that the good is an inferior good. If income increases, does the equilibrium price and quantity increase or decrease? Use the implicit function rule and illustrate your answer in a graph