Suppose that the demand function is given as follows: Of = 360-2P + P, + / and Of =-120 +P, where P denotes price of good x, P, denotes the price of a related product y, I denotes income. a-) (8 points) Find equilibrium price and output ( Prob and (29 ) as a function of exogenous variables income (I) and price of the related product ( P, ). Using comparative statics, find how the equilibrium price and output change as Price of the related product ( P, ) and income (1) change (i.e. find Ox aQeb apeqb apeab -). Support aPy al ap al your findings with graphs (how demand and supply are affected?) Are goods x and y complements or substitutes? Is good x a normal good or an inferior good? b-) (6 points) Suppose now that exogenous variables are given as follows: Income (1) - 180, Price of the related product ( P, ) = 60. Find the equilibrium price and output values. Calculate the price elasticity of demand at the equilibrium? Is total revenue maximized at the equilibrium price? If not, what would you do to increase total revenue? Why? c-) (6 points) Find the income elasticity of demand at the equilibrium price and output found in part c. Is good x a normal good? Find the cross price elasticity of demand for x with respect to price of y? Are the products complements or substitutes? Are you consistent with part a? d-) (8 points) Consider that Income (1) = 180, Price of the related product (Py ) - 60. Suppose now that government imposes $24 per unit tax on sellers. Find the new equilibrium price and quantity after the tax. What is the burden on sellers and burden on buyers? Show the original no tax equilibrium (in part a) and the equilibrium after tax on a diagram and indicate the burden on buyers and sellers. Find the relationship between the share of burden and price elasticities of demand and supply