Problem 1 {30 marks) Suppose a consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y)=5\\IXY. I=$20 PX=$2 Where I is income level, PX is the price of good X 1) Find the optimal basket that maximizes utility and calculate its corresponding utility level.(S marks) 2) Show your answer for Questions (1) on a graph. ( 5 marks) 3) Suppose a $0.5 per unit Subsidy is levied on good X whose Supply Curve is perfectly inelastic. What is the new optimal basket that maximizes utility, and calculate its corresponding utility level.( 5 marks) 4) Does the given utility function have a diminishing MRSEK? Why? ( 5 marks) 5) Does the given utility function satisfy the law ofdiminishing MU? why? ( 5 marks) 6) Does the given utility function satisfy the assumption that more is better? why