Suppose a consumer buys two goods, good X and a composite good Y. The utility function is given as: (,) = (). I=$10 = $ . Where is the natural logarithm, I is income level, is the price of good X 1) Find the optimal basket that maximizes utility and calculate its corresponding utility level. (5 marks) 2) Show your answer for Questions (1) on a graph. (5 marks) 3) Suppose a $0.3 per unit subsidy is levied on good X whose supply curve is perfectly elastic and its demand curve is negatively sloped. What is the new optimal basket that maximizes utility? (5 marks) 4) Suppose instead of the $0.3 per unit subsidy levied on good X, the government imposed a $0.3 per unit tax on good X. Assume that the supply curve of good X is perfectly inelastic, and its demand curve is negatively sloped. What is the new optimal basket that maximizes utility? (5 marks) 5) Does the given utility function have a diminishing MRS? Why? (5 marks) 6) Does the given utility function satisfy the law of diminishing MU? why? (5 marks) 7) Does the given utility function satisfy the assumption that more is better? why? (5 marks)