Consider the following utility functions: U(X, D) = X2 + 2 a-) For the above utility function. derive the demand functions for X and Y as functions of prices and income. Explain whether these goods are normal goods. Explain whether two goods are complements or substitutes. b- ) Suppose now that Price of good Y is $48 and income equals 1440. Using three distinct values of price of X ( Py = 6. P. = 12. Py = 24 ). draw Price consumption curve and then using Price Consumption curve draw the demand curve for X C- Suppose Price of good Y is $48 and price of X is equal to 6. Using three distinct income values ( 1' =1440.1 = 2880.1' = 4320). draw Income Consumption curve and then using Income Consumption curve draw the Engel curve for good X d- Consider initially that Income (1) = $1440. Py - 6 and Py - 48. What is the initial optimal consumption levels of X and Y? Suppose that P. rises from $6 to $12. Find the substitution effect. income effect and total effect on good X. Explain the steps carefully and support your result with an explanation and a graph