SUBSTITUTION and INCOME EFFECTS: Suppose we are given the followingutility function for a consumer: U(X,Y) = X1/2y1/2 : Suppose also that her income (I)is $1000, Px = $6 and Py = $4.a) Find the consumer’s optimal choice given the prices and income above. What is theutility she derives from this income?b) Find the new optimum if Py falls to $3.c) Show that the income required to just make the previous utility from (a) attainablewith Px = $6 and Py = $3 is $866.03. Show and explain the process you use to get thisresult. (Eg. you have the answer so just show the steps to get there.)d) Given the "new" income in (c) with Px = $6 and Py = $3, find the new optimum. Confirmthat it yields the same utility as in (a).e) What are the Hicks Substitution and Income Effects of the fall in the price of y? eg find∆X and ∆Y.f) What is the Compensating Variation for the fall in Py? Explain your reasoning.g) Show that the income required to just make the new utility in (b) attainable at the oldprices (Px = $6 and Py = $4) is $1154.70. Show and explain the process to get this result.h) What is the Equivalent Variation for the fall in Py? Explain your reasoning.