1.A) Given the following utility function U(X, Y) = X'Y find the marginal rate of substitution (MRS). B) Let Px be the price of good X, Py be the price of good Y, and M be income. Find the Marshallian demand functions for good X and good Y. C) If Px=Py=$1 and M=$30 how many units of good X and good Y will maximize this consumers utility S.T. the budget constraint? What is U"? Show that the MRS(Xi*, Yi*) = Px/Py. D) Show your solution to part C) graphically (be precise!). E) Assume now the price of good Y rises to Py = $2 and nothing else changes, redo parts C) - D). (use the same graph). F) Calculate the income and (Hicksian) substitution effects for good Y when the Py increase to $2 and show them on your graph. G) Find the Hicksian Compensated demand functions for good X and Y. H) Let Px = $1, Py' = $2 and U(X, Y) = 4000. Find the Hicksian Compensated quantity demanded for goods XHC and YHC. Compare your answers to XHC and YHC from part F). Does this make sense to you? Explain I) Let Px = $1, Py = $1 and U(X, Y) = 4000. Find the Hicksian Compensated quantity demanded for goods X and Y. Compare your answers to X1" and Y," from part C). Does this make sense to you, given what you know about Marshallian and Hicksian Compensated demand functions? Explain