Thank you so much for solving it!

1.A) Given the following utility function U(X,Y) = X²Y find the marginal rate of substitution (MRS).

B) Let P_x be the price of good X, P_y be the price of good Y, and M be income. Find the Marshallian demand functions for good X and good Y.

C) If P_x=P_y=$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(X₁^*,Y₁^*) = Px/Py.

D) Show your solution to part C) graphically (be precise!).

E) Assume now the price of good Y rises toP_y^' =$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 P_y^' increase to $2 and show them on your graph.

G) Find the Hicksian Compensated demand functionsfor good X and Y.

H) Let Px = $1, Py^' = $2 and U(X,Y) = 4000. Find the Hicksian Compensated quantity demanded for goods X_HC and Y_HC.Compare your answers to X_HC and Y_HC 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 Y₁^* from part C). Does this make sense to you, given what you know about Marshallian and Hicksian Compensated demand functions? Explain