Thank you so much !

2. A) Given the following utility function U(X,Y) = X^0.25Y^0.75 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 demand functions for good X and good Y.

C) If P_x=P_y=$1 and M=$24 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 to P_y^' =$2 and nothing else changes, redo parts C) - D).

(use the same graph).

F) Calculate the income and substitution effects for good Y when the P_y increase to P_y^' = $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) = 13.68. 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) = 13.68. 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