Can you please solve it thank you so much!

DEFINE ALL UNDERLINED WORDS.

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

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

3. Explain the difference between a Marshallian Demand Function and a Hicks Compensated Demand Function.

4. Write out the Slutsky equation and illustrate why it is an identity.

5. For a normal good, draw a Marshallian and Hicks Compensated demand function. Which demand function is more elastic? Explain.

For an inferior good, draw a Marshallian and Hicks Compensated demand function. Which demand function is more elastic? Explain.

6. Assume that a consumer maximizes his/her utility, S.T. their budget constraint by purchasing good x and good y. Let P_xbe the price of good x, P_y be the price of good y, and M be income.

A. Given the following utility function U(x,y) = x²y find the demand functions for good x and good y.

B. 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^*?

C. Assume now the price of good y rises to P_y' = $2 and nothing else changes, redo part B.

D. Graph your solution to parts B) and C) VERY carefully and find the change in consumer surplus when the price of good y increases from $1 to $2. Assume that the Marshallian demand curve for good y is linear between $1 and $2, otherwise you will need to use integration to calculate the change in consumer surplus.

E. Find the compensating variation (CV) when the price of good y increases from $1 to $2 and illustrate it on your graph Explain

Hint: Find the Hicksian compensated quantity demanded of good x and y (