Show how to get marshallian demand and indirect utility function. John views goods X and Y as

Show how to get marshallian demand and indirect utility function.

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John views goods X and Y as perfect substitutes in the proportion 1 of X to 3 of Y. His utility function is thus given by U(x, y) 3x + 1y. a) For a given amount of income I, and prices px and py, find John's Marshallian demand functions for X and Y (You will have three cases depending on the price ratio). (5 points) Marshallian demand: 1 Px 2) If* > 3: x = 0 and y = Py Px 1) If P < 3: x= Py and y = 0 I Py 3) If x= 3: X and Y any non-negative value as long as Pxy + Pyy = I. Py b) Find the indirect utility function (You will have three cases depending on the price ratio). (5 points) Px 1) If <3: V = Py 2) If P* > 3: V = Py Px 3) If = 3: V = Py Px I Py 31 I Px Py = V(Px. Py, 1) = 3x* + 1y* John views goods X and Y as perfect substitutes in the proportion 1 of X to 3 of Y. His utility function is thus given by U(x, y) 3x + 1y. a) For a given amount of income I, and prices px and py, find John's Marshallian demand functions for X and Y (You will have three cases depending on the price ratio). (5 points) Marshallian demand: 1 Px 2) If* > 3: x = 0 and y = Py Px 1) If P < 3: x= Py and y = 0 I Py 3) If x= 3: X and Y any non-negative value as long as Pxy + Pyy = I. Py b) Find the indirect utility function (You will have three cases depending on the price ratio). (5 points) Px 1) If <3: V = Py 2) If P* > 3: V = Py Px 3) If = 3: V = Py Px I Py 31 I Px Py = V(Px. Py, 1) = 3x* + 1y*

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