1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good.

1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good.

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 6QFR

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Question

1. Assume you spend your entire income on two goods X & Y with prices given as P_X & P_Y, respectively. Prices and income (I) are exogenous and positive. Given that U = X² + Y² , derive the Marshallian demand function for good Y and evaluate the type of good.

2. Assume you spend your entire income on two goods X & Y with prices given as P_X & P_Y, respectively. Prices and income (I) are exogenous and positive. Given that U= X²Y² , derive the Hicksian demand function for good Y.

3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ P_Y)+(0.5P_X/P_Y)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.

4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: U_A (X_A,Y_A) = X^0.25Y^0.75, U_B (X_B,Y_B) = X0.75Y 0.25
Show that pareto-improvement is possible if, initially, goods are divided equally between the two individuals.

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