y y QUESTION 1 Consider the standard utility maximization problem: maxU = U(x,y) subject to Px+Py = B, where P P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the Lagrangian function and obtain the first-order conditions. (6 marks) (b) Assume that U = xy, P = 1,P = 4 and B=120. Find A along with the optimal levels of purchase x and y. Calculate U. (10 marks) (c) Using the Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (9 marks) y and
y y QUESTION 1 Consider the standard utility maximization problem: maxU = U(x,y) subject to Px+Py = B, where P P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the Lagrangian function and obtain the first-order conditions. (6 marks) (b) Assume that U = xy, P = 1,P = 4 and B=120. Find A along with the optimal levels of purchase x and y. Calculate U. (10 marks) (c) Using the Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (9 marks) y and
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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y
QUESTION 1 Consider the standard utility maximization problem: maxU = U(x,y) subject to Px+Py = B, where P
P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the
Lagrangian function and obtain the first-order conditions. (6 marks) (b) Assume that U = xy, P = 1,P = 4 and
B=120. Find A along with the optimal levels of purchase x and y. Calculate U. (10 marks) (c) Using the
Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (9 marks)
y
and
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