1. Use the method of Lagrange multipliers with inequality first-order conditions to determine if corner solutions arise with the following utility functions. If not, explain why not. If so, outline the condition under which a corner solution arises and find the Marshallian demands in these cases. (a) U(1, y) = (x +1)y (b) U(1,y) = Vr + Vỹ
1. Use the method of Lagrange multipliers with inequality first-order conditions to determine if corner solutions arise with the following utility functions. If not, explain why not. If so, outline the condition under which a corner solution arises and find the Marshallian demands in these cases. (a) U(1, y) = (x +1)y (b) U(1,y) = Vr + Vỹ
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.7P
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Transcribed Image Text:1. Use the method of Lagrange multipliers with inequality first-order conditions to determine if
corner solutions arise with the following utility functions. If not, explain why not. If so,
outline the condition under which a corner solution arises and find the Marshallian demands
in these cases.
(a) U(1, y) = (x+1)y
(b) U(x, y) = Vr+ V
%3D
2. Find the Marshallian demands for r and y for the utility function in part (a) of the previous
question when an interior solution exists. Use your solution to confirm the condition that
you found previously for a corner solution to arise.
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