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(x, y) = (x + 1)y (b) U(x, y) = √x + √y

Microeconomic Theory
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Chapter2: Mathematics For Microeconomics
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Problem 2.7P
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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(x, y) = (x + 1)y
(b) U(x, y) = √x + √y

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