Question 2 2.1 A consumer has a utility function u(x₁, X₂) √1+2 and faces a budget constraint y = P₁x1 + P22. Assuming an interior solution to the consumer's utility maximisation problem (i.e. excluding the possibility of any corner solutions where x = 0 or x = 0), solve for xi (p, y) and x(p, y), the consumer's Marshallian demand functions. 2.2 Derive the consumer's indirect utility function. 2.3 Derive the consumer's expenditure function. 2.4 Suppose the assumption of an interior solution, as set out in question 2.1 above, is no longer maintained. Discuss how (under what conditions) a corner solution to this specific =

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Question 2
2.1 A consumer has a utility function u(x1, x2) = VT1 + x2 and faces a budget constraint
y = P1x1 + P2x2. Assuming an interior solution to the consumer's utility maximisation
problem (i.e. excluding the possibility of any corner solutions where x = 0 or x = 0),
solve for x(p, y) and x(p, y), the consumer's Marshallian demand functions.
2.2 Derive the consumer's indirect utility function.
2.3 Derive the consumer's expenditure function.
2.4 Suppose the assumption of an interior solution, as set out in question 2.1 above, is no
longer maintained. Discuss how (under what conditions) a corner solution to this specific
utility maximisation problem may arise (i.e. where x = 0 or x = 0). Then re-write the
solutions for xi(p, y) and x(p, y) (the consumer's Marshallian demand functions), as well
as the new indirect utility function v(p, y), so as to allow for the occurrence of a corner
solution.
Transcribed Image Text:Question 2 2.1 A consumer has a utility function u(x1, x2) = VT1 + x2 and faces a budget constraint y = P1x1 + P2x2. Assuming an interior solution to the consumer's utility maximisation problem (i.e. excluding the possibility of any corner solutions where x = 0 or x = 0), solve for x(p, y) and x(p, y), the consumer's Marshallian demand functions. 2.2 Derive the consumer's indirect utility function. 2.3 Derive the consumer's expenditure function. 2.4 Suppose the assumption of an interior solution, as set out in question 2.1 above, is no longer maintained. Discuss how (under what conditions) a corner solution to this specific utility maximisation problem may arise (i.e. where x = 0 or x = 0). Then re-write the solutions for xi(p, y) and x(p, y) (the consumer's Marshallian demand functions), as well as the new indirect utility function v(p, y), so as to allow for the occurrence of a corner solution.
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