Max’s preferences can be represented by the utility function u(x1, x2) = 2√ x1 + x2. Take good 2 to be the numeraire (p2 = 1). a) For any price p1 and income m, write down and solve his utility maximization problem, i.e. find the demand x1(p1, m) and x2(p1, m) using the Lagrangian method (assuming an interior solution). Illustrate why this method is equivalent to using the two conditions (1) |MRS| =price ratio and (2) Budget constraint. b) In doing so, also solve for λ ∗ . c) Given any p1 and income m, find the utility of Max corresponding to his demand. Denote this by v(p1, m). That means, find v(p1, m) = u(x1(p1, m), x2(p1, m)). d) To understand how v(p1, m) changes with m, i.e. compute ∂v(p1,m) ∂m . Compare with your answer to b).
Max’s preferences can be represented by the utility function u(x1, x2) = 2√ x1 + x2. Take good 2 to be the numeraire (p2 = 1). a) For any
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