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Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...

Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22.
(a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex.
(b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.]
(c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences.
(d) Write down Alex’s budget constraint.
(e) Using the equations you wrote in (c) and (d), find Alex’s ordinary demand functions for goods 1 and 2 (in other words, find out how much Alex will consume of good 1 as a function of p1, p2, and m, and how much Alex will consume of good 2 as a function of p1, p2, and m).
(f) Suppose that m = 100, p1 = 2 and p2 = 3. How much of good 1 will Alex choose to consume? How much of good 2 will Alex choose to consume?

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3X1粒 3 x) 3x7. dy, 5l NUL Cunditun - 31了2. y2. 4么 X22 2 5 4 (3)

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