2. Suppose Dion's preferences are represented by u(x,x2) = { xx. (a) Find the marginal utilities...

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2. Suppose Dion's preferences are represented by u(x₁,x2) = { x²x³. (a) Find the marginal utilities of x₁ and 2 (b) Show that Dion's utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (c) Find the MRS. (d) Write down Dion's budget constraint. (e) Write down the tangency condition needed to find an optimal con- sumption bundle for well-behaved preferences. (f) Using the equations you wrote in (c) and (d), find Dion'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). (g) 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? 2. Suppose Dion's preferences are represented by u(x₁,x2) = { x²x³. (a) Find the marginal utilities of x₁ and 2 (b) Show that Dion's utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (c) Find the MRS. (d) Write down Dion's budget constraint. (e) Write down the tangency condition needed to find an optimal con- sumption bundle for well-behaved preferences. (f) Using the equations you wrote in (c) and (d), find Dion'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). (g) 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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a The marginal utilities of x1 and x2 are ux1 25 x23 ux2 ... View the full answer