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Consider a consumer whose preferences over the goods are represented by the utility function U(x,y) =...

Consider a consumer whose preferences over the goods are represented by the utility function U(x,y) = xy^2. Recall that for this function the marginal utilities are given by MUx(x, y) = y^2 and MUy(x, y) = 2xy.

(a) What are the formulas for the indifference curves corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9? Draw these three indifference curves in one graph.

(b) What is the marginal rate of substitution MRSxy?

(c) What is MRSxy for the utility function U(x,y) = 5xy2 ? Explain without recomputing.

(d) Are the preferences of this consumer satisfy the ‘more is better’ assumption and the ‘declining MRS’ assumption?

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