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Claraís utility function is u (x; y) = (x + 2) (y + 1) where x...

Claraís utility function is u (x; y) = (x + 2) (y + 1) where x is her consumption of good x and y is her consumption of good y.

(a) Write an equation for Claraís indi§erence curve that goes through the point (x; y) = (2; 8).

(b) Suppose that the price of each good is $1 and Clara has an income of $11. Can Clara achieve a utility level of at least 36 with this budget? (

c) What is Claraís marginal rate of substitution at an arbitrary consumption bundle (x; y)?

(d) Write an expression for Claraís budget line when the price of each good is $1 and her income is $11.

(e) We saw in Chapter 5 that at an interior solution to the utility maximization problem with 2 goods, the absolute value of the marginal rate of substitution is equal to the price ratio of those goods. Use that fact and your answers to Part c and Part d to solve for the consumption bundle that maximizes Claraís utility.

(f) What is the maximized level of Claraís utility function at the consumption bundle you solved for in Part e?

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