Luna likes chips (C) three times as much as pretzels (P), and views a bag of chips as a perfect substitute for three boxes of pretzels. The price of a bag of chips is $5, the price of a box of pretzels is $1, and Luna has $40 to spend on salty snacks.

(a) Write down a utility function that represents Luna's preferences.

(b) How much of each snack will Luna buy?

(Hint: the first order conditions will not help; think about what you would do in this situa- tion.)

(c) Now, suppose that the price of a box of pretzels rises to $5. What is Luna's new optimal consumption?

(d) What is Luna's demand for chips and pretzels as a function of prices and income {pc, pp, I}? You will have three cases depending on the relationship between pc and pp.