My old aunt always drinks each cup of tea (good x) with two spoonfuls of sugar (good y). She would never consider consuming these two goods in any different proportion. Suppose that my aunt's monthly income is $33, the price per cup of tea is $0.20 and the price per spoonful of sugar is $0.05.

(a) Write a utility function that represents her preferences for the two goods. Draw several of her indifference curves.

(b) Can you help my aunt find her optimal monthly consumption plan?

(c) Suppose that, due to new tea import taxes, the price of tea goes up to $0.23. Find her new optimal choice. How much will she be paying in tea taxes per month?

(d) Suppose that prices go back to the initial levels, but that my aunt's monthly income is reduced to $30. Find her optimal choice and compare to that in part (c). Make sure to comment.

(e) Derive her demand functions for cups of tea and spoonsful of sugar. Are the goods normal or inferior, ordinary or Giffen, substitutes or complements?