Two types of utilities from the United States are:

(, ) = / . /

(, ) = / . /3

Where x is the consumption of luxury goods and y is the consumption of non-luxury goods for individuals with (utility types a and b). Considering this information, please answer the following questions below:

a) Find the Marshallian demand for both goods considering both types of individuals (show all work) and explain results.

b) Calculate the substitution effect and the income effect for both types of individuals and explain results.

c) The United States decided to introduce a tax on luxury goods. Discuss the implications of this using the lump sum principle.

d) If you are an individual of this country, what type do you think you are?