Joseph likes roses (R) and tulips (T) equally, and views them as perfect substitutes in proportion 1 to 1. The price of a rose is $4, the price of a tulip is $8, and Joseph has $40 to spend on flowers.
a) How much of each flower will Joseph buy? (Hint: the first order conditions will not help; think about what you would do in this situation.)
b) Now, suppose that the price of a rose rises to $10. How does the consumption of Joseph change?
c) What are the Joseph's demands for roses and tulips as a function of prices and income{PR, PT, I}? You will have three cases depending on the relationship between PR and PT."
d) How much should Joseph's income increase to compensate for the rise in the price of roses? (Hint: use the indirect utility function before and after the change)