Suppose that my tastes for roses (x) and other goods (y) can be represented by the utility function u(x, y) = βxα + y , where MUx = αβxα-1 and MUy = 1. Roses cost $5 each and my income is $125 per week. Assume that py is by definition equal to 1, and α = 0.5 , β = 50.
a. Calculate my optimal consumption of roses and other goods as a function of px and M.
b. Calculate my optimal consumption of roses for income of $125 and when my income increases to $500 per week.