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