$1.$ Optimal Consumer Choice: Suppose that your utility function:

U $=5$XY $+6$X $+2$Y

$($a$)(6$ points$)$ If the price of X is Px $=$ $$10,$ the price of Y is Py $=$ $$20,$ and your income is $$100,$ find the optimal

amount of each good to purchase.

I

$($b$)(6$ points$)$ Suppose that the price of good Y decreased to Py $=$ $$5.$ Find the new optimal quantities of goods

X and Y to purchase.

$($c$)(6$ points$)$ Find the total effect for both X and Y as a result of the decrease in the price of good Y $($enter your

answers in the boxes above$).$ For both X and Y$,$ which is larger $($in absolute value$)$ the income or substitution

effect? Explain your answer.