Problem Set $2$

ECON$104$A: Intermediate Microeconomic Theory

Answer all $3$ questions. In order to get full credit you must show all of your work. If questions have multiple parts please clearly label which part of the question you are answering. You will be awarded $2$ Extra Credit Points if you complete the assignment on this document.

$(20$ points$)$ Optimal Consumer Choice: Suppose that your utility function:

$U=5xY+6x+2Y$

$($a$)(6$ points$)$ If the price of $x$ is $P_x=$$$10,$ the price of $Y$ is $P_Y=$$$20,$ and your income is $$100,$ find the optimal amount of each good to purchase.

$($b$)(6$ points$)$ Suppose that the price of good $Y$ decreased to $P_Y=$$$5.$ Find the new optimal quantities of gooc $x$ 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 $Y($ent answers in the boxes above$).$ For both $x$ and $Y,$ which is larger $($in absolute value$)$ the income or subs effect? Explain your answer.