Mathematics Homework Help

A.

(i) David spends $12/week on orange juice (OJ) and apple juice (AJ).
Price of OJ is $2/cup and price of AJ is $1/cup. David views 1 cup of OJ
as a perfect substitute for 3 cups of AJ. What is David’s optimal
consumption bundle every week?  (SHOW  WORK)

(ii) Suppose the price of OJ doubles
while price of AJ remains the same. How much are the income and
substitution effects of this price change on David’s consumption of OJ?
(SHOW WORK)

B.

(i) Bianca has the same income and faces the same prices as David in
(a)(i). But she views 1 cup of OJ as a perfect complement with 2 cups of
AJ. What is Bianca’s optimal consumption bundle every week?  (show work)

(ii) Suppose the price of OJ doubles while price of AJ remains the same. How much are the income and substitution effects of this price change on Bianca’s consumption of OJ? (SHOW WORK)