Intermediate Microeconomics

Please solve the following two problems.

(4.1)

Each day Paul, who is in the 3rd grade, eats lunch at school. He likes only Twinkies (t) and soda (s), and these provide him a utility of

utility = U(t, s) = (ts)^1/2

a.) If Twinkies cost $0.10 each and soda costs $0.25 per cup, how should Paul spend the $1 his mother gives him to maximize his utility?

b.) If the school tries to discourage Twinkie consumption by increasing the price to $0.40, by how much will Paul's mother have to increase his lunch allowance to provide him with the same level of utility he received in part (a).

(4.2)

a.) A young connoisseur has $600 to spend to build a small wine cellar. She enjoys two vintages in particular: a 2001 French Bordeaux (Wf) at $40 per bottle and a less expensive 2005 California varietal wine (Wc) priced at $8. If her utility is:

U(Wf, Wc) = W^2/3f * W^1/3c

then how much of each wine should she purchase?

b.) When she arrived at the wine store, this young oenologist discovered that the price of the French Bordeaux had fallen to $20 a bottle because of a decrease in the value of the euro. If the price of the California wine remains stable at $8 per bottle, how much of each wine should our friends purchase to maximize utility under these altered conditions?

c.) Explain why this is wine fancier is better off in part (b) than in part (a). How would you put a monetary value on this utility increase?