Anthony spends his income on fishing lures (L) and guitar picks (G). Lures are priced at $2, while a package of guitar picks cost $1. Assume that Anthony has $30 to spend and his utility function can be represented as U(L,G) = L0.5G0.5. For this utility function, MUL = 0.5L-0.5G0.5 and MUG = 0.5L0.5G-0.5.
a. What is the optimal number of lures and guitar picks for Anthony to purchase? How much utility does this combination bring him?
b. If the price of guitar picks doubles to $2, how much income must Anthony have to maintain the same level of utility?