Parts C - E only!

(Ch 4-Problem 17 in Book) Anthony spends his income on fishing lures (L) and guitar picks (G). Lures are priced at $2, while a package of guitar picks costs $1. Assume Anthony has $30 to spend and his utility function can be represented as U(LG)-Lo.5G0.5 1. What is the optimal number of lures and guitar picks for Anthony to purchase? How much utility does this combination bring him? If the price of guitar picks doubles to $2, how much income must Anthony have to maintain the same level of utility? Suppose that the prices of lures and guitar picks are $2 and $1 (as they were before the price change) and that Anthony still has only $30 to spend. Use a Lagrangian to solve his constrained utility-maximization problem and confirm that the answer is the same as that to part (a) Now suppose that the prices of lures and guitar picks are $2 and $2 (as they were after the price change). Assuming Anthony wants to maintain the same level of utility as he did before the price change with the lowest possible expenditure, a. b. c. d. i. ii. Write a statement of Anthony's constrained optimization problem Use a Lagrangian to solve Anthony's expenditure-minimization problem and confirm that the answer is the same as that to part (b). Again suppose that the price of lures and guitar picks are $2 and $2 (as there were after the price change). This time, however, assume that Anthony still only has $30 to spend. Use a Lagrangian to solve his constrained utility-maximization problem. How much utility does this combination bring him? e. (Ch 4-Problem 17 in Book) Anthony spends his income on fishing lures (L) and guitar picks (G). Lures are priced at $2, while a package of guitar picks costs $1. Assume Anthony has $30 to spend and his utility function can be represented as U(LG)-Lo.5G0.5 1. What is the optimal number of lures and guitar picks for Anthony to purchase? How much utility does this combination bring him? If the price of guitar picks doubles to $2, how much income must Anthony have to maintain the same level of utility? Suppose that the prices of lures and guitar picks are $2 and $1 (as they were before the price change) and that Anthony still has only $30 to spend. Use a Lagrangian to solve his constrained utility-maximization problem and confirm that the answer is the same as that to part (a) Now suppose that the prices of lures and guitar picks are $2 and $2 (as they were after the price change). Assuming Anthony wants to maintain the same level of utility as he did before the price change with the lowest possible expenditure, a. b. c. d. i. ii. Write a statement of Anthony's constrained optimization problem Use a Lagrangian to solve Anthony's expenditure-minimization problem and confirm that the answer is the same as that to part (b). Again suppose that the price of lures and guitar picks are $2 and $2 (as there were after the price change). This time, however, assume that Anthony still only has $30 to spend. Use a Lagrangian to solve his constrained utility-maximization problem. How much utility does this combination bring him? e