Intermediate Microeconomics Assignment

1) Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has four times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on X-axis and beer measured in six-pack on Y-axis)

a) Devise a utility function to represent these preferences. b) What is his marginal rate of substitution of a bottle of vodka for six packs of beer? c) Suppose a bottle of vodka costs $45, a six-pack of beer costs $15 and Tony has $180 budget. Write the budget constraint. d) Solve Tony's utility maximization problem and find out optimal combination? e) Now suppose that a bottle of vodka cost has increased to $60. What will be his new optimal combination?

2) Suppose Sara does not like to consume apple pie by itself or vanilla ice-cream by itself. However, she loves to consume 2 slices of apple pie with 3 scoops of vanilla ice-cream. (use apple pie on X-axis and bread on Y-axis).

a) Devise a utility function to represent these preferences. b) Suppose a slice of apple pie costs $2 and scoop vanilla ice-cream costs $1. If she has $35 budget to spend on these goods. Write the budget constraint. c) Solve Sara's utility maximization problem and find out optimal combination?