Answer all questions. Explain all steps. No assumptions.

3. (45 points). Angela consumes two goods, sausage, denoted by S, and beer, denoted by 1 B. Her utility function for the two goods is equal to U (S ,B) = S 3B . The price of sausage is equal to $2 and the price of beer is $1. Angela has $160 to spend. a) (5 points) Find Angela's optimal consumption bundle. If you can remember the demand functions, then you do not need to derive them. b) (5 points) Suppose the price of beer increases to $2. Find Angela's optimal consumption bundle. c) (10 points) Decompose the change in Angela's consumption of beer into the substitution and income effects. (1) (10 points) Explain the directions and relative magnitude of the two effects. e) (5 points) Decompose the change in Angela's consumption of sausage into the substitution and income effects. f) (10 points) Explain the directions and relative magnitude of the two effects