Question

1. Angie has 24 dollars to spend, and she spends all her money on books and coffee. Each book costs $3 and each coffee $1. She always buys 3 cups of coffee to go with every new book. She would never buy her coffees without a book, or a book without three coffee.

a. What is Angie’s opportunity cost for buying coffee?

b. What is an equation for Angie’s budget line?

c. What sort of preferences is Angie exhibiting? Create a utility function that describes her preferences.

d. Find Angie’s best affordable bundle of books and coffee.

Answer 1

a. Angie’s opportunity cost for buying coffee is the price she pays which is $1.

b. The equation for Angie’s budget line is M = B * PB + C * PC where M = income = 24, B = books, PB = price of book = $3, C = Coffee, PC = price of coffee = $1. This results in changing the equation of budget line to 24 = 3B + C

c. A utility function that describes her preferences is U (B, C) = min (C, 3B). For B = 1, the same utility is received only when C = 3 so that C = 3B. This is because B and C are always consumed together in C/B = 3/1 ratio.

d. Angie’s best affordable bundle of books and coffee has C = 3B and C = 24 – 3B from the budget line. Then we have

3B = 24 – 3B or B = 24/6 = 4 units. This implies C = 3*4 = 12 cups. Hence the best affordable bundle is 4 books and 12 cups of coffee