Pat and Kris are roommates. They spend most of their time studying, but they leave some time for their favorite activities: making pizza and brewing root beer. Pat takes 4 hours to brew a gallon of root beer and 2 hours to make a pizza. Kris takes 6 hours to brew a gallon of root beer and 4 hours to make a pizza.

Question

The price of pizza can be expressed in terms of gallons of root beer. What is the highest price at which pizza can be traded that would make both roommates better off?

Hint: think opportunity cost. To make 1 gal of root beer, what does Pat need to give up? what does Kris need to give up. This becomes the price of root beer.

Answer 1

To find the highest price at which pizza can be traded that would make both roommates better off, we need to consider the opportunity cost of making a gallon of root beer for each person.

For Pat: Pat can make 1 pizza in 2 hours, and since it takes 4 hours to brew a gallon of root beer, Pat can make 2 pizzas in the time it takes to make 1 gallon of root beer. So the opportunity cost for Pat to make 1 gallon of root beer is 2 pizzas.

For Kris: Kris can make 1 pizza in 4 hours, and since it takes 6 hours to brew a gallon of root beer, Kris can make 1.5 pizzas in the time it takes to make 1 gallon of root beer. So the opportunity cost for Kris to make 1 gallon of root beer is 1.5 pizzas.

In order for both to be better off, the price of pizza has to fall between the opportunity costs of both roommates. So, for a mutually beneficial trade, the price of pizza should be between 1.5 and 2 gallons of root beer. The highest price at which pizza can be traded that would make both roommates better off is therefore 2 gallons of root beer.