Question

A firm has won the bid to complete a renovation of a hotel and you are to manage the labor to complete the job. The firm is assigning two workers named Ben and Jerry. The floors and walls must be redone and there are 60 hotel rooms to complete. The firm is not receiving payment by the hour but by the job. The firm's goal is to minimize time spent on this project. The table below shows the time it takes to complete a single room which has two aspects of the job.
Floors     Walls
Ben     3 hours    4 hours
Jerry   2 hours    3 hours
How many hours would it take to complete the entire hotel if each worker specialized in a task in which they had the comparative advantage? Do not let time pass with idle workers.

Answer 1

Ben and Jerry specialize on the basis of their comparative advantage.

We need to compare the opportunity cost of redoing floors and walls by Ben and Jerry.

Ben requires 3 hours to redo the floors and in those 3 hours he could have redone 3/4 walls so opportunity cost of redoing floors for Ben is 3/4.

Ben requires 4 hours to redo the walls and in those 4 hours he could have redone 4/3 floors so opportunity cost of redoing walls for Ben is 4/3.

Jerry requires 2 hours to redo the floors and in those 2 hours he could have redone 2/3 walls so opportunity cost of redoing floors for Jerry is 2/3.

Jerry requires 3 hours to redo the walls and in those 3 hours he could have redone 3/2 floors so opportunity cost of redoing walls for Jerry is 3/2.

Comparing the opportunity cost we see that Ben has lower opportunity cost in redoing walls as compared to Jerry. So, Ben will specialize in redoing walls.

Jerry has lower opportunity cost in redoing floors as compare to Ben. So, Jerry will specialize in redoing floors.

Time required to complete a single room will be 4 hours by Ben to redo walls and 2 hours by Jerry to redo floors. Total hours required to complete a single room will be 6 hours. There are 60 hotel rooms, so 60*6=360 hours will be required to redo the entire hotel.