5.. A firm has won the bid to complete a renovation of a hotel and you are to ma

Question

5.. 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
a) Who has the absolute advantage in each task?
b) What is the opportunity cost of each task for each worker?
c) Who has the comparative advantage in each task?
d) How many hours would it take for Ben and Jerry to complete the entire hotel if each worker completed an entire room before moving on to the next?
e) 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.

Explanation / Answer

Ans A)

Jerry has an absolute advantage in floors and Walls becuase he takes much less time than Ben

Ans B)

Opportunity Cost for Ben to Produce 1 more Floor is 0.75 walls

Opportunity Cost for Ben to Produce 1 more Wall is 1.33 Floors

Opportunity Cost for Jerry to Produce 1 more Floor is 0.66 walls

Opportunity Cost for Jerry to Produce 1 more Wall is 1.5 Floors

Ans C)

Opprotuntiy Cost for Jerry to Produce Floor is less than Ben and SImilar case Opportunity Cost for Ben to produce Wall is less than JErry Hence Comparative advantage for Ben in producing Walls and Jerry has in Producing floors

ANs D)

Assuming A Room has X windows and Y floors then Ben Will take 3X+4Y hours to complete 1 room similarly Jerry will take 2X+3Y hours to complete 1 room

then Ben completes K rooms and Jerry completes M rooms hence number of hours taken will be

3XK+4YK and 2XM+3YM where K+M=60

3X(60-M)+4Y(60-M)=180X+240Y-M(3X+4Y)>2XM+3XM

Assuming X=1 and Y=1 number of hours taken by Ben is 7 hours for 1 room whereas Jerry would take 5 hours hence in 35 hours 12 rooms will be completed together and 175 hours to complete the hotel now if they specilalise into the task they have comparative advantage in we get

Ben must produce Walls and Jen would produce Floors then Ben will take 240 hours to produce all walls whereas Jerry would take 120 hours to produce all floors then till 120 hours Ben would have done with 30 walls then each worker will start working on walls therefore in 12 hours they will be producing 7 walls hence 48 hours needed to do 28 walls hence 171 hours needed if task is done collectively on the basis of comparative advantage

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