Leontief-Model

[Sailorman]

These two lessons are part of a Leontief Unit in ecnonmics but I can not solve them. You can use Gauss-Jordan or Leontief-model.


Chris and Ed decide to help each other by doing repairs on eachothers houses. Chris is a carpenter, and Ed is an electrician. Chris does carpentry work on his house as well as on Ed's house. Similarly, Ed does electrical repairs on his house and on Chris'house. When they are all finished they realize that Chris spent 60%of his time on his own house, and 40% of his time on Ed's house. Onthe other hand Ed spent half of his time on his house and half onChris's house. If they originally agreed that each should get abouta $1000 for their work, how much money should each get for theirwork?

Solution: Chris 1250, Ed 1000



Chris, Ed, and Paul decide to help each other by doing repairs oneach others houses. Chris is a carpenter, Ed is an electrician, andPaul is a plumber. Each does work on his own house as well as on theothers houses. When they are all finished they realize that Chrisspent 30% of his time on his own house, 40% of his time on Ed'shouse, and 30% on Paul's house. Ed spent half of his time on his ownhouse, 30% on Chris' house, and remaining on Paul's house. Paulspent 40% of the time on his own house, 40% on Chris' house, and 20%on Ed's house. If they originally agreed that each should get abouta $1000 for their work, how much money should each get for theirwork?

Solution: no solution available

 

[Ishuda]

These two lessons are part of a Leontief Unit in ecnonmics but I can not solve them. You can use Gauss-Jordan or Leontief-model.


Chris and Ed decide to help each other by doing repairs on eachothers houses. Chris is a carpenter, and Ed is an electrician. Chris does carpentry work on his house as well as on Ed's house. Similarly, Ed does electrical repairs on his house and on Chris'house. When they are all finished they realize that Chris spent 60%of his time on his own house, and 40% of his time on Ed's house. Onthe other hand Ed spent half of his time on his house and half onChris's house. If they originally agreed that each should get abouta $1000 for their work, how much money should each get for theirwork?

Solution: Chris 1250, Ed 1000

...

This doesn't make sense to me. First of all, is there a typo? Chris spent proportionally more time working on his own house yet he should be paid more? Since it isn't stated, I would assume that the value of Chris' and Ed's time were the same. Is that a wrong assumption?

Assume the original estimate was 50 hrs for each house for each task: 50 hrs Ed (electrical) work on each house and 50 hours Chris (carpentry) work on each house. So Ed and Chris both would put in 100 hrs work. At the end, Ed did put in the 100 hours, 50 on his house and 50 on Chris' house. Now consider two different scenarios:
(1) Chris put in the 50 hrs on his house but it didn't take as long to do the work on Ed's house, in fact it only took 33 hrs., 20 min. so Chris only worked 83 hrs. 20 min. But he did work on his own house 60% of that time and on Ed's house 40% of that time. Obviously Chris should be paid less than the original estimate.
(2) Chris put in the 50 hrs on Ed's house but it took longer to do the work on his house, in fact it took 75 hrs. ...