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A shadow price:
The additional contribution generated from one additional unit of limiting factor
The opportunity cost of not having the use of one extra unit of limiting factor
The maximum extra amount that should be paid for one extra/additional unit of scrace resource
Coming to example Cara CO past paper exam question march june 2019
question number 23
1) The production manager would be willing to pay existing staff a maximum overtime premium of $125 per hour for the next 2000 hours
2) The production manager would be willing to pay a maximum of $170 per hour for an additional hours of temporary staff
Dear Tutor, what i do not understand here the differences between 1 and 2 is that, since labor pay per hour 45$ and contribution 125 and maximum amount togetger 170$, how it is possible maximum overtime premium 125$ for the next 2000 hours?does not mean next 2000 hours as additional 2000 hours either?
I know that maximum amount is shadow price plus any labor cost per hour or material cost per kg accodinting to the limiting factor in the question.
One more thing, could you just give a brief explanation of surplus saying that surplus occurs when more than a minimum reqquirement is used
In month 2 there are 12,000 hours normally available and they normally pay $45 per hour.
If they want more hours then it will have to be overtime and so any extra hours will be paid more than $45 per hour. The extra over and above $45 is the overtime premium.
Given that the shadow price is $125 it means that they are prepared to pay up to $125 extra per hour for any extra hours above 12,000. So the maximum premium to pay is $125, and the maximum total pay for any extra hours is $170 per hour.Surplus applies to greater than or equal to constraints – for example a constraint is that they must produce at least 10 units, in which case X >= 10. If they actually produce 15 units then there is a surplus of 5 units above the limit.
Dear Tutor, one more thing shadow price is zero where there no binding constraint but shadow price is positive where there is a binding constraint?
I am sorry Dear tutor, Please ignore the above
Dear Tutor, one more thing shadow price is zero where there a binding constraint but shadow price is positive where there is a non-binding constraint?No – what you wrote first time was correct.
If it is a binding constraint then the shadow price is positive – buying more will enable you to produce more, therefore make more profit, and therefore you will be prepared to pay extra.
If it is a non-binding constraint then there is no point in buying more and therefore there will be no shadow price.
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