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Hi Mr. Moffat,
I am not quite sure about the wording of Shadow prices. In the text book, it says:
1. The shadow price of a resource can be found by calculating the increase in value (usually extra contribution) which would be created by having available one additional unit of a limiting resource at its original cost.
2. It therefore represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint.
3. Non-critical constraints will have zero shadow prices as slack exists already.I am not understanding point 1 and 2. I mean if at point 1, it says limiting resource at its original cost, doesn’t that mean the cost remains the same; then why in point 2, it is a maximum premium that the firm should be willing to pay. It seems the cost has changed.
In demonstration, there is an example in the textbook:
The original optimal contribution is $360, the revised optimal contribution after given the additional constraint unit is $366.67.
The increase of $6.67 in contribution is the shadow price for the constraint unit. This represents the premium that the firm would be willing to pay for each additional constraint unit. The current constraint cost is $10 per hour and therefore the maximum price that would be paid for the extra hour of constraint is $16.67.I do not understand what is this $16.67? Why adds up the increase premium will be the shadow price? Why cost will change, because in point 1, it says the cost is original?
Further, if the constraint is put in place, how can there be extra unit? If the contraint is, say, skilled worker’s labour hour, is this extra unit the over-time labour?
Thank you!
First, in real life there are not really any resources that are completely limited. You can always get more of something if you are prepared to pay enough.
So, using labour as an example, it may well be that we can only get (say) 1000 hours at normal rate per hour. However we can get more if we pay extra – i.e. if we pay overtime.Using the illustration you use in your question. If we have one extra hour of labour then because we can make more the total contribution increases by $6.67. However it will only increase by $6.67 if the contributions from the products remain the same. They will only stay the same if the cost of labour stays the same at $10 per hour.
But…..we will not be able to get more labour at $10 per hour. ‘Normal’ supply is limited and to get more we will have to pay extra (a premium – overtime). If we had to pay $11 for an extra hour (i.e. a premium of $1) would it be worth it? Yes it would because the total contribution would increase by $6.67 – $1.
We will be prepared to pay up to $6.67 extra for each extra hour i.e. up to $16.67. If we had to pay more than that then the total contribution would decrease.Hope that makes sense.
It might help to watch my free lecture on linear programming.- Topics: 43
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Hi Mr Moffat,
I get it now. Thank you!
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