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information:
selling price $80
skilled labour-2 hours at $20/h ($40)
unskilled labour-1 hour at $10/h ($10)
material-3kg at $5/kg ($15)Profit per unit $15
shadow prices:
skilled labour $12/h
unskilled labour zero
material $3/kgassuming that the constraint cannot be relaxed, should the new product be manufactured?
Textbook Solution:
revised profit statement :
selling price $80
skilled labour-2 hours at $(20+12)/h ($64)
unskilled labour-1 hour at $10/h ($10)
material-3kg at $(5+3)/kg ($24)Profit per unit -$18
to incorporate the contribution lost elsewhere by reallocating scarce resources, the product is not viable
i would have said, Yes, it is profitable to produce the new product so go ahead.
Questions:
-the question said that the constraints (skilled labour and materials) could not be relaxed so why add the premium to these scarce resources in the revised profit statement?-is my understanding flawed?
-i understand relaxing constraints to mean:
a- buying more of the goods or services from outside
b- adding capacity or redesigning to use those already existing resouces more efficiently-the statement “to incorporate the contribution lost elsewhere by reallocating scarce resources, the product is not viable”…
-shadow prices are not contributions lost ELSEWHERE… would that not be opportunity cost instead? shadow prices are the premium that the firm should be willing to pay for 1 extra unit of constraint (due to the increase in contribution created by that extra 1 unit of constraint)
what did i miss in this topic?
I don’t know where you found this question – it is rather strange, although the answer is correct.
Just as the shadow price is the extra contribution that would be earned from one extra unit of the limited resource, it is also the contribution that would be lost by having one less unit of the limited resource.
Since the shadow cost of skilled labour is $12, then every hour taken for the new product would lose $12 contribution currently being earned and therefore the new product would have to earn at least $12 per hour for it to be viable. Similarly for materials.thanks
i am reading through the Kaplan Text (sept 2016-june 2017).
Chapter 4: page 138-139if i understand your reasoning then the keywords are
“assuming that the constraint cannot be relaxed, should the new product be manufactured?”
because otherwise,there would be no need
“to incorporate the contribution lost elsewhere by REALLOCATING scarce resources, the product is not viable”
since more labour can be hired and materials bought in
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