Shadow Price/dual price — OpenTuition Forums

MMeerza5y ago

This is a query... Good morning, Referring to lecture 4 of chapter 6, increasing the Materials to 81kg produced an additional contribution of $1.125, defined as the shadow price. This is well understood. Nevertheless, increasing the production capacity, which is the reason of acquiring more materials, shall be associated with an increase into other variable costs/inputs including the labor hours but the increase in the raw materials resulted into a reduction from 30 hrs to 29.25 hrs. This is a bit strange. Please correct me as I might be wrong, In order to maintain constant slopes for both constraints, changes into variable inputs of either constraints should be in proportion to the defining equations of each. Your comments are highly appreciated. Thanks and regards, Meerza

John MoffatTutor5y ago#1

When calculating the shadow price of a limited resource we only consider the possibility of getting more of that one limited resources. We assume that the limits on all the other resources remains unchanged. Therefore it is only the contraint line for that one resource that will move, all the other constraint lines remain unchanged. Having more materials will mean we make more of one chair and less of the other, but the total labour being used will not change. All the matters is whether as a result we can make a higher contribution.

MMeerza5y ago#2

Thanks Mr. John... I assume the reduction in the hours of manpower (0.75 hr) subsequent to increasing RAM to produce additional 1 unit of E is offset by an equivalent increase to produce S. Technically, it is to maintain the max hrs of labor, as being a constraint. Otherwise, increment of contribution for $1.125 is not viable for comparison because the slope of Labor Hrs will not remain the same. Your further eleboration is appreciated. Thanks,

John MoffatTutor5y ago#3

The slope of the labour line will not change because the labour constraint remains the same. The hours of labour per unit remain unchanged as to the kg of material used per unit. The only change is that there is 1 extra kg of material. The object is not to maintain the maximum hours of labour. The object is to maximise the contribution which we do by moving out the contribution line as far as possible from the origin. The optimum mix of chairs is where the new materials line crosses the labour line. I do suggest that you watch my free lecture again.

MMeerza5y ago#4

Thank you... this is to the point.

John MoffatTutor5y ago#5

You are welcome :-)

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