# You asked ... could you explain the concept of shadow prices.

With shadow prices you are trying to work out how much better off you would be as a result of having one more unit of a particular scarce resource (materials or labour, for example). Having drawn a linear programming (LP) graph you will have identified the optimum production mix as the intersection of two or more constraint lines within the feasible region.

Take a scenario where labour and material are the limiting factors in a problem and the optimum production plan is where the company should make 1,000 units of X and 500 units of Y, leading to a contribution of [pounds sterling]5,000.

You can identify that labour is one of these limiting factors and currently the labour constraint is given by the equation 3X + 4Y = 2,000 (meaning you only had 2,000 hours of labour available and each unit of X uses 3 hours and Y uses 4 hours). To find out the shadow price of the labour you would now work out what the new optimum production plan and contribution would be if you had one more hour of labour available (meaning you now set 3X + 4Y = 2,001) and solve usually using simultaneous equations.

Let's say that the new optimum contribution becomes [pounds sterling]5,020. This means that as a result of having one more labour hour, our overall contribution has increased by [pounds sterling]20. The shadow price of labour is therefore [pounds sterling]20 (the maximum extra amount per hour that it may be worth paying for extra labour hours).

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