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Respond to the question: sign of Lagrange multipliers in multi ta?

08/16/2004 12:16 AM by Laurent Franckx; sign of Lagrange multipliers in multi task moral hazard problems

In a one task moral hazard, it has been shown repeatedly that the Lagrange mulitplier linked to the IC constraint is positive. The interpretation of this sign is clear to me.

Suppose however if have now a multi-task problem and that I have shown that the Lagrange multipliers are all positive. What does this imply?

To be more formal, my problem is the following. Suppose that the FOC of the moral hazrd problem is given by B' + A' x = 0, where B' is the colum vector with the derivatives of the objective function, A' is the matrix with the derivative of the n constraints, and x is the colum vector with the n Lagrange multipliers. I have shown that in the problem I consider all elements of x are non-negative. A' is negative definite (otherwise, the SOC for the agents are not-fulfilled). Does this imply anything at all on the sign of B'?

From mathematics at least I see no immediate implications. [Manage messages]