The correct sign in the Lagrangian before the household's stochastic discount factor

Hello!

I have a question about expanding brackets in the Lagrangian from the producer’s problem. When we derive the expressions for period t+1, what sign should we place in front of the household’s stochastic discount factor – plus or minus?

I’m attaching a photo for reference.

Thank you very much!


I am not sure I understand the problem. There is a large sum sign around the bracket, which is a summing up of terms that enter with a plus sign in front of whatever sign you have in the bracket terms.

Professor, you are absolutely right. However, I happened to come across a minus sign in front of the profit expression for the t+1 period in a researcher’s work. It might have been a typo, or perhaps there is some underlying intuition behind it.

If there is an unaccounted minus, it’s usually a typo.

Thank you very much. I appreciate it.