Labour contracts signed at end of period t-1

General DSGE Modeling
1

Hi everyone
If the labour contract is signed at end of period t-1,And the wage income is paid at the same time, How do we define the utility function of the household for period t? In an article it is defined as follows:
image
And the budget constraint is defined as follows:
image
It is stated in this article:

image
image801×84 18.5 KB

Is this utility function correct?

Shouldn’t it be a function of N(t-1)?That is, as follows:
image

Because in period t; household executes the working hours that signed in period t-1

2

Which article is this? I find it indeed strange, because why would you incur disutility already today from agreeing to working a particular amount of hours tomorrow?

3

Thanks Professor
I attached the paper
This timing is due to non state contingent and costly state verification contract between the firm and the bank.
Nikolay Hristov.pdf (924.9 KB)

4

I understand that there must be a lag, but it nevertheless looks odd in the utility function.