Darracq Paries et al. (2011) vs. Darracq Paries et al. (2016)

General DSGE Modeling
1
  1. I want to introduce banking risk of Darracq Paries et al. (2016) in Darracq Paries et al. (2011), but I only find corporate risk and there is not default in representative family. So I am thinking that interest rate received from the loans to the retail lending bank could be same both the to entrepreneurs and households.

That is, instead of equation 7 of Darracq Paries et al. (2016)

OP(w) = wRL-RdD+PiD+PiB

could I use

OP(w) = wR(L1+L2)-RdD+PiD+PiB ?

where L1 is for entrepreneurs and L2 for households

  1. Also, section wholesale branch of Darracq Paries et al. (2011), 3.4.1, would be replaced with section of bankers of Darracq Paries et al. (2016), 4.2.3. And section of commercial lending branches of Darracq Paries et al. (2011), would be replaced with section of loan officers of Darracq Paries et al. (2016), 4.2.5.

Will this implie that the spread between the lending rate in the optimal credit contract and the financing rate for the commercial lending banks would be then zero?

2

Unfortunately, your question is very specifically tied to papers I (and I guess most other users) have not read. Only referring to equations and given setups is not helpful for conveying the economic logic behind the questions. Maybe you could phrase your question in intuitive economic terms.