Is it possible that Tarun's paper had a mistake which you copied here in your image for interest rates? From looking at the compound whitepaper and this blog (https://ian.pw/posts/2020-12-20-understanding-compound-protocols-interest-rates), it seems like the borrow rate is just (beta_0 + beta_1*U)... and it is the supply/lending rate that is U*(beta_0 + beta_1*U), forgetting about protocol reserve fees here. Could you please confirm that this is correct, otherwise I'm really confused.
Spoke with Tarun, he confirmed this: "Actually, seems like our B_t should be B_0 + b_1 * U_t and l_t should be U_t * (1 - r_0) * B_t;" (where r_0 is the reserve factor).
Is it possible that Tarun's paper had a mistake which you copied here in your image for interest rates? From looking at the compound whitepaper and this blog (https://ian.pw/posts/2020-12-20-understanding-compound-protocols-interest-rates), it seems like the borrow rate is just (beta_0 + beta_1*U)... and it is the supply/lending rate that is U*(beta_0 + beta_1*U), forgetting about protocol reserve fees here. Could you please confirm that this is correct, otherwise I'm really confused.
Spoke with Tarun, he confirmed this: "Actually, seems like our B_t should be B_0 + b_1 * U_t and l_t should be U_t * (1 - r_0) * B_t;" (where r_0 is the reserve factor).