If I have an adjustment cost in the model, say costly adjustment for banks to change their interest rate and I subtract the cost from the bank’s profit (profit equation included in the model), do I also need to add the adjustment cost to the market clearing? i.e. Y_t = C_t+I_t + ADJCOST_t or not?
That depends on your assumptions. But usually, you assume that adjustment costs consume actual resources. What you refer to as the market clearing is actually the resource constraint. You could derive it from the budget constraint and market clearing conditions. If you plugged in for profits in the budget constraint, you would see that adjustment costs show up.
Thank you very much for your clarification. It was really helpful.