Abstract
This study proves mathematically that in any bank if the growth rate of sales is higher than the absolute growth rate of bank's lending rate, then bank's profits will not decrease. This mathematical expression can be considered as the condition for keeping a bank profitable. An econometric analysis using panel data from the Western European banking sector supports our afore-mentioned mathematical theory.
Notes
This implies that one should rather make simulations for various arbitrarily predefined κ values. In doing so, it is found that as restrictions and regulations on banking sector are released (as κ in the present model exceeds the critical value of 0.99) then the proposed mathematical theorem holds. Specifically, it is found that as the value of κ increases, the coefficient of relative growth becomes significant.