“…As the income is strictly increasing with 𝑟 𝑚 * and the income is negative for low 𝑟 𝑚 , there should exist a unique 𝑟 𝑚 * that satisfies the above equations, and the large bank will thus charge this loan rate as the equilibrium rate (Randl et al, 2023;Repullo and Suarez, 2013). Regarding the equilibrium choice for the capital of the large bank, we have Proposition 1:…”