Microfinance Banks and Household Access to Finance

of this extra interest in terms of extra benefits of having an account with a retail bank due tobroader services.In our model decisions of banks and households take place in three steps: First, banksdecide simultaneously whether to open a branch in a location. Second, households decidewhether to open an account at one of the bank branches in their location. Third, householdswith bank accounts decide on the share of their assets to deposit in their account. In thefollowing we solve the model by backward induction.Household deposit decisionsSuppose a household has opened an account at a bank j. The household then chooses an*optimal share α ∈ [0,1] so as to maximize the net benefits from an account at bank j:j[2] R ⋅α⋅A −c ⋅( t⋅A −(1 −α) ⋅A)−ϕj i i i i jThe first term in equation [2] represents the gross benefits from the account, the secondterm represents the incurred transaction costs due to not holding cash and the third term thetotal costs of opening the account. For simplicity we have assumed linearity of costs andbenefits of depositing money. As a consequence a household will either deposit all assets**( α = 1) if Rj ≥ cior not deposit anything ( α = 0 ) if Rj < ci.We assume that the transaction costs of households are distributed so that some householdshave no transaction costs ( c = 0 ). These are households which live close to the economic hubof the region where a bank would be located. The rest of the households have prohibitivelyhigh transaction costs as they live far away from the economic hub of the region. Forreasonable levels of interest rates they will not open an account: c> R1,R2. Given theseassumptions, within any region only households which live close to the economic hub willconsider opening an account. Households that do open an account will deposit their entireassets in the account.7