Search model: debit card or cash

Abstract

This model addresses a strategic complementarity problem with a search-theoretic model to analyze two payment systems: cash and debit cards. The trade-off between cash and debit cards is incorporated such that the sellers incur in a cost of having a point of sale terminal and buyers receive an interest rate for having a debit card. From four pure-strategy equilibria, two efficient equilibria where trade exist are found: where every agent has a debit card and a terminal, and where cash is used and nobody holds a terminal. This model’s result shows that there cannot be a growth of debit cards without a growth in the number of terminals. This is what we observe in the debit card and terminal growth in Mexico. Also, we find that as the cost of debit card holding decreases a debit card equilibrium is more feasible: as the cost of the terminal decreases debit cards provide enough liquidity to the economy. Finally, conditions over the discount factor showed that agents need to be more patient to achieve the cash equilibrium and need to be more impatient in the card equilibrium.