We develop a measure to capture an audit firm's competitive position in a local audit market based on the transaction costs of changing audit firms included in DeAngelo's (1981) multi-period audit pricing model. Our competition measure reflects the size difference between the largest audit firm in a market specified by client industry at the city level and the other audit firms operating in that market. We find that audit fees of a client decrease as this size difference increases. This result suggests that smaller audit firms charge lower audit fees because of their competitive disadvantage to the local largest firm.