Consider the choices available to a shopper driving to a city and trying to park downtown. One option, typical to many cities, is to follow the signposts to an off-street parking facility, which is often privately operated. Another option is to search for an on-street spot. If this proves unsuccessful, it is always possible to return to the off-street facility. We formalise such a setting and examine optimal on-street parking policy in the presence of an off-street market. Not surprisingly, the amount of socially-wasteful searching behaviour is shown to depend on the prices of both the off- and on-street market. If the off-street market is run competitively, optimal on-street policy reduces to a simple and attractive rule: set the on-street price equal to the resource cost of off-street parking supply. Other pricing rules result in either excessive searching behaviour or excessive off-street investment costs. Time restrictions - a common alternative to on-street fees - are also shown to be inefficient. In practice, however, off-street markets are unlikely to be competitive. We examine the case of a single off-street supplier playing as a Stackelberg follower to the government regulated on-street market. Based on a numerical example (calibrated to London), optimal on-street policy is shown to either involve setting a relatively high on-street price, such that the monopolist is induced to undercut and gain the entire parking demand, or setting a relatively low price, while the monopolist maximises profit on the residual demand curve. Which strategy is optimal is shown to be parameter dependent.
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