Paying by the Hour: Are Wages the Cost of Waiting?
Consumers dislike waiting. In modeling consumer behavior for services, this obvious fact is often captured by assuming that consumers incur a cost per unit time spent waiting. A natural question that arises is: where does this waiting cost come from? Is it merely foregone earnings or something different? In this paper, we address these question by assuming an agent faces a utility maximization problem that focuses on time allocation subject to time and budget constraints. The cost of waiting is then the minimum monetary compensation required to keep the agents utility level constant as the agents loses time waiting. We show that the relationship between the cost of waiting and wages depends very much on the agents compensation structure. We prove that agents cost of waiting is equal to her hourly wage only when the compensation structure is linear. The equivalence between hourly wages and waiting costs breaks down when a more general compensation structures are introduced such as fixed shifts or even piece-wise linear wages. Furthermore, we show that hourly wages can overestimate or underestimate the cost of waiting in the presence of such non-linear compensation structure. These results are robust to several modifications of our basic model.