On bribing and balking in a simple queuing model of resource allocation

We analyze two versions of a simple queuing model of resource allocation in which an impatient citizen of a transition economy or a developing country wishes to purchase a scarce good, namely, bread. In the first version of the model, our citizen must pay a bribe to obtain bread immediately from a government shop. In the second version of the model, when the government shop is too crowded, our citizen refuses to join the crowd. In other words, he balks and goes instead to a private shop to purchase bread. In this setting, we study three questions from the standpoint of resource allocation. First, in the presence of bribery, what is the expected monetary benefit per citizen to a corrupt government official? Second, in the presence of balking, what proportion of all citizens eventually get bread? Finally, and once again in the presence of balking, what is the expected amount of time a citizen spends waiting to get bread?