Question

to each incoming customer is assessed. Given the price (and delay) some customers do join in the queue, others walk away. Let us denote by λ(p) < 1 the effective rate of arrivals. The delay in the queue is D(λ(p)) 2A(p). A customer that opts-in has a surplus u-p-D(A(p)) > 0 u where v is the customer willingness to pay. a. Assuming t is uniformly distributed in 0 1 find a closed-form expression for λ(p) (hint: What condition holds true for the marginal customer if the service fee is p?) b. Assuming that the cost of providing service is zero, find the optimal monopoly price. c. (bonus) What is the socially optimal service fee?