of service quality. Thus, for any price p, consumer usage decisions will result in an equilibrium level of service quality, that is, an equilibrium level of congestion represented by the waiting time W. The equilibrium amount of congestion equates demand for service D(p, W) with supply of service: The equilibrium amount of congestion depends on the price of network service and the amount of network service capacity, W* = W*(p,M). The equilibrium usage of the network is * = D(p, W*(p, u)). Therefore, congestion acts as another type of price by rationing demand. The solution is represented in Figure 3.12. Rationing usage by congestion is necessarily inefficient because consumers may prefer a somewhat higher price with less congestion. Consider the effects of network pricing on congestion. Differentiate the equation (39) with respect to price and substitute using equation (39) to obtain aw*(p,M) Dp(p,W*) Demand is downward sloping in price and decreasing in waiting time. So congestion is decreasing in the price per call: 9*****ap<0. There is no market-clearing price of capacity because of congestion effects. By specifying a desired quality of service, the price that allocates capacity can be Pricing Network Services D(p, WR) Figure 3.13. The price that rations network capacity is pR given an exogenously specified quality of service WR. determined. Suppose that a regulator specifies a maximum average waiting time, which sets a minimum quality of service level. The regulated quality level WR determines the available capacity by equation (38), Therefore, the price that rations capacity with quality of service WR is the price that equates demand to available capacity, D(p,WR) This is represented in Figure 3.13. This is equivalent to the capacity allocation model when there are no congestion effects. Thus, with a given minimum quality of service, the model of pricing with congestion effects corresponds to the basic problem of allocating scarce capacity that was discussed previously. The discussion of congestion thus far 