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1. Pricing Network Services (30 points) a Consider a monopolistic network provider (e.g., an ISP) who wishes to find the revenue maximizing price for the service. There are N potential consumers of the service with a value of consumption that uniformly varies between [a, b]. For any given price, find the point between [a, b] that represents the utility of the consumer who is indifferent between buying and not buying. Then proceed as we discussed in class. The network has a fixed and variable delay. The fixed delay (or latency), denoted by L, does not depend on the number of users, i.e., this amount of delay is incurred regardless of the number of users. The variable component of the delay (or the congestion delay) is linear in the number of users and is given by a congestion constant (), times the number of users (9). The disutility of delay with n users is therefore given by L + In a) Show that the number of users that will consume the service (n) at a given price (p) is given by: (10 points) 72 = N(b-p-1) (b-a)+k-N b) Show that the revenue generated by the provider is given by: (5 points) ( 2 N(bp-p? - Lp) Revenue (R) = (b-a) +k-N c) Assuming the following, N= 10000; a = 10,b= 100, L = 20. k= 2, find the maximizing price. (10 points) revenue d) Does the revenue maximizing price depend on the size of the market (N)? Why or Why not? (5 points) 1. Pricing Network Services (30 points) a Consider a monopolistic network provider (e.g., an ISP) who wishes to find the revenue maximizing price for the service. There are N potential consumers of the service with a value of consumption that uniformly varies between [a, b]. For any given price, find the point between [a, b] that represents the utility of the consumer who is indifferent between buying and not buying. Then proceed as we discussed in class. The network has a fixed and variable delay. The fixed delay (or latency), denoted by L, does not depend on the number of users, i.e., this amount of delay is incurred regardless of the number of users. The variable component of the delay (or the congestion delay) is linear in the number of users and is given by a congestion constant (), times the number of users (9). The disutility of delay with n users is therefore given by L + In a) Show that the number of users that will consume the service (n) at a given price (p) is given by: (10 points) 72 = N(b-p-1) (b-a)+k-N b) Show that the revenue generated by the provider is given by: (5 points) ( 2 N(bp-p? - Lp) Revenue (R) = (b-a) +k-N c) Assuming the following, N= 10000; a = 10,b= 100, L = 20. k= 2, find the maximizing price. (10 points) revenue d) Does the revenue maximizing price depend on the size of the market (N)? Why or Why not? (5 points)
