Pricing with Network Effects This problem set explores what happens to pricing when we add network effects, which are a sp You've invented # 30 fox machine, This cool technology is almost like a Stor Trek teleporter. You c machine, which creates an exact copy at another 30 fax machine. It is so valuable that as more p valuable, and the price any given user is willing to pay increases in turn. Consider a scenario in which there are 12 possible users, who each value the fax machine at I'm (from 1 to 12), and a is the number of other purchasing users. So, if no one buys the 30 fax machi However, as soon as one person buys the device, then the 12 possible users begin to value the p 2 people purchase, the 12 possible users' valuations Increase to 2, 4, .. 24, and soon, Because yo initial number of users is zero, but you want to price it so as to encourage purchase and ultimate look to maximize your profits, it is important to keep in mind that it costs you $2 to make each Clarifying assumptions. Three points will help you think about the problem: 1. Assume that only one user can adopt a particular machine, Le., users cannot share e mach 2. Assume that the marginal buyer does purchase, meaning that if the price is $3, then some will purchase 3. Machines are manufactured just-in-time; there is no inventory beyond that demanded by based on an increase in the number of units demanded. 4. Consumers are forward-looking, with respect to one other consumer, Le, they consider we