In a small city, there are two companies that use airwaves to broadcast: a cellphone company (Sprint), and a local radio station (KPOW). The cell tower has a strong enough signal that it does not receive interference from the radio station, but the radio station gets interference from the cell tower. The profit functions for the two firms are as follows (C denotes the number of cellphones operating in the city): Pie_Sprint (C) = 300,000 + 1,000C – 0.5C^2 Pie_KPOW (C) = 800,000 – 600C Derive the functions representing the marginal benefit of another cellphone user to Sprint and the marginal cost ofa cellphone user to KPOW. Plot them on a graph. Suppose that the city council decides to support local business and gives the rights of airwaves to KPOW. Now, KPOW can sue for interference, unless the two parties come to an alternative agreement. Assume that KPOW has all the bargaining power (This means that all gains from bargaining will go to KPOW). Indicate the number of cellphone users they will agree on in this scenario, and the profits of Sprint and KPOW both before and after a lump-sum payment from Sprint to KPOW. The FCC is selling the rights to use another wavelength that will not interfere with the radio station. Assuming the same conditions as in part b, how much will Sprint be willing to pay for the right to use this wavelength
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