Sprint and T-Mobile compete against each other offering wireless service to US customers. The monthly demand...

 

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Sprint and T-Mobile compete against each other offering wireless service to US customers. The monthly demand curves (with quantities in millions) are Qs 37.630.479Ps+0.158 Pt Qt = 41.81 0.498Pt+ 0.191 Ps. While most of the cost associated with offering wireless service is fixed, each firm faces a $2 marginal cost per customer (coming mostly from the additional demands on customer support functions). (a) Solve for the Betrand Nash equilibrium prices, equilibrium monthly quantities, and equilibrium monthly profits (not including fixed costs) for each firm. (b) Suppose the two firms merge to form a single firm known as T-Sprint. Suppose T-Sprint continues to offer separate plans and charge separate prices for former Sprint customers and former T-Mobile customers. Assuming T-Sprint wants to maximize its profits, how should it adjust its former-Sprint- customer price (Ps) and its former-T-Mobile-customer price (Pt). How many former-Sprint and former-T-Mobile customers will it have, and what will the combined firm's monthly profit (not including fixed cost) be? (c) Now suppose the firms have not yet merged, and let's think about the negotiations surrounding a potential merger. Suppose that Sprint is proposing to buy T-Mobile. If the deal goes through, then the combined firm will earn the monthly profit from (b) for the next twelve months. (To keep things simple, let's ignore any cash flows coming from time periods more than a year out.) If the deal doesn't go through, Sprint will earn its monthly profit from (a) for next twelve months while T-Mobile will earn its monthly profit from (a) for next twelve months. (Further, you can ignore any time-value-of-money considerations for this problem.) What is the most that Sprint would pay for T-Mobile? What is the least that T-Mobile would accept? What accounts for the gap? Sprint and T-Mobile compete against each other offering wireless service to US customers. The monthly demand curves (with quantities in millions) are Qs 37.630.479Ps+0.158 Pt Qt = 41.81 0.498Pt+ 0.191 Ps. While most of the cost associated with offering wireless service is fixed, each firm faces a $2 marginal cost per customer (coming mostly from the additional demands on customer support functions). (a) Solve for the Betrand Nash equilibrium prices, equilibrium monthly quantities, and equilibrium monthly profits (not including fixed costs) for each firm. (b) Suppose the two firms merge to form a single firm known as T-Sprint. Suppose T-Sprint continues to offer separate plans and charge separate prices for former Sprint customers and former T-Mobile customers. Assuming T-Sprint wants to maximize its profits, how should it adjust its former-Sprint- customer price (Ps) and its former-T-Mobile-customer price (Pt). How many former-Sprint and former-T-Mobile customers will it have, and what will the combined firm's monthly profit (not including fixed cost) be? (c) Now suppose the firms have not yet merged, and let's think about the negotiations surrounding a potential merger. Suppose that Sprint is proposing to buy T-Mobile. If the deal goes through, then the combined firm will earn the monthly profit from (b) for the next twelve months. (To keep things simple, let's ignore any cash flows coming from time periods more than a year out.) If the deal doesn't go through, Sprint will earn its monthly profit from (a) for next twelve months while T-Mobile will earn its monthly profit from (a) for next twelve months. (Further, you can ignore any time-value-of-money considerations for this problem.) What is the most that Sprint would pay for T-Mobile? What is the least that T-Mobile would accept? What accounts for the gap?

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