Question

The market demand for long-distance telephone service is given by Q = 28 – 2P + s, where Q is quantity demanded, P is price, and s is an index of service quality. The market served by these two long-distance carriers is currently competitive. In addition, both long distance carriers currently use the same technology for producing long-distance telephone service which is given by Q = K + 1/2L. AT&T CEO, Michael Armstrong, has told Wall Street analysts that the merger will result in efficiency gains. This implies that the production function for long-distance telephone service post-merger will be given by Q = x [K + 1/2L], where x > 1 is the productivity factor. Suppose that r = 10 and w = 5, and the pre-merger service quality index is s = 12
Continue to assume that x = 5/4, but the market for long-distance telephone service remains perfectly competitive following the merger. For what values of s will the DOJ approve this merger?

Answer 1

$$Q=10+\frac{5}{2}=12.5$$

$$12.5=28-2p+12$$

$$p=13.75$$

Since the merger should not affect the price of the service provided to the end customer, we get the following:

$$\frac{5}{4}\times12.5=28-2\times13.75+s$$

$$s=15.125$$