Answer to Question #118055 in Microeconomics for Rosi

Question

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.
c) Derive the cost function for AT&T/Sprint post-merger for any value of x. Suppose that service quality declines by one-third to s = 8 following the merger. In addition, assume that the market for long-distance telephone service remains perfectly competitive following the merger. Determine the values of x for which the DOJ will approve this merger.

Answer 1

$$Q=28-2p+s$$

$$p=13.75$$

$$Q=x(10+\frac{5}{2})$$

$$Q=12.5x$$

$$12.5x=28-2\times13.75+8$$

$$12.5x=8.5$$

$$x=\frac{17}{25}$$