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

$Q = x [K + 1/2L],$

x > 1 is the productivity factor.

r = 10 

w = 5

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

$12.5=28-2p+12$

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