Question

The Department of Justice (DOJ) is charged with overseeing mergers in the United States to determine if they are in the public interest. A merger is considered in the public interest if consumers’ surplus does not fall as a result of the merger. The DOJ is currently deciding whether to allow the pending merger between AT&T and Sprint to proceed. 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.

1. Suppose that the long-distance market is a monopoly following the merger between AT&T and Sprint and that x = 5/4. Assume that s remains constant at 12. Should the DOJ allow this merger to proceed? Provide a careful economic analysis in support of your recommendation. (20)
2. 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? (15)

3. 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. (20)

Answer 1

A) Initial demand:Q=28-2p+12=40-2p

P=20-0.5q

Q=K+0.5L

So inputs are perfect substitues

Per dollar Marginal product of k=1/10

Per dollar marginal product of L=0.5/5=1/10

So both input are same per dollar productive,so

TC=10q

MC=10

Perfect competition equilibrium,

P=MC

20-0.5q=10

Q=10/0.5=20

P=20-0.5*20=10

CONSUMERs surplus=1/2*20*(20-10)=10*10=100

After merger,

Demand:P=20-0.5p

MR=20-p

Q=1.25[k+0.5L]=1.25K+0.625L

Q=1.25K

K=Q/1.25

TC=10*Q/1.25=8Q

MC=8

Monopoly equilibrium,at MR=MC

20-q=8

Q=12

P=20-0.5*12=14

CONSUMERs surplus=1/2*12*(20-14)=6*6=36

So merger lead to decrease in consumer surplus,so DOP shouldn't approve merge.

B) Demand:Q=28-2p+s

P=14+0.5s-0.5q

MC=8

Perfect competition equilibrium,

14+0.5s-0.5q=8

Q=12+s

P=MC=8

CONSUMERs surplus=1/2*(12+s)*(20-8)=6*(12+s)

So required CS to approve merge=100

100=72+6s

s=28/6=14/3

So s=14/3, DOP will approve merge.

C)TC=(10Q)/x

MC=10/x

Demand:Q=28-2p+8=36-2p

P=18-0.5q

Perfect competition equilibrium,

18-0.5q=10/x

Q=36-20/x

P=MC=10/x

CONSUMERs surplus=1/2*(36-20/x)*(18-10/x)=(18-10/x)*(18-10/x)={18-10/x)^2

Required CS, to approve merge=100

100=(18-10/x)^2

10=(18-10/x)

-8=-10/x

x=10/8=1.125

S