Question

SS and LG are duopoly cell phone producers in S. Korea. Both firms are seeking to expand the 4GB cell phone market in Dubai. The managerial team is carefully studying the level of competition and the market demand for 4 GB cell phone. A study shows that the market demand curve for 4GB cell phone is P = 180 –Q. Also, they conclude that there are will be no competitors other than SS and LG, if they both enter, in Dubai at least for a few years. Both firms have similar MC: MC_SS=40 and MC_LG= 44. What are the Cournot competition quantities and profits? What would be the monopoly output and profit if only one firm enter?

The following questions are no need to answer for your ICA. You can practice the following questions after CH 10 discussion. However, my answer will show the following questions' answers as well.

What would be the likely outcome of the entry decision? Which firm would enter? or both? Show your work and game table in order to support your answer.

Answer 1

a)

Cournot Equilibrium:

P = 180 - Q

SS:

TRss = 180Qs - Qs^2 -QsQL

MR = 180 - 2Qs -QL

MC = 40

MR = MC

180 - 2Qs -QL = 40

140 -Ql = 2Qs

Qs = 70 - 0.5QL ...................(1)

LG:

TR = 180QL - QL^2 - QLQs

MR = 180 - 2QL - Qs

MC =44

180 - 2Ql - Qs = 44

136 - Qs = 2QL

QL = 68 -0.5Qs ...............(2)

Substituting equation 2 in 1:

Qs = 70 -0.5(68 -0.5Qs)

Qs = 70 -34 +0.25Qs

0.75Qs = 36

Qs = 36/0.75

= 48

QL = 68 -0.5(48)

= 44

P = 180 - (44+48)

= 88

Profit of LG : 88 *44 -44*44

= 1936

Profit of SS : 88*48 -48*40

= 2304

b)

Monopoly if only one firm enter:

P = 180 -Q

TR = 180Q - Q^2

MR = 180 - 2Q

MC =40

MR = MC

180 - 2Q = 40

140 = 2Q

Q = 70

P =180 - 70

= 110

Profit = 70*110 - 40*70

= 4900

if only second firm enter:

MR = 180 - 2Q

MC = 44

180 -2Q = 44

136 = 2Q

Q = 68

P = 180 - 68

= 112

Profit = 112*68 - 44*68

= 4624

Both firms are earning the positive profit in the both market setting. Thus, there is strong incentive to enter the market.