Question

Consider an industry with three firms, with demand curves as given below.

Q₁ = 140-12P₁+3P₂+3P₃

Q₂= 130-10P₂+3P₁+2P₃

Q₃ = 135-9P₃+2P₁+2P₂.

Each firm has a marginal cost of 4.

1. Calculate the pre-merger prices.

2. Assume that firms 1 and 2 merge, to form a new firm “M”. Assume also that the merger allows M to reduce marginal cost from 4 to 2. Firm 3’s marginal cost remains at 4. What are the new equilibrium prices?

3. Calculate the UPPIs for brands 1 and 2.

Answer 1

1. Pre-merger costs.

Each firm will endeavor to expand their benefit for example MR=MC for each firm will decide the balance prices.For each firm MC=4

For firm 1,

TR=P1 × Q1= 140P1-12(P1​​​​​) ​​​​​2​​​​​​+3P2P1​​​​​​+3P3​​​​​P1

MR=dTR/dP1​​​​​​= 140-24P1​​​​​​+3P2​​​​​​+3P3=4(MC)

P1​​​​​​=(136+3P2​​​​​​+3P3​​​​​)/24 condition (1)

For firm 2,

TR=P2 ×Q2​​​​​​= 130P2​​​​​​-10(P2​​​​​) 2 +3P1​​​​​P2+2P3P2

MR=MC

P2​​​​​​=(126+3P1​​​​​​+2P3​​​​​)/20 condition (2)

For firm 3,

TR=P3​​​​​​×Q3= 135P3​​​​​​-9(P3​​​​​) 2+ 2P1P3​​​​​​+2P2P3

MR=MC

P3=(131+2P2+2P1​​​​​)/18 condition (3)

Illuminating for condition 1,2,&3,we get balance costs as pursues:

P1​​​​​​=7.84

P2​​​​​​=8.38

P3​​​​​​= 9.08

2. At the point when firms 1&2 converge, to shape firm M then their absolute yield, Q=Q1​​​​​​+Q2​​​​​​ and costs P1​​​​​​=P2​​​​​​=P

In this manner, for firm M,

Q=(140-12P+3P+3P3​​​​​) +(130-10P+3P+2P3​​​​​) = 270-16P+5P3

MC=2

TR= P × Q = 270P-16P2+5P3P

MR= 270 - 32P +5P3​​​​​​= 2(MC)

P= (268 + 5P3​​​​​​​​​​​​)/32 equatiin (4)

For firm 3,

TR=P3 × Q3​​​​​​= 135P3​​​​​​-9(P3​​​​​) 2​​​​​​+4PP3

MR=MC

135-18P3​​​​​​+4P = 4

P3​​​​​​=(131+4P)/18 condition (5)

Comprehending for conditions 4&5,we get, new harmony costs,

P= 9.85

P3=9.46