Question

Over the years, the market for instant noodles in Indonesia has developed into a duopoly market where two companies Indofood (Indomie – Firm 1) and Wings Food (Mie Sedaap – Firm 2) are competing. Nevertheless, as the first entrant, Indomie has created advantages which rendered it as the market leader. The inverse demand function for the market is P = 100 – 0.75(Q1+Q2), and the cost function for both Indomie and Mie Sedaap is identical and given by Ci(Qi) = 4Qi.

a. Under the above conditions, what is the market price for the instant noodles in Indonesia?

b. What are the quantity produced by each Indofood and Wings Food, and the total production in the market?

c. What is the profit for Indofood and Wings Food?

d. What would be the market price for instant noodles if there is no market leader and each firm makes an output decision under the belief that is rival will hold its output constant when the other changes its output level?

Answer 1

Over the years, the market for instant noodles in Indonesia has developed into a duopoly market where two companies Indofood (Indomie – Firm 1) and Wings Food (Mie Sedaap – Firm 2) are competing.

Now, nevertheless, as the first entrant, Indomie has created advantages which rendered it as the market leader.

The inverse market demand function is

P = 100 - 0.75.(Q1+Q2)

Where, Q1= Production of Indofood and Q2= Production of Wings Food.

Where, Q=Q1+Q2 is the total output.

Now, Firm 1 (Indomie) acts as the leader in the market. Hence, Indomie puts Firm 2's (Mie Sedaap) Reaction Function in his maximization problem.

Hence, for Firm 2 (Mie Sedaap),

Total Revenue is

TR2 = P.Q2 = [100 - 0.75.(Q1+Q2)].Q2

or,

Hence, Marginal Revenue is

MR2 = dTR2/dQ2 = 100 - 1.5Q2 - 0.75.Q1........(1)

Now, Total Cost of Firm 2 is

TC2 = 4.Q2

Hence, Marginal Cost of Firm 2 is

MC2 = dTC2/dQ2 = 4.........(2)

Hence, at profit maximizing level of production Firm 2 will set

MR2 = MC2

or, 100 - 0.75Q1 - 1.5Q2 = 4

or, Q2 = 64 - 0.5.Q1.........RF2

This is the reaction function of Firm 2. Remember this function, as we will use it in part d.

Now, for Firm 1 (Indomie)

Total Revenue is

TR1 = P.Q1 = (100 - 0.75.(Q1+Q2)].Q1

Now, Firm 1 will put Firm 2's Reaction Function in his revenue function. Hence, we put

Q2 = 64 - 0.5.Q1

TR1 = [100 - 0.75.(Q1 + 64 - 0.5Q1)].Q1

or, TR1 = [100 - 48 - 0.375Q1].Q1

or,

Hence, Marginal Cost of Firm 1 is

MR1 = dTR1/dQ1 = 64 - 0.75.Q1.........(3)

And, Total Cost of Firm 1 is

TC1 = 4.Q1

Hence, Marginal Cost of Firm 1 is

MC1 = dTC1/dQ1 = 4

Hence, at profit maximizing level, Firm 1 sets

MR1 = MC1

or, 64 - 0.75.Q1 = 4

or, Q1* = 80

putting this in the Reaction Function of Firm 2 we get

Q2* = 64 - 0.5.Q1 = 64 - 0.5×80

or, Q2* = 24

Hence, Total Production is

Q* = Q1*+Q2* = 80+24 = 104

Hence, Price of instant noodles in Indonesia is

P* = 100 - 0.75(Q1*+Q2*)

or, P* = 100 - 0.75.(80 + 24)

or, P* =22

Answer of (a): The price of instant noodles in Indonesia is P*=22.

Answer of (b): Quantity produced by Indofood is Q1*=80.

Quantity produced by Wings Food is Q2*=24.

Total production in the market is Q*=104.

Now, for Indofood,

Toral Revenue is

TR1 = P*.Q1* = 22×80

or, TR1 = 1760

And, Total Cost is

TC1 = 4.Q1 = 4×80

or, TC1 = 320

Hence, Profit of Indofood is

π1 = TR1 - TC1 = 1760 - 320

or, π1 = 1440

Similarly, for Wings food

Total Revenue is

TR2 = P*.Q2* = 22×24

or, TR2 = 528

And, Total Cost is

TC2 = 4.Q2* = 4×24

or, TC2 = 96

Hence, Profit of Wings Food is

π2 = TR2 - TC2 = 528 - 96

or, π2 = 432

Answer of (c): Profit for Indofood is π1=1440

and profit for Wings Food is π2=432.

If there is no market leader, then its a simple Cournot duopoly game and each firm makes an output decision under the belief that is rival will hold its output constant when the other changes its output level.

Hence, we got Reaction Function of Firm 2 from above i.e.

Q2 = 64 - 0.5.Q1.........RF2

Now, for Firm 1,

Total Revenue is

TR1 = P.Q1 = [100 - 0.75(Q1+Q2)].Q1

or,

Hence Marginal Revenue of Firm 1 is

MR1 = dTR1/dQ1 = 100 - 1.5Q1 - 0.75Q2........(4)

And, Total Cost of Firm 1 is

TC1 = 4.Q1

Hence, Marginal Cost of Firm 1 is

MC1 = dTC1/dQ1 = 4..........(5)

Hence, At profit maximizing situation, Firm 1 will set

MR1 = MC1

or, 100 - 1.5Q1 - 0.75Q2 = 4

or, Q1 = 64 - 0.5Q2.........RF2

This is the Reaction Function of Firm 1.

Now, we solve RF1 and RF2 to get Q1 and Q2.

Hence, By solving RF1 and RF2 we get

Q1 = Q2 = 42.67

Hence, the market price for instant noodles will be

P = 100 - 0.75.(Q1+Q2)

or, P = 100 - 0.75.(42.67+42.67)

or, P = 35.995 ~ 36

Answer of (d): If there is no market leader, then the market price of instant noodles is P=36.

Hope the solutions are clear to you my friend.