Coke and Pepsi are two big firms competing in a beverage mar

Coke and Pepsi are two big firms competing in a beverage market. Since Coke and Pepsi are substitute goods, the demand for Coke increases as the price of Pepsi increases and the demand for Pepsi increases as the price of Coke increases. As a result, their demand curves are given by: Ppepsi QCoke100 Pcoke + Pcoke QPepsi100 PPepsi + The total cost of producing either Coke or Pepsi is given by the equation TC = 20q (a) What are Coke and Pepsi\'s profits when they both set the price equal to $80? Show how you found your answer. (1/2 point) (b) What are Coke and Pepsi\'s profits when they both set the price equal to $100? (1/2 point) (c) What are Coke and Pepsi\'s profits when Coke charges $80 and Pepsi charges $100 for its product? (1/2 point) (d) Fill in the payoffs for the reduced form matrix representation of this game. What is the equilib- rium? (1/2 point) Pepsi Pepsi80 Coke,11 Pepsi)- 80 PPepsi 100 oke IPepsi) PCoke80 Coke lCoke, IIPepsi okeIPepsi) PCoke 100

Solution

Solution: a) Ppepsi = Pcoke = $80

Then, according to the question, Qcoke = 100 - 80 + 80/2 = 60

Since, Pepsi has similar demand curve, and the prices charged by both is same, Qpepsi = 60

Since, quantities are same and their total cost functions are same TC(q) = 20q, their total cost is same = 20*60 = $1200

Thus, Profit(pepsi) = Profit(coke) = P*Q - TC(Q)

= 80*60 - 1200 = $3,600

b) Ppepsi = Pcoke = $100

Then, Qcoke = Qpepsi = 100 - 100 +100/2 = 50

TCpepsi = TCcoke = 20*50 = $1,000

So, Profit(coke) = Profit(pepsi) = 100*50 - 1000 = $4,000

c) Ppepsi = $100, Pcoke = $80

So, Qcoke = 100 - 80 + (100/2) = 70

Qpepsi = 100 - 100 + (80/2) = 40

TC(coke) = 20*70 = $1,400 ; TC(pepsi) = 20*40 = $800

Profit(coke) = Pcoke*Qcoke - TC(coke)

= 80*70 - 1400 = $4,200

Profit(pepsi) = Ppepsi*Qpepsi - TC(pepsi)

= 100*40 - 800 = $3,200

d) From all above parts, we can fill for the payoffs as follows (NOTE: I have written payoffs as (Profit(coke), Profit(pepsi)), just as asked in the question)

Pcoke = Ppepsi = $80 : (3600,3600)

Pcoke = Ppepsi = $100 : (4000,4000)

Pcoke = $80, Ppepsi = $100 : (4200,3200)

Pcoke = $100, Ppepsi = $80 : (3200,4200)

We don\'t need to solve for the last one as both of their demand fuctions and total cost functions are similar; if you wish to verify you may solve it entirely like done in part c) of the question.

Hope you find the answer helpful. Thank you!