Suppose we have a duopoly in the production of mineral spring water. Each firm h

Question

Suppose we have a duopoly in the production of mineral spring water.  Each firm has the same
cost structure where MC(Q) = 10. The market demand for mineral spring water is given by:
P = 70 - Q/50
Each firm, wishing to maximize profits, assumes that the other firm will not change his
current level of production. What will be the final level of production for the market (after a
Cournot equilibrium is reached)? How much is produced by each firm? How much profit is
earned by each firm?

Suppose the two firms in the question above collude to maximize joint profits. What would the
equilibrium price and quantity be? How much profit is made in the industry and by each firm?
(You can assume that the two firms evenly divide production.) How do the profits earned in
the question above compare to those earned in this question ? What does this say about cartel behavior?

Explanation / Answer

cournot duopoly:

MC1 = 10, MC2 = 10

P= 70-(Q1+Q2)/50

Profit for firm 1:

MR=MC

Revenue R1 = 70Q1-(Q1+Q2)*Q1/50

MR1= 70-(Q2+2Q1)/50

MR1=MC1

70-(Q2+2Q1)/50=10

Q2+2Q1= 3000

similarly Q1+2Q2 = 3000

Q2= 1000, Q1=1000, P = 30

Profit for each firm = Revenue- cost = PQ1-MC*Q1 = 30000-10000=20000

Joint profit maximisation:

MR=MC

MR = 70-Q/25 = 10

Q = 1500, Q1= 750, Q2=750,

Price = 40

Profit1 = 45000/2= 22500

In cartel, firm are joint maximising the profit, as a result they are behaving like monopoly. therefore, market price, profit is higher and their joint production is less compare to cournot equilibrium.

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