Suppose that there are only two firms in the petroleum market Saudi Aramco (SA)

Question

Suppose that there are only two firms in the petroleum market Saudi Aramco (SA) and Kuwait Petroleum Corporation (KPC). They give you some information about the petroleum market and you have to answer the questions below.

# Demand Equation: P = 110 – Q

# For each firm marginal cost MC = $20.

# [Quantity of outcome (qSA), Price (pSA), Profit (SA)] , [Quantity of outcome (qKPC ), Price (pKPC), Profit ( KPC)].

# Q = qSA + qKPC

Required ( the Answer should be Computerized )

Suppose that one firm is expected to produce the same quantity in cartel contract. But another firm wanted to cheat, then:

In your opinion, what are the main incentives that push the firm to deviate and cheat?

Calculate the following for both firms:

1- Quantity of output.

2- Price.

3- Profit to each firm.

Explanation / Answer

There are two possibilities: (1) they maximize their own profits, or (2) they maximize their collective (joint) profits by forming a cartel. But if one cheats, the cartel falls apart and both produce at the quantity to maximize their own profits.

Since they have identical costs, but both want to produce where MC=MR.

P=110-qSA-qKPA

Revenue= P*(qsa+qkpc)

1. If each firm maximizes its own profits.

This is saying that the firms are engaged in (typical) competitive behavior. To maximize their own profits, the firms must produce where their own marginal revenue is equal to their marginal cost. Each firm's MR and MC are:

Firm SA's MR

MRA = 100 - 2qA – qKPC

Firm KPC's MR

MRB = 100 - qA - 2qKPC

Firm A's MC

MCSA = 20=MCKPC

Find equilibrium output for each firm for case 1.

Firm SA

Firm KPC

1. Set MR = MC

110 - 2qSA - qKPC = 20

110 – qSA - 2qKPC = 20

2. Solve for (own) q

qSA = 45 - 0.5qKPC

QKPC = 45 - 0.5qSA

3. Plug qSA equation into qKPC equation

QKPC = 45 - 0.5(45 - 0.5qKPC)

4. Solve for qKPC*

QKPC* = 30

5. Plug qKPC* into QSA equation

QSA = 45 - 0.5(45-0.5QSA)

6. Solve for qSA*

QSA* = 30

B. Find the equilibrium market price.

1. Plug qSA* and qKPC* into the market
demand equation

P = 110 - (30) - (30)

2. Solve for P*

P* = $50

C. Find each firm's equilibrium profits.

Firm A

Firm B

1. Find (P - MC)q*
for each firm

((50) - 20)(30)

((50) - 20)(30)

2. Calculate profits

pSA* = $900

pKPC* = $900

Summary: the firms each produce 30 units, charging a common price of $50 and making $900 in profits.

2. If the two firms maximize their collective profits.

This says that the firms are colluding and may have formed a cartel. It is as though the firms merged into a single firm (forming a monopoly). The cartel sets the (market) marginal revenue equal to their marginal cost. The cartel's MR and MC are:

Cartel's MR

MRC = 110 - 2Q

Cartel's MC and AC

MCC = 20

A. Find equilibrium output and price for the cartel for case 2

Firm A

1. Set MR = MC

110 - 2Q = 20

2. Solve for Q*

Q* = 45

5. Plug Q* into market demand

P = 110 - (45)

6. Solve for P*

P* = $65

B. Find each firm's equilibrium profits.

Firm A

Firm B

1. Find each firm's output share

QSA* = 45/2 = 22.5

qB* = 45/2 = 22.5

1. Find (P - MC)q* for each firm

(65 - 20)22.5

(65 - 20)22.5

2. Calculate profits

pA* = $1012.5

pB* = $1012.5

Summary: the firms each produce 22.5 units, charge a common price of $45 and make $1012.5 in profits. With a lack of competition, we see prices rising and output falling.

If the firms operate independently, maximizing their own profits, they make profits of $900. However, if they collude, then they can make profits of $1012.5.

3. Collusion and the incentive to cheat

When firms form an agreement to fix prices (i.e. collude) there is always some incentive to cheat on the agreement. To understand why, consider the following.

Suppose firm SA decides to increase their output slightly, to 30 units (i.e. the amount they would produce if maximizing their own profits). This would have no effect on their own MC, but would change the market price. Firm SA would produce 30 units while KPC would continue producing their share of the cartel output, so the price would be: P = 110 - (30) – 22.5 = 57.5

Profits for firm SA become: pA* = ((57.5) - 20)(30) = $1125

While firm KPC's profits are: pB* = ((57.5) - 20)(22.5) = $843.75

Firm SA obviously benefits, at firm KPC's expense, from cheating on the collusive agreement. Of course, once firm KPC realizes that firm SA is doing this, then firm KPC should increase their output too. The result is that the cartel falls apart and both firms end up producing their original (competitive) output levels. This problem illustrates a classic conflict between maximizing one's own welfare - in this case, profits - vs. that of the group.

Thus the main incentives that push the firm to deviate and cheat is to sell more output at the cartel price as this price is higher that the firm's indiviual profit maximization price. The firm believes that by cheating and producing more in a cartel as compared to the other players, they can earn more revenue. However they fail to realize that firm B follow suit once it realizes and cartel breaks, resulting into lesser overall profits. Another incentive to chaet is to gain a larger market share or to eradicate the competitor out of the business.

Firm SA's MR

MRA = 100 - 2qA – qKPC

Firm KPC's MR

MRB = 100 - qA - 2qKPC

Firm A's MC

MCSA = 20=MCKPC

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