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 )

Summarize this case in the pay-off matrix and decide what is the right behavior each firm will take in the market?   

Explanation / Answer

SA = (110-qSA-qKPC)qSA -20qSA

FOC:

SA’(qSA) = 110-2qSA - qKPC – 20 =0

qSA = (90 –qKPC)/2 -----------------------(1)

KPC = (110-qSA –qKPC)qKPC -20qKPC

KPC’(qKPC) = 110-qSA – 2qKPC -20 =0

qKPC = (90-qSA)/2 ---------------------------------(2)

Put eq 2 in 1

qSA = 45 -1/2*[45- ½*qSA]

qSA = 45/2 +1/4 *qSA

¾*qSA = 45/2

qSA =( 45/2)*(4/3)

qSA = 30

Put qSA in equation (2)

qKPC = 30.

1. pSA = pKPC = 50.

2. SA = (1500- 600) =900

KPC = (1500-600) = 900

A.)

The objective of the cartel is to charge high price to increase profit.

C = (110-Q)*Q – 20Q

FOC:

C’(Q) = 110-2Q -20 =0

Q = 45.

P =( 110-45) = 65

Profit = (65*45) – (20*45) =2025

Profit to each firm = 2025/2 = 1012.5

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