# Calculate the optimal output

Suppose that Saudi Arabia lets other members of OPEC sell all the oil they want at the existing price which the Saudis set and other members accept. The daily world demand for OPEC oil is given by:

P =88 -2Q

where P is the price per barrel of oil and Q the total quantity of OPEC oil (in millions of barrels per day). The supply function for other members of OPEC who behave like a â??competitive fringeâ? is given by:

Qr = .6P

The Saudisâ?? cost of production of oil is given by:

TCs =15Qs+20

where Qs is the daily output of oil produced by the Saudis.

Calculate the price that Saudi Arabia will set to maximize its own profit. Also calculate the optimal output and profit of the Saudis. Determine the output produced by other members of the OPEC as well as the total market output.

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#### Solution Preview

Given Saudi's total cost function, we can find its marginal cost curve,

Marginal cost = d(TC)/dCs = 15.

We know that if Saudi wants to maximize its profit, it must follow the rule marginal ...

#### Solution Summary

Calculate the optimal output in an oligopoly market.