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Calculate the optimal output

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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.

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Cost and Revenue Functions: Calculating Optimum Output and Price Level

Sparkling Pipes, Inc. offers professional furnace duct cleaning to home owners in Danville, Illinois. The company estimates that each additional room of ducts it cleans costs the firm $10. The owner's daughter did a study and estimated the firm's demand could be described by the following equation, where P stands for price, and Q for Quantity demanded.

She also estimated the marginal revenue equation for the company could be described by the equation below the demand equation. Lastly, since each additional room costs $10 to clean, she also derived a marginal cost equation.

Demand, P = $40 - $0.001Q (or Q = 40,000 - 1,000P)
marginal revenue, MR = $40 - $0.002Q
marginal cost, MC = $10

a. Calculate the output level (Q - number of rooms of ducts cleaned) at which profits are maximized. (Hint: remember that profits are maximized at that output where marginal revenue (MR) = marginal cost (MC))

b. In order to sell the amount computed in part A. above; at what price would the company have to offer its service? (Hint: which curve (equation) gives the relationship between the price of a good or service and how much of it is demanded?).

c. What is this firm's total revenue at the optimum price/output computed in parts A. and B.?

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